{ "cells": [ { "cell_type": "markdown", "id": "99923d6e", "metadata": {}, "source": [ "# Practice: Chp. 14" ] }, { "cell_type": "code", "execution_count": 1, "id": "b6c1590a", "metadata": {}, "outputs": [], "source": [ "source(\"iplot.R\")\n", "suppressPackageStartupMessages(library(rethinking))" ] }, { "cell_type": "markdown", "id": "a4c823f9", "metadata": {}, "source": [ "**14E1.** Add to the following model varying slopes on the predictor *x*.\n", "\n", "\n", "\\begin{align}\n", "y_i & \\sim Normal(\\mu_i, \\sigma) \\\\\n", "\\mu_i & = \\alpha_{GROUP[i]} + \\beta x_i \\\\\n", "\\alpha_{GROUP} & \\sim Normal(\\alpha, \\sigma_{\\alpha}) \\\\\n", "\\alpha & \\sim Normal(0, 10) \\\\\n", "\\beta & \\sim Normal(0, 1) \\\\\n", "\\sigma & \\sim Exponential(1) \\\\\n", "\\sigma_{\\alpha} & \\sim Exponential(1)\n", "\\end{align}\n", "\n", "\n", "**Answer.** See section **14.1.3**. Notice the distinction of $i$ and $j$ indexes.\n", "\n", "\n", "\\begin{align}\n", "y_i & \\sim Normal(\\mu_i, \\sigma) \\\\\n", "\\mu_i & = \\alpha_{GROUP[j]} + \\beta_{GROUP[j]} x_i \\\\\n", "\\begin{bmatrix}\n", "\\alpha_{GROUP} \\\\\n", "\\beta_{GROUP}\n", "\\end{bmatrix}\n", "& \\sim\n", "MVNormal(\n", "\\begin{bmatrix}\n", "\\alpha \\\\\n", "\\beta\n", "\\end{bmatrix}\n", ", \\mathbf{S}) \\\\\n", "\\alpha & \\sim Normal(0, 10) \\\\\n", "\\beta & \\sim Normal(0, 1) \\\\\n", "\\mathbf{S} & =\n", "\\begin{pmatrix}\n", "\\sigma_{\\alpha} & 0 \\\\\n", "0 & \\sigma_{\\beta}\n", "\\end{pmatrix}\n", "\\mathbf{R}\n", "\\begin{pmatrix}\n", "\\sigma_{\\alpha} & 0 \\\\\n", "0 & \\sigma_{\\beta}\n", "\\end{pmatrix} \\\\\n", "\\sigma_{\\alpha} & \\sim Exponential(1) \\\\\n", "\\sigma_{\\beta} & \\sim Exponential(1)\n", "\\end{align}\n", "\n", "\n", "**14E2.** Think up a context in which varying intercepts will be positively correlated with varying\n", "slopes. Provide a mechanistic explanation for the correlation.\n", "\n", "**Answer.** If you believe that education leads to greater wealth, then in the prediction of wealth\n", "based on parent's wealth. If you come from family with a lot of money you'll start off with a lot of\n", "money (the intercept), and because wealth builds on wealth the addition of education will help more\n", "than for someone who doesn't have as many resources to work with to start (the slope). You could\n", "replace education with ambition or something else along that theme, as well.\n", "\n", "We could also adapt the cafe example to use an M indicator (for morning) rather than an A\n", "indicator for afternoon. The intercepts would have to become the afternoon wait. Long afternoon\n", "waits are correlated with even longer morning waits.\n", "\n", "**14E3.** When is it possible for a varying slopes model to have fewer effective parameters (as\n", "estimated by WAIC or PSIS) than the corresponding model with fixed (unpooled) slopes? Explain.\n", "\n", "**Answer.** When there is some relationship between the intercepts and slopes that helps the model\n", "regularize itself. That is, if there is some correlation between intercepts and slopes, the model\n", "should be able to detect this and effectively learn to predict intercepts from slopes, and vice\n", "versa. This is similar to how in an intercepts-only multilevel model knowing some intercepts should\n", "help the model predict other intercepts; the known intercepts are a regularizing prior for new\n", "intercepts.\n", "\n", "**14M1.** Repeat the café robot simulation from the beginning of the chapter. This time, set rho\n", "to zero, so that there is no correlation between intercepts and slopes. How does the posterior\n", "distribution of the correlation reflect this change in the underlying simulation?\n", "\n", "**Answer.** Rerun the simulation:" ] }, { "cell_type": "code", "execution_count": 2, "id": "0eca95ae", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\n", "Attaching package: ‘ellipse’\n", "\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "The following object is masked from ‘package:rethinking’:\n", "\n", " pairs\n", "\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "The following object is masked from ‘package:graphics’:\n", "\n", " pairs\n", "\n", "\n" ] }, { "data": { "image/png": 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roQAAAAAIAjcdJJZO9esnPnv6wcHCR//Ss56SRyBGPjRSKR0+lsa2vLZDJ79uwJ\nh8MzVeocqKRQRXEc19fX19vbS6cn1uv1ra2trklmawMAAAAAqAQuFzn7bPL//h/55BNSX08k\nEuLxkN5esnw5Wb78yB+WNq14PJ6+vr5wOOxyuaY+f7GAKimohMPhO+644+mnn/b5fGNuqq+v\nv+KKK26++WalUilIbQAAAAAA07dkCWloIJ9+Snw+wrLEZiOnnDLZFVSmiGEYp9NpNBrpqJW6\nujqLxTIT9c6iigkqHo9nxYoVfX19ra2tZ555ZkNDA73uZiwW6+npeffdd3/84x9v3rz57bff\nNhqNQhcLAAAAAHCEjEbypS/NyiMrlcr29nav1zs4OBiJROrr62flaWZIxQSVdevWDQ8Pb9q0\n6cILLxx/a6FQ2LBhw9q1a9evX3/ffffNfXkAAAAAAOWPYZiamhq9Xj8wMLB3716bzSZ0RQdV\nMYPpt2zZ8o1vfGPClEIIEYvF11577UUXXfTiiy/OcWEAAAAAAJVFqVS2tbU5HI7h4WGhazmo\nigkqwWCwubl58m06Ojq8Xu/c1AMAAAAAULkYhrHb7e3t7UIXclAVE1ScTudnn302+TaffPKJ\n0+mcm3oAAAAAACqdQqEQuoSDqpigsnr16hdeeOGee+7JZrPjb00mk7fddtvLL7988cUXz31t\nAAAAAAAwsypmMP1PfvKTrVu33nLLLbfffvvy5ctdLpdGo+E4LpFIDAwM7NixI5VKnXzyybfe\neqvQlQIAAAAAwHRVTFAxGAzbt29/8MEHn3rqqXfeeadQKPA3SaXSY489ds2aNWvWrBGLxQIW\nCQAAAAAAM6JiggohRCaT3XTTTTfddFMmkxkaGqJXptfpdPX19TKZTOjqAAAAAABgxlRSUOEp\nFIrW1lahqwAAAAAAgNlSMYPpAQAAAABg/kBQAQAAAACAsoOgAgAAAAAAZQdBBQAAAAAAyg6C\nCgAAAAAAlB0EFQAAAAAAKDsIKgAAAAAAUHYQVAAAAAAAoOxU5AUfAQDKViZDPv6YjIyQWIyY\nTKSxkRx9NBGLhS6LkGKxyHHcYd1FJBIxDDNL9QAAAEwOQQUAYMaMjpJnniFiMWlpITU1JBQi\nf/kL2bGD/Nd/EbV64rsUCgVCSD6f5ziueABdWSgU+DUcxxUKBfpzzK+lK2fjRdG4wjCMWCwm\nhPA/GYbhb6IL4zegN4nFYolEIhaL6cJsFAkAANUH/zAAAGYGy5JnniELFpBVq3dMPTEAACAA\nSURBVAjDFPP5fKFQOOGE/HPP5R9/PH/++flCoZDP5+n6/AHjH4ce3PMYhpFIJPxKsVgsk8lo\nKijdRjxRqw29deovgX8QmppoBCIH0hT9yQen8RuwLMvHLbpACMnn82NCFJ9YDrZQunxY9QMA\nQDVBUAEAOAzFYjGXy+VyudKwQZc/+STv9eZPO63wj3/k6TE69YUvSJ5/XvL55+K6OolEIlEo\nFPRAnOKbJujChHmjChQOoLtrzAK/P+ma0r1H9wwfXaRSqVQqlclk0gNoihPwpQEAwCxBUAEA\nGKtYLLIsy7JsLpfjf9IFvg1EJBLxSYMuhMOKxYslLpd4zHpCyJ49RC4nLS2CvipB0bAxxY05\njpswzxQKhVwuF4/H8/k8y7I0z9AWp/EBhjebLwsAAGYRggoAzFOFQmF8GqE/aUcmhmH4Y1+F\nQqHT6fijYYlEMr5LklpNzGZiNk/wXEolYdk5eE1Vgu75Q2YMmlt4LMvm8/l0Ok1/nTzGyGQy\nmUxWre1XAADVAUEFAKpcLpfLZrOZTIY9gB7U0gNZkUjEH7mqVCr+cJb+PKwn0utJMDjBeo4j\nwSA5+ugZeTXwf2grjUKhmPDWqcQYiUQiHweNMAAAZQJBBQCqRz6fp5mE/5nNZguFAsMwsgM0\nGk1pGpnBSag6Osjvfkd8PmKz/cv6PXtIOk1aW2fqeWBKJo8x9KPCi8fjgUAgl8sRQkQi0fj0\nQicwmNtXAAAw3yGoAEBFKhQKpQeaLMvSk+WEELFYLJfLlUql0WikR5kKhWIOJo9asIC0t5Pf\n/Y6sWkWamwnDkEKBfPopeeMNcsopRKOZ7eeHw0CHD6n/ddJojuNYlqUfJz7AZDIZ2vzCf64U\nCgUfYNB5DABg9iCoAEC5KxaLfPMI31pCB7VLpVKaQ7RarcVioUeQAk5oe+655C9/Ic8+S0Qi\notWSaJRIpeS008jxxwtVERwGhmFo/ChdyXEc7T3IC4fDtKWOECKRSJQHKBQKpVKJ6AIAMFMQ\nVACgvHAcl81m0+l0KpVKp9PpdJplWXJgOAEd1G61WmkmKbeDQomEfO1r5JRTiMfzzyvTOxxE\nJhO6LJgGvt+gVqstXc93Hkun05lMJhqNZrNZQohMJhsTXdBnDADgyCCoAIDACoUCH0tSqRTt\nacOfqDYajTSTVNAVzVUq0twsdBEwy8Z3HisWi+kDkslkIBDI5/O0lUZZYkyLDQAAHEzF/OMH\ngKqRy+VSqVQymcxkMvRsND1prVAo9Hp9TU0NPQ8tdJkAh0ckEqnV6tLoQkM4/ZwnEgmfz1ca\nXRQKhVqtpjlcwLIBAMoWggoAzC56rEbRZpNisSgWi5VKpUql0ul0KpVqbga7A8wxsVis0Wg0\nJRMp0BFW9M8hEomMjo5yHEfbD1UqFc05MnQWBAAghCCoAMCMKxQKqVQqkUjQWEI77svlcpVK\nRRtMVCoVDsVgfqKD9fV6Pf2V47hMJpPJZFKpVCqVCgQChUKB9ijjldtALACAOYOgAgAzIJPJ\nJJPJZDKZSCQymQwhRKVS8Q0mSqUSDSYA4zEMw4/Fomv4P6VoNOrxeDiOUygUfGOLSqXC0HwA\nmD8QVADgSBSLRXoOOJFIxOPxfD4vlUpVKpXBYKB9XZBMAI6AQqFQKBRms5kcaG+h+d/v9w8N\nDdHxLWq1WqPRqNVqDOUCgOqGoAIAU5XL5RKJBO3TlUwmCSFyuVyj0dTV1dFmE6ELBKgqfHuL\nxWIhJfPjJRIJt9udy+X4sV707IBUKhW6ZACAmYSgAgAHxY82oX1RaLOJWq3W6/W1tbUqlQrN\nJgBzhh+ab7PZCCEsyyYPCAQCxWJRJpNpNBqtVqvVajGTGABUAQQVAPgXLMvG4/HS0SZKpVKj\n0ZhMJrVajaMfgDJBL0NJB7dwHEcv3pJMJmlji1Qq1el0NLfgzxYAKhSCCgCQQqEQj8djsVg8\nHs9kMhKJhCYTjUaDZhOA8scwDJ2+wmq1EkKy2Ww8Ho/H4zS0yGQy7QGYcA8AKgiCCsA8RU/B\n0nASj8cZhtFoNGazmc7TJXR1AHDk6CTIdGQLDS10WAvLslKpVKPR6HQ6nU6H0AIAZQ5BBWAe\nKQ0niUSC4zilUqnT6ex2u1arxbSnANVnfGiJxWIjIyMDAwN0MgyaWxBaAKAMIagAVD/+6ITO\nIyyXy7VabWNjo06nw7XkAOaPyUOLVqulY1oQWgCgTCCoAFSnXC7Hd+tiWVYmk+l0OpfLpdVq\nMYcpAJSGllQqRb8rhoaGCoWCSqXS6/V6vV6tVgtdJgDMawgqANWjWCzSU6SxWIyOiddqtTU1\nNTqdDtP+AMDB0IH4drud47hUKhWLxaLRqMfjoVOH6fV6tL4CgCAQVAAqXj6fj0ajkUgkFosR\nQjQajcVi0Wq1GBMPAIeFYRi1Wq1Wqx0ORy6Xi0aj0Wi0v7+f4zitVkubWXDWAwDmDIIKQKXK\nZrP0MCIej4vFYq1WW19fbzAYcOITAKZPKpVaLBaLxcJxXDKZjEajfr9/aGhILpfTxIIZOABg\ntiGoAFSYdDodDoej0WgqlaJHDJizCwBmD527XKPR1NbW8udH/H4/wzBardZgMOj1eox8A4DZ\ngKACUAGKxWIikYhGo+FwOJfLKRQKo9HY0NCAzl0AMJfkcrnNZrPZbHREXCQScbvdAwMDdPy9\nwWDAlxIAzCAEFYDyRQefUIQQrVbrdDpx8hIABCcSiWgHML5jWCQS8Xg8MpmMJhY08wLA9CGo\nAJSdbDYbiUSi0WgikRCLxXq9vrGxUa/Xi0QioUsDAPgXE3YM279/v1gsNhqNJpNJo9EIXSMA\nVCoEFYBykclkQqFQJBJJp9NyudxgMDgcDo1Gg7OSAFAR+I5h+Xw+EomEQqGuri6pVGo0Go1G\nI67KAgCHC0EFQGC5XC4UCoVCoVQqpVQqTSaTXq9XKpVC1wUAcIQkEgmdMSyXy4XD4XA47PV6\n5XI5bWPB9xsATBGCCoAwisViNBoNBoOxWEwqlRoMBgyOB4AqI5VKaRsLy7KRSCQcDo+OjtLE\nYjabFQqF0AUCQFlDUAGYUxzHxWIxeoqRYRiDwdDS0qLT6YSuCwBgFslksvGJhU5gaDabcRFJ\nAJgQggrAHEkkEuFwOBQKFYtFrVbb2NhoMBgw/gQA5hU+sdBReeFw2OPxILEAwIQQVABmVzqd\npkNQcrmcVqutq6vDxeMBABQKhdPpdDqdqVQqHA4Hg0GPx6PRaEwmk9FolEhwfAIACCoAs4Nl\nWZpP0um0Wq222+1GoxHXPwEAGEOlUqlUqtra2mQyGQqFPB7P0NCQXq+3WCx6vV7o6gBASAgq\nADMpn8/T/l2JREIul5tMpqamJgwYBQA4JLVarVarXS5XLBYLBAI9PT1SqdRisZjNZplMJnR1\nACAABBWAmZFMJv1+fzgcppc5q6urw0UDAACOgE6n0+l0+Xw+GAwGAgG32803sGBcH8C8gqAC\nMC2FQiEUCvn9/nQ6rdPpFixYgH+lAADTJ5FI7Ha73W5PJBKBQKCvr08sFpvNZovFgjH3APME\nggrAEcpkMn6/PxAI0P+dzc3N+N8JADDjNBqNRqNxuVzhcNjv94+OjqpUKqvVajKZRCKR0NUB\nwCxCUAE4PPRCjYFAIBaLqVQql8uFf5YAALNNLBbTq92nUqlgMDgyMjI8PGw0Gq1WKy6VC1Ct\nEFQApiqTydAO0xzHGY3GRYsWKZVKoYsCAJhf+FnC6Dmjzs5ONLAAVCsEFYBD4DguHA4HAoF4\nPK5Wq+vq6oxGI/4dAgAISCQSGY1Go9GYTqcDgQDfwGKxWDCRCUDVQFABOKhsNhsIBGgTislk\ncrlcaEIBACgrSqXS5XLV1dXRM0r79u2jl64yGAyY1wSg0iGoAIzFcVw0GvX7/XQUitPpNJlM\nuJY8AEDZYhjGZDKZTKZsNuv1evv7++mkYWazGd/eAJULQQXg/xQKhUAg4PP58vm80Whsb29H\nFwIAgAoil8vr6+udTmcgEBgdHXW73RaLxWaz4ZKRAJUIQQWAEEJyuZzP5/P7/SKRyGazWa1W\nnIQDAKhQEomkpqbGbreHQiGv1+vz+YxGo91ux/xgAJUFQQXmu2w26/P5AoGAVCp1Op0WiwUD\n5QEAqgDDMGaz2Ww2JxKJ0dHRzs5OjUZjs9kwfAWgUiCowPyVSqV8Pl8oFFIqlfX19SaTCf+6\nAACqj0ajaWlpoVfp7e/vl0qlNpsNp6UAyh+CCsxH9OxaNBrVaDTNzc16vV7oigAAYHYpFAqX\ny+VwOHw+n8fj8Xg8dPiKVCoVujQAmBiCCswv0WjU4/GkUimTyYQrNgIAzDcSicTpdDocjlAo\nNDo66vV6TSaT3W7HvwOAMoSgAvNCsVgMBAJerzefz1ut1qamJswAAwAwb/HDVyKRiNfr3bt3\nr16vt9vtWq1W6NIA4P8gqECVy+fzdDovhmGsVqvNZsN0XgAAQBkMBoPBkEqlvF5vd3e3RqNx\nOp0ajUbougCAEAQVqGIsy3q9Xjqdl8PhwLhJAACYkEqlWrBggdPpHB0d7erqUqvVTqcTrSsA\ngkNQgSrEsqzH4wkGg0qlsrGxETNRAgDAIcnl8oaGBpvN5vF4urq69Hq9w+HAZX8BBISgAlUl\nn8+Pjo76/X6FQtHS0qLT6YSuCAAAKolSqWxqakqlUh6PZ9++fQaDweFw4EqRAIJAUIEqUSwW\nfT7f6OioVCqtr683m81CVwQAAJVKpVI1Nzen02mPx9PZ2anX651OJ+IKwBxDUIGKx3FcMBh0\nu90Mw9TV1ZnNZnT0AgCA6aOtK8lkko8rtbW1mMgYYM4gqEAF4zguFAp5PJ5CoWC32202G4bL\nAwDAzFKr1S0tLYlEwu12792712g0Op1OhUIhdF0A1Q9BBSpVOBx2u90sy9pstpqaGkw6DAAA\ns0ej0SxcuJDGlT179hiNxtraWrlcLnRdANUMQQUqTywWGxkZSafTZrPZ6XRKpVKhKwIAgHmB\njysjIyN79uwxmUwOhwNxBWCWIKhAJaH/G5LJpMViaWlpQUQBAIC5p9Fo2traotEobV2x2+0O\nhwN9jwFmHIIKVIZUKuV2u6PRqMlkamxsxOkrAAAQll6v1+v14XB4eHg4GAzW1tZiwkmAmYWg\nAuWOZdnh4eFwOKzX6xctWoTpVgAAoHwYjUa9Xu/1egcHB/1+v8vlwjUiAWYKggqUr2Kx6PV6\nR0dHVSpVW1ubRqMRuiIAAICxRCKRw+Ewm80jIyP79u0zm821tbXonAwwfQgqUKbi8fjg4GCh\nUHC5XBaLRehyAAAAJiOTyRYsWGCz2YaGhnbv3m2322tqajBwBWA6EFSg7LAs63a7Q6GQ1Wp1\nOp2YdxgAACqFWq1ub28PBoMjIyPBYNDpdGLgCsARQ1CBMlIsFkdHR71er0ql6ujowHAUAACo\nRGaz2Wg0jo6ODg4OBoNBl8uF/2gARwBBBcpFNBodGhoqFov19fU4/wQAABVNJBLR5pSRkZG9\ne/eazea6ujqJBMddAIcBfzAgvGw2OzQ0FIvF0NcLAACqiVwub2pqisfjdOBKTU2N3W5nGEbo\nugAqA4IKCInv66VWq9HXCwAAqpJWq+3o6OAHrtTV1en1eqGLAqgACCogmEgkMjQ0RAhpbGw0\nGo1ClwMAADBbGIaxWCwGg8Htdvf09BgMhvr6evQEA5gc/kJAAJlMZmhoKB6P2+12h8OB2RsB\nDqZYLOYPKBQKHMcVD6C/lq7kOC6fz5duM+FjFgqFSZ6R9r0Ui8UMwzAMIxKJGIbhV47fQCKR\niMVisVhcuoA/aoAJSSSS+vp6i8XS39+/Z88el8tlMpmELgqgfCGowJwqFosej8fr9Wq12kWL\nFikUCqErAhBGLpcrFAqlIWTCZY7j6PY0M9B4UPqTrqQhgf5KjRnrNfWhXzTnkAN5Jp/PE0Jo\nCuLjEI1JNCPRgin+QWh5fHThlyUSiUQikR6A08kwP9GZLUdHR/v7+8PhcH19Pa4OCTAh/JOA\nuZNMJvv7+wuFwoIFC9DXC6oePYhnWZZl2Vwux/+kC3wC4Y/jKZlMxv9aur78J5mgzTs0ZY1f\nyOfz2Wy2UCjkcjn+5TMMI5VKZTKZdCKIMVDFGIZxOBwGg2FgYIA2rWC6S4Dx8G8A5gLHcV6v\n1+12o1cuVJ9CoZDJZLLZ7Jg0wreH0DYEejiu0+noAh9Iqmb+H9oNTCKRyOXyQ26cz+fpjqJZ\njv5MJpOlMUYkEtHkJv9X+AKBqqFUKtva2vx+/+DgYCgUamhokMlkQhcFUEYq++ueZdnPPvss\nkUg0NjYuWLBA6HJgYul0ur+/n2XZpqYmg8EgdDkAR65YLNJMUvqTdo6ih9Q0gahUKj6ZyGQy\nDNgYj0aag030l8vl+ACTzWaz2Ww0GuV3tVgsHhNdZDKZTCarmsgH8wrDMDabTa/X06YVh8NR\nU1MjdFEA5aJigsrPfvazFStWfOlLX+LXbNiw4Qc/+EE4HKa/HnvssY8++uiSJUsEKhAmUNqQ\n0traivOgUEGKxSI9RKZphC7kcjlCCG00UCgUer1eoVDQY+Xy75pVQWjXr/Exhn9TqFQqFQ6H\nWZblOI5hGNr2olAolEqlUqlUKBR4U6BSyOXyhQsXBgKBoaGhaDTa0NCAMZwApIKCyrp1677/\n/e/zQWXLli3XXHONXC4/99xzbTbb7t27t23bduqpp/79739vbm4WtlSgstlsf39/Op2mM5wI\nXQ7AIbAsm0ql0ul0Op1OpVLZbJYcOHmvUCg0Go3FYkHXI2GJRCIaQkpXchzHsiyfXjKZDG1+\nIYTIZDLlATTAoNUFypnFYtFqtQMDA52dnQ6HA5eGBKjUf7c33XSTXq/fvn17R0cHXfPiiy9e\ncMEFd9xxx2OPPSZsbUAIoaeFNBrNokWL0OMWyhDtxFWaTAqFAj0OVqlUdrudHtoik5Q/hmFo\ngCxdSQcO0Tc3mUwGAoF8Pk+3VJaYynAagLnEN60MDw9HIpHGxkY0rcB8VpH/g/1+f3d39w9/\n+EM+pRBCzjvvvHPOOefPf/6zgIUBIYRl2f7+/lQq5XK50JAC5SOXy9FYQn9ms1mO4+h4Eo1G\nY7VaVSoVDlurhlgsVqvVarWaX5PP59MHRKNRr9fLR1P1AfgAQJmwWCx6vX5wcBBNKzDPVWRQ\nyWQyhJDSlEItXrx4y5YtQlQE/+T3+4eHh9VqNRpSQHAcx6VSqWQymUgkkskky7IikUihUKhU\nKqvVSltOMIZh/pBIJFqtVqvV8mtoP7FkMplKpUKhUD6fl0gkarVapVLR3IL2NBCQVCptbm5G\n0wrMcxX5Lex0OvV6/fDw8Jj1bre79J8QzCWWZQcGBhKJRG1trc1mE7ocmKdyuRyNJfTos1gs\nKhQKtVrtcDjUarVCocBZSeDRDmN6vZ7+ms1m6ScnFot5vd5isSiXy2liUalUKpUKs7fB3KNN\nK3TUSkNDAy5jD/NNJQWVwcHBnTt3GgwGg8Fw7bXXbty48frrr1epVPTWffv2Pf/886eddpqw\nRc5P4XB4cHBQLpd3dHTglA/MpfHNJrTPj1arramp0Wg0aDOBKaK5hR4IchxHB7ckk0m/35/J\nZBiGoZ3EaLMMGltgzkil0paWFp/P19/fH4vF6uvrkZlh/qikr9pnn3322WefLV3z+uuvn3/+\n+YSQZ5555qqrrkqn0+vWrROounmqUCgMDAxEIhGn04lOtDA3isUiPe2dSCTGN5sc7NIcAFPH\nMAxtRbFarYSQQqGQPGBgYKBQKCiVSppYNBoNQgvMAZvNplare3t79+3b19TUhHOCME9UzNfr\n448/HikRjUYjkYjRaKS3RiIRg8Hw3HPPLVu2TNg655V0Ot3T08MwTEdHB44OYVbRM9yxWCwe\njycSCY7j0GwCc0YsFut0Op1ORw404tHPYSAQKBaLdD4GmlvwUYTZo1arOzo6+vv70Q0M5o+K\nCSrf+ta3Jrn1sssuu+aaa9AYOpdCodDAwIBOp2tsbMT/Zpgl2Ww2Ho/TfJLP5+VyuVarbWxs\n1Ol0+NSBIBiG4ecT4/NzIpEIBoOFQoFecoemGnxEYcZJJBJ0A4N5pWKCyuQ0Go3QJcwjHMcN\nDw/7/X6n01lTUyN0OVBtcrkcH05YlpXJZFqt1uVyabVaqVQqdHUA/4fvIUYI4TgumUzG4/F4\nPN7f389xnEql0uv1er2eH0s5oUiE+P1ELCY2G8G/MpgKm82m0Wh6e3s7OzubmprQowGqWJUE\nFZgzLMv29vZms9nW1lbMsQYzKJlM0l6d6XSaziRbU1Oj0+lwaQuoCAzDaDQajUbjcDg4jksk\nEvF4PBKJuN1umUym0+kMBoNWqy09/+31kldfJSMjRCYjhQIpFMjCheSsswi+WeGQVCpVR0fH\nwMDAvn37cNUyqGLVE1R6enquvvpqQsibb74pdC1VKx6P9/X1yeXyRYsW4dw2TF+xWKQHc9Fo\nNJfLqdVqk8mk0+kmPwMNUOYYhqFDVpxOJ8uy0Wg0Go329vYSQrRaLW1miUZljz9OmpvJ6tXE\nbCaEELebvPEGefxxcuWVBKfI4ZDEYnFTU5PP5xscHEwkEugGBlWpeoJKPB5/6623hK6imo2O\njrrdbqvVWldXh9m9YDry+Xw8HqdTYnAcp9FoampqjEYj0i9UH5lMZrVarVZrsVhMJBLRaHR0\ndHRwcPDNN+Vqtf6MM/Q6nZZ+o9bWkm98gzz8MNm6lZxxhtB1Q4VANzCobtUTVNrb23ft2iV0\nFdWpUCj09/fH4/EFCxbwM60BHK5sNktn7Usmk2KxWK/X02HxOAsI84FIJKKD7F0uVzicDgaj\ny5dH9u/3SSQSvV5vMBj0er1Uyhx/PHnvPQQVOAzoBgZVrHqCikKhWLx4sdBVVKFUKtXb2ysS\nidrb2zFxOxyBVCoVDocjkUgmk5HL5QaDoba2Vq1Wo10O5q1cTqlWK48/vkYqzdOOYX19fQzD\nGAwGhcIYjeqKRQb5HaaOdgPzer2Dg4PJZNLlcuEEEFSHygsqHMf19fX19vbG43FCiF6vb21t\ndblcR/ZoXq/329/+djabnWSbkZER+rxH9hQVLRAIDA0NGQyGhoYGfOvBYclms6FQKBQKZTIZ\ntVptNpsNBgOyLgAhhHZyZFmiVErMZrPZbC4Wi5FIJBwOd3f3BIPiwUGD2WzSaDTI8zB1drud\ndgPr7u5ubm7GpUihClTShzgcDt9xxx1PP/20z+cbc1N9ff0VV1xx8803H27vTLVa/cUvfpFl\n2Um2EYvFnZ2d8+2/BeYghiOTz+cjkUgwGEwkEgqFwmg0ms1mzNwFUMpgIGo16eoi/DWKRSKR\nyWQymUydnYW2tkg+H+7u7qY9JOkME4LWCxVDrVa3t7fv379/3759LS0tODcElY6plIYCj8ez\nYsWKvr6+1tbWFStWNDQ00OttxWKxnp6ed9991+12H3PMMW+//faMD6LYsGHDNddcE4/H58/V\nWliW7enpyefzTU1NdD8DTK5YLEaj0WAwGIvFJBKJ0Wg0Go3z508G4HBt20a2bSOXXUZKTwR1\ndZHnnycXX0wWLiSFQoG2scRiMalUajAY8DcFU1QsFvv6+hKJRFNTEy4kAIfEsqxcLt+2bduJ\nJ54odC1jVUyLyrp164aHhzdt2nThhReOv7VQKGzYsGHt2rXr16+/77775r68apJOp7u7uxUK\nRWtrKxqOYXIcx8VisVAoFIlEGIYxGo24wA7AVJx4IvH5yKOPkqOOIg4HKRTI4CDp7iannkoW\nLiSEELFYTHuF5XK5cDgcCoV8Pp9cLqcrZTKZ0K8AypdIJGpqahoeHu7u7m5oaDDTCbABKlDF\ntKg4HI4zzzxz48aNk2zzn//5nx988MHg4ODMPvW8alGJx+M9PT06na6xsRGDUmASyWQyGAyG\nw+FisUh7p+j1+vnWQxJgmrq6yO7d/7wyvd1OvvAFUld30I1Zlg2FQsFgMJvN6nQ6i8WCPzqY\nXCAQGBwctFqtRzyUF+YDtKjMgGAw2NzcPPk2HR0df/zjH+emnqoUDof7+/stFgu+0eBgisVi\nKBTy+/2pVEqr1dbV1RkMBrFYLHRdABVp4cJ/tp9MhUwmq6mpqampicfjgUCgr6+PtrpYLBYM\nA4MJWSwWmUzW29uby+Vw/hEqUcUEFafT+dlnn02+zSeffOJ0Ouemnurj8/mGh4cxdB4OJpPJ\nBIPBQCDAcZzRaGxsbMSVxQAEQS97XygUwuGw3+8fHR1VqVRWq9VkMuFIFMbQ6XRtbW379+/H\nVGBQiSrm87p69erf/OY3y5Yt+853vjP+1FEymfzFL37x8ssvf//73xekvEo3MjLi9XobGxtN\nJpPQtUB54TguEokEAoFYLKZSqWpra3EwBFAOxGKxxWKxWCypVMrv9w8PDw8PDxuNRpvNhpMI\nUEqpVGIqMKhQFTNGJRKJnH766R9//LFWq12+fLnL5dJoNBzHJRKJgYGBHTt2pFKpk08++bXX\nXpvxkSTVPUaF47j+/v5oNNrc3Iwx0FAqk8kEAoFgMMhxHO1egqMfgLJFu2UGAoFkMqnRaCwW\ni8lkwggW4BWLxd7e3mQy2dzcXJXHM3DEMEZlBhgMhu3btz/44INPPfXUO++8UygU+JukUumx\nxx67Zs2aNWvWoK/8YSkUCr29vel0euHChSqVSuhyoCzQJhS/3x+Px9GEAlApRCIRbWBJp9P0\nWr0jIyM2m81isaC3DxBCRCJRc3Pz8PBwV1cXOlBApaikLy+ZTHbTTTfddNNNmUxmaGiIXple\np9PV19djosYjkMvl9u/fXywW29vbsQOBEFIoFAKBgM/ny+fzJpOprq4O8RWg4iiVSpfL5XQ6\n6Z+zx+Mxm812ux0D7oFhGJfLJZfL+/v7M5kMhvVC+aukoMKjl/gQuorKlk6n9+/fL5PJFi5c\niGYoyOVyPp/P7/eLRCKbzWa1WvGpAKhoYrHYbrfbbLZIJOL1enfv3m0wwucA6QAAIABJREFU\nGOx2O/r8gM1mk8lkfX19uVyuoaFB6HIAJlORQYV3zz33vPTSS++//77QhVSYRCKxf/9+nU63\nYMEC9GCe57LZrM/nCwQCUqnU6XRaLBb08gKoGvQyrEajMZVK+Xy+rq4upVJps9kwfGWeMxgM\nCxcu7O7uJoQgq0A5q+ygsn///m3btgldRYWJRCJ9fX24WArQA5dQKKRUKuvr63HgUlY4jgwO\nEp+PZLPEZiONjQTdM2E6VCpVY2Ojw+Hw+XyDg4Nut9tqtaLtdD5Tq9U0qxSLxcbGRnz/Q3mq\n7KACh4tepLa2ttZutwtdCwgmFouNjo7G43G9Xr9w4UJ0BSk3Ph/ZvJkEAsRiIVIp2bqViMVk\n5Upy1FFCVwYVTi6Xu1wuh8NBh6+Mjo5arVa73Y7R9vOTSqVqbW3t6uoaGBhobGwUuhyACeC7\naR4JBoODg4P19fUWi0XoWkAAHMeFw+HR0dFMJmMymRYtWoTphstQIkGeeorU15PLLiNqNSGE\nFApk+3by4otEJiMYnQfTJ5FIampq7HZ7KBTyeDx+v99ms9ntdrSuzEMqlYq2q/T39zc0NKBd\nBcoNgsp8EQ6HBwYGXC4XUsr8FA6H3W43y7JWq7WlpQXzvJWtrVuJTkcuuIDwY4XEYnLSSSSV\nIn/+M4IKzBiGYcxms8lkCgaDHo/H5/PRwfeIK/MNbVfp7u7u6+vDyFUoN5U9avbnP//50NCQ\n0FVUADouxel0Wq1WoWuBuRaLxTo7O/v6+jQazeLFi+vq6pBSyll3N/niF8n4GQ2WLiWBAAmH\nhagJqhfDMBaLZfHixS6XKxgM7t692+12l16pDOYDmlXi8XhfX1+lXAcc5onKblExGAwGg0Ho\nKspdLBbr7e11Op01NTVC1wJzKplMjoyMxONxo9HY1NSEqyhUhHicTPitRlfG48RonOOKoPqV\ntq643W6/309bVzAH4PxB+4B1dXWhXQXKSmUHFTikeDze09NTU1ODlDKvZDIZt9sdDof1ej3G\nolQWpZIkkxOsT6UIIUQqzWcy+UKhkM/n8/l/LnAcR38Wi8VisTjmV37lVJ6ddvsRi8UMw4hE\nIvqzdEEsFovFYolEMn4BB7WVjraumM1mGle8Xi/iyryiVCqRVaDcIKhUM3q9FKvViqvPzh/Z\nbNbtdodCIb1e39HRgUvLV5Z8Pu905nbsYJ1ONpfLsSzLB5KPP85HIvmREeJ2E0KISCSiIYEm\nBD5FyOVyPlTQNfTXyZ9XJBJxHEezTekC7QLE/ywWiyzL0nRUOIB/EIZhxGKx9F/JZDKJRCKT\nyaRSKY57KgKNKyaTyefzeb1en89Hr7AkdF0wF5RKZVtbG7IKlA8ElaqVTCb3799vsVjq6uqE\nrgXmQi6X83g8gUBArVa3tbVh0uGyxXEcy7KZTCabzeZyORpIWJbN5XLFYtFsJlu3iqRS2Qkn\nSOVymUKhEIvFQ0OSri7JuedKjjpKUlbNFzTMlEaX3AGpVIou5PN5urFEIqHpRf6vyuS1QCmR\nSFRTU2O1Wn0+3/DwsN/vd7lc+FaZDxQKBdpVoHwgqFSnVCq1f/9+o9GIqzrOB8Vi0ev1jo6O\nKhSK5uZmvV4vdEXwTzSTZLPZbDZLk0kmk2FZluM4kUgkk8loU4NGo6EL9GdDg+TFF8kbbxCX\ni0ilZHSUuN3kS18i//7vQr+ecRiGkUgkEolkkhFQxWIxV4KmsmQymc1maYMMjS4ymYyPLgqF\nAlf2KAdisdjhcFgslpGRkc8//9xoNGI2jvkAWQXKB/4TVKF0Ot3d3a3X6xsaGoSuBWZdNBod\nGhoqFov19fVms1nocua7bDabSqXS6XQ6nabJhOM4hmHowbdCodDr9QqFgh6XH+xBFi4k119P\ndu8mXi/JZMjChWTVKmKzzeXrmEkikYjGj/E35fP5bIl4PB4IBHK5HCFEKpUqlUqlUqlQKFQq\nlUKhQMOLUKRSaWNjo9VqHRoa2rNnj91ur6mpwdtR3RQKBb0WZH9//4IFC4QuB+YvBJVqk8lk\nuru7dTodUkrVY1mWDkehw5Bw9YO5VygU0gfQfFIsFsVisVKpVKlUOp2OHqDLZLLDPSWpUpHl\ny2ep6jJCW2PU9MKWBxSLxUwmw+/YcDjMsiwhRC6XK0soFAqBqp6n1Gp1e3t7OBweHh4OBAK1\ntbU4M1Ld6Nj6zz//fGRkpLa2VuhyYJ5CUKkq2Wy2q6tLrVY3NjairbaKFYvF0dFRr9erUqk6\nOjowqdecKRaLqVQqkUgkk8l0Op3NZgkhcrlcpVLp9fqamhqVSoWOMdMkEolUKlXpPBClgTAe\nj/t8vkKhIBaLVSqV+gCpVCpgzfOH0WjU6/Wjo6ODg4N04MqYnAnVRKlUNjc3d3d3y2QyXIcN\nBIGgUj1yuVxXV5dKpWpqakJKqWLo6zXHstlsMplMJpOJRCKdThNClEqlWq3W6XQqlUqpVKIP\nzGwTi8UajaZ0JDcd5ULfFJ/PVywWZTIZTSw0veBNmT0ikYjOA+Z2u/ft22c2m2traxEUq5VW\nq62vrx8cHJTL5TqdTuhyYN5BUKkSxWKxp6dHJpMhpVSxbDY7NDQUi8VsNpvD4UBfr1lS2myS\nTCZzuRztnkRHEuMguBzQeQiMRiMhhOO4TCZD36xgMDgyMkIIUSgU2gPwlzIbZDJZY2Oj2fz/\n2bvzKDmu6mDgr6r3rt73bXp6enpWWWC8YYQdA5HtRAZ/xOdwLHESkpgosS0CMYHvmCU22BzH\nLMkxYIsYiG0gEAMnLLETscQ2Nhgc2cZWkGZG0z3T+7539VbdXVXfHxXPpyONZkayuqu66v7+\n0Bn1SDO3p6er3n3vvvus3MYVn88HLYzFymazURS1vr4+Pz8PJZdgxCBREYl4PN7v9+fn52EI\nJUpcrVcul9PpdIuLi3CrGIZ2u91oNEiSbDabLMuq1WqdTuf1egmCgB+4kGEYxu1a4QbKG3km\ntzWfYRitVstlLDqdDpKWC0uv1y8sLBQKhWQyWa1WJycnofRRlLxeb6/XC4fD8/PzsHoGRgkS\nFTHI5XK1Wm1ubg4uH6LUarVisRhN01NTU9wUMrhQKIrikhOSJAeDgUaj0ev1DocDRrTjC8dx\nrk7M5XKxLNtqtbjXt1gssiyr1Wp1Oh2Xt8C0zgWBYZjT6TQajfF4fGlpyev1wmYGUZqcnFxd\nXY1EInNzc/DeASMDicrYazQamUxmamoKziAXH5Zl8/l8JpMxmUx+vx9OlrggaJqu1+tcftLr\n9ZRKpV6vn5iY0Ov1kOqLDIZhXNLidrvPTFr0er3RaDQajVscAgN2SK1Wz83NlUqlVCpVqVQm\nJydhHVJkcBwPhUIrKyuxWCwYDPIdDpAKGPeMt263u76+7na7YaJdfDqdTiwW6/V6wWDQZDLx\nHc7Y6/V6tVqtXq+TJInjuF6vd7lcer0ehlMScWrSwjBMs9ms1+tczZJarTaZTEajkSAI2OP3\nethsNoPBEI/Hl5eX3W630+mEn6eYyOVyLleBhsVgZCBRGWODwSASiej1erfbzXcs4EI6dSFl\nZmYGFlJej06nU6/X6/V6s9lUKpUGg2F6etpgMMD4ScpwHDcYDAaDYWJigqIo7jckn89vPG40\nGmF57fwolcqZmZlyuZxKpWq1WiAQgLkAMVGr1dCwGIwSDIDGFcuy6+vrMpkMjowVGYqiYrFY\np9Px+/3QRef8sCxLkiS3ftLr9bRarclkmpiYgPJIcCaVSuVwOBwOx2AwaDQa9Xo9lUolEgm9\nXm+xWEwmE+xWOg9Wq9VgMCQSiaWlJafT6fF4YGpANPR6/eTkZDweVyqVRqOR73CAyEGiMq6S\nyWS324U2XyJTKBTS6bRer9+1axdM6J6HVqtVqVQqlQpN01xxl9FohDZEYCfkcrnFYrFYLCzL\nNptN7gj2eDxuNBrNZrPJZIKL7TlRKBTT09PlcjmZTDabzampKXgniobVau12u9FodG5uDk4c\nBkMFicpYKhaLpVJpdnYWrvui0ev1YrFYu92emJiAhZRz1e12ufyEoihuE4LFYoGSOXB+MAzj\n2oJNTEy0Wq1qtZpMJuPxuF6vN5vNZrMZMpads1qter0+Go0uLy8HAgGYgBcNr9dLUVQkEoGG\nxWCo4EY+fkiSTCaTk5OTp57TDMZavV6PxWIajWZxcRGSz53r9/tcftJutzUajd1uN5vN8AME\nF8rG/nuv19toNKrVaiKRSCaTJpOJG3/zHeB4UCqVs7OzmUxmbW0NysDEJBAIrK6uRqPR2dlZ\nvmMBogWJypjp9Xrr6+sOh8NqtfIdC7gwcrlcJpOB+/fOsSxbq9WKxSJJkkql0mKxBAIBKD+Q\nApZFL7+Mfvc7VCggHEcOB3rTm9Du3WjY7xscx00mk8lkYhimVqtVKhVuM7HNZrNarTCdvC0M\nw7xer8FgiEajJEkGg0GYUBABHMenpqaWl5dzuZzL5eI7HCBOkKiME5qmI5GIVquFtoDiMBgM\notFoq9WCBsQ7RFFUqVQqlUosy5rNZo/HA+uK0kHT6PHHUSqFLrsMXXklYlmUSqEnn0SRCPqj\nPxp6rsLBcZzbx9Lv90ulUrFYzGQyRqPRZrNBUdO2uGPs19fXoQxMNFQqld/vj8Vier2eIAi+\nwwEiBInKOEkkEizLBoNBmHcXgXa7zfVtW1hYgPPmttVoNEqlUq1WU6lUTqfTbrdDLyap+eUv\nUS6H/uqv0EZSv7iILr4YPfIIeukldPnlIw1GoVC43W63291oNCqVCvdetlqtNpsN3s5bUCgU\ns7Oz2Wx2bW3Nbrf7fD64nY07i8VSr9ej0eji4iJs3wIXHCQqY6NWq1Wr1bm5ORifiUC5XE4k\nEiaTaXJyEq7sW+DmrUul0mAwMJvNc3NzMGknTSyLXnoJvf3t6LSlR4cD7dmDXnxx1InKBu7c\nFZ/PVy6XS6VSLpczGo1OpxN2sJwNhmEej4fbYc+tJ0MZ2LibnJxcWlpKJBKBQIDvWIDYQKIy\nHgaDQTwed7lcMEobdwzDJBKJarUK3b221mq18vk8t4TCbcqCLl5SRpKo1UKbnho1NYWeeQbR\nNOJxDkculzudTqfT2Ww2C4VCOBzWaDROp9NsNsOKwaZOLQObnp6GGs6xxm1WOXnypMFgsFgs\nfIcDRAVu/OMhFosplUo4gX7cURS1trZG0/Tc3BwcPng2jUYjl8uRJGk0GmdmZmBmGiCEGAYh\ntHkqwj3IMHwmKhu4LmG9Xi+fzycSiXQ6bbfboVJxU1wZWCqVWl1dDQQCMMAdawRBuN3uRCJB\nEARUP4ILCBKVMVAqlRqNxsLCAszMjTWSJNfW1giCmJ2dhcWBTdXr9Ww22263LRbL4uIiNPIC\nG/R6pFCgbBaduQE7m/3fzwqHUqmcmJjweDzlcjmfz2ezWYvF4nQ61Wo136EJC4ZhExMTKpUq\nFotRFAWTcWPN7XaTJMmdAgnDFXChwGhJ6Hq9XiqV8nq9MGgba9VqNRqNOhwOn8/HdyyCwzBM\nqVTK5/M0TdtsNqhZB2eSydCuXejZZ1EohE5N87td9Pzz6A1v4C+ys5PJZA6Hw263V6vVfD6/\ntLRkMpncbjdczE/jcDhUKtX6+jpFUZOTkzDGHV9TU1NLS0vZbNbj8fAdCxAJ2MUrdNw5gE6n\nk+9AwPkrFArRaNTlckGWchqaprPZ7O9+97tcLmez2Xbv3u3z+SBLAZvauxd1u+iRR9DqKmq1\nEEmi5WX0z/+MlEr0e7/Hd3Bnh2GYxWJZWFiYmZmhaXppaSkajXa7Xb7jEhaj0Tg/P0+S5Orq\n6mAw4DsccJ4UCsXk5CRXu8t3LEAkYEVF0PL5fLvdXlxc5DsQcP7S6XQ+n4cK7NMwDFMsFnO5\nHI7jHo/HarVC9zOwNYJAf/EX6Gc/Q9/7HqJphBBSKNAb34j27kVjkdvq9Xq9Xt9sNjOZzNLS\nksVicbvdUM2/QaPRzM/PRyKRlZWVUCgEZXJjymQy2Wy2WCy2sLAARc7g9YPfIeHqdruZTMbv\n98ME85hiWTYWi9Xr9VAoZDAY+A5HQKrVajqdpmna6XQ6HA5IUcAOEQT6oz9C/+f/oEoF4Tgy\nm0d0zuMFpNPpZmdnuXTl+PHjZrPZ6/VCusJRKBRzc3Pr6+snT56EVmDjy+fzNZvNRCIRDAb5\njgWMPUhUBIpl2Wg0ajAYrFYr37GA80HT9NraWrfbnZubg5L0DdVqNZPJ9Pt9LkWBVkjgPOA4\nGvfO3ly60mg0MpnMiRMnbDab2+1WCKohAE9wHJ+enk4mk+FwOBAImM1mviMC54zrVry8vFwu\nl2EMA14nSFQEKpvN9nq9UCjEdyDgfPR6vUgkghCan5+HBTFOvV7PZDLdbtdut7tcLigJAIA7\nLJJ7axw/ftzlcjmdTlhgxDDM7/erVKpoNMo12OA7InDONBqNx+NJpVImkwkmpMDrAWMFIWq3\n27lcbmpqCibYxlG32w2Hw0qlMhQKwQUaIURRVDKZbDQaVqt1enoaMjcATmU0Go1GY6lUymQy\npVLJ5/PBMgJCyOl0ymSyRCKBEIJcZRw5nc5yuZzJZCYmJviOBYwxSFQEh2GYaDRqsVjgXjWO\nut3uyZMn9Xp9IBCAmVGGYXK5XD6fJwhiYWEBSuAAOBubzWaxWHK5XCwWKxaLPp8PzoTl8hPI\nVcYUhmE+n29tbc1ms8HFH5w3SFQEhztNAmYgxhFFUaurqzqdbmpqCo4CqNfriUSCZVm/3w9l\nygBsa6MDXjqdXl5etlqtXq9X4uvqNpsNx/FYLMayrN1u5zsccG641cJkMjk7O8t3LGBcQaIi\nLIPBIJ/P+3w+KBkaO71eb3V1VaPRBINBiWcp3W43mUySJOl0Ot1uN6wsAbBzKpUqGAw2Go1k\nMnnixAmPx+NwOPgOik9cY3cuV5H4j2Ic+Xy+paWlarUKRSLg/ECiIizpdFqhUMD089jhshS1\nWj09PS3lLIVhmGw2m8/n9Xr94uIinIQAwPkxGAyLi4vFYjGTyVSr1UAgIOUWxhu5CkIIcpXx\nolKpHA5HKpUyGo0waQXOAyQqAtLtdsvlcigUkvJIdxwNBoNwOKxQKKanp6V8IW61WrFYjGGY\nqakpmDwD4HXCMMzhcJhMpng8vrS0xC2tSPbuYLFYMAyLRqMIcpVx43a7K5VKLpfzeDx8xwLG\nDyQqApJKpfR6PZwMOF4Gg8Hq6qpcLp+ZmZFslsKybD6fz2QyJpPJ7/dD62EALhSlUjkzM1Ot\nVhOJRKVSmZyclOwme7PZzJ2ii2EY7FcZIziOe73eWCxmsVhgmR2cK4mOqwSIJMlGo+Hz+fgO\nBJwDbi0Fw7BQKCTZLKXT6aysrOTz+WAwGAwGIUsB4IIzm82Li4tKpXJlZSWdTrMsy3dE/LBY\nLIFAIJlMVqtVvmMB58Biseh0unQ6zXcgYPxIdGglQKlUymq1Qgu/MULTdCQSYVl2ZmZGms0P\nWJbNZrPLy8sqlWrXrl0mk4nviAAQLa64dHJyslQqraysdLtdviPih8Vi4abnW60W37GAczAx\nMVGv1+v1Ot+BgDEDiYoglEqlbrcL5ZtjhGVZ7tTk2dlZaa4hcCfGFAqFqakpWEgBYDSsVuvi\n4qJCoVheXq5UKnyHww+n02m1WiORCEVRfMcCdkqj0djt9mQyKdn1QHB+IFHhH9coyeVySbxf\n/nhJp9PNZjMUCklzgF6tVpeXl+Vy+eLiIuybB2CUFApFKBTyeDyxWCwejzMMw3dEPJiYmCAI\nIhKJ0DTNdyxgpzweD03T+Xye70DAOIFEhX/5fJ5lWafTyXcgYKfK5TK3kiDBhqEsy6bT6Wg0\n6nQ6Q6EQZNcA8MLpdM7NzZEkuby83Ol0+A5n1DAM487V5epv+Q4H7IhMJvN6vblcrt/v8x0L\nGBuQqPCs3+9zPfskuxV77LRarXg87vP5jEYj37GMGtc8oFQqcRO6fIcDgKQRBLGwsKDRaFZW\nVkqlEt/hjJpMJpuZmen1evF4nO9YwE7ZbDaFQlEoFPgOBIwNGBzzLJPJqFQqOOFxXPT7/bW1\nNYvFIsFG/iRJLi0tsSy7uLgITbQBEAKZTBYMBj0eTyKRiMfjUltb4BoMVKvVbDbLdyxgp1wu\nV7FYhJo9sEOQqPCJO+HR5/NJ9gyv8cIwzNramkqlmpyc5DuWUcvn8+Fw2Gw2z87OQrkXAILC\nlYE1Go3V1dXBYMB3OCOl1WqDwWA2m5Vsa4GxY7FYZDJZsVjkOxAwHqS4D1g4stksnPA4RmKx\nWL/fX1hYkFRiyZ2wVqvVAoGAxWLhOxywlcFgQNP04DU0TTMMwzAMy7I0TXN/nu3/ci22ZTIZ\nhmEYhslkMrlcLpPJNj6Qy+VQoSpYBEHMz89HIpGVlZVQKCSpY/WMRqPX643H4xqNBlr8Cx+G\nYQ6HI5/PO51OSd1MwfmBRIU3/X6/Wq2GQiG+AwE7ks1m6/X6/Py8pNp8cYtInU5nbm5Osudh\nC02v16Moqtfr9fv9U/88dX8qjuNcdoFhmFwuxzAMx3Ecx0898If7LEJoI5lhGIam6Y2Uhkt1\nTs1tZDKZQqFQKpWK16heAwMO3ikUirm5uWg0urKyMj09rdfr+Y5odJxOZ7PZjEaj8/PzkE4L\nn81my2az5XLZZrPxHQsQup0OuWKxWCQSKZVK9XrdaDTabLZQKBQIBIYZm8gVCgWVSgXLKWOB\nJMlsNhsMBiU1Xdfv9yORCMMw8/PzSqWS73CkiGGYTqfT6XQoiqIoqtvtUhTFMAyXfihfo9Pp\nuLRhSEsfGws1XFI0GAx6vV673e71er1ej2uPq1QquYxFrVZzE9tQIjh6OI4Hg8FMJhMOhycn\nJyW1+3FycnJpaSmdTk9MTPAdC9iGTCaz2+35fB4SFbCtbRKV9fX1Bx544MiRI5FI5MzPhkKh\nffv2/c3f/M3U1NRwwhMtlmVLpRL0TRoLNE3HYjG73S6pk9cpigqHw3K5fG5uTlKLSPzq9/vt\ndrvT6XB/UhTFsqxSqVSr1SqVymazcZmAUqkc5QqGXC6Xy+Vna8bNpSsbqVS5XO52uyzLyuVy\nLmPRarUEQUiqGIlHGIZ5vV6VShWPx7vdrtfr5TuiEZHL5VNTU+FwWK/XS+paPaacTmehUKjV\navBiga2ddfxRLBbvvPPOb37zm4PBwOFw3HzzzTMzMw6Hw2Qy1Wq1QqEQDoeffvrpL33pS4cP\nH37f+953//332+32UYY+1srlMsuykpruGl/JZJK79/MdyOg0m821tTWdTjc1NQV1FEPFsmyn\n02k2m61Wq9ls9no9HMe58b3D4eA+OLVeS4A2VnU2HmFZttvtdl5TrVb7/b5MJuMyFoIgdDod\nZL9DxTWBXV9fHwwG0mn+odfrnU5nPB4nCAIW9AROLpdbLJZcLgeJCtja5reKX/ziFzfffHO5\nXN6/f/+HP/zhN73pTZvO3rEs+8orr/zjP/7jN77xjSeffPJ73/veNddcM+SARaJQKNhsNhgC\nCl+tVqtUKnNzc9J5ser1+vr6utVqnZiYgI0Hw8CybLvdJkmy0Wi0Wi2GYdRqNUEQLpdLp9Op\n1epx/7FjGHbatuZer9d6TaFQYBhGo9Ho9Xq9Xg9Jy5AYjcbZ2dlwOIwQkk6u4vF4SJKMRqOz\ns7N8xwK24XK5Tpw40Ww2T53mAOA0m98errvuure85S2PPPLI9PT0Fv8Zw7BLLrnkX/7lXz71\nqU+9//3vv/baa3u93nDiFBWSJLvd7tY/WyAEg8EgkUi4XC6CIPiOZUTq9fra2prb7Xa73XzH\nIja9Xq9erzcaDZIkaZrmRupOp5MgCNGP1LlVF7PZjE7J00iSLJVKDMNotVqDwWAymaTzRhsN\ngiBmZmYklatwJ9YvLy9zTaX4DgdsRaVSmUymXC4HXYXAFja/O95555133333zusNQqHQ008/\n/elPf/rCBSZmhULBaDSereAbCEcikVAoFNIZspMkub6+7nK5pPOUR6DdbtdqtXq93m63lUql\nwWDw+/16vV6ypSkYhnEFYC6Xi2XZVqtFkmS9Xs/lcnK53Gg0Go1Gg8Eg8IK3cUEQBLeuwrKs\nRPrfqFSqiYmJeDyu0+kg9RU4p9O5srLS6XQk1agGnJPNE5V77rnnzAdJkkwkEl6vd9OCQplM\ntun/AqfhZlVnZmb4DgRso1wuc/2Ix70OZ4eazWYkErHZbNDj4YJotVqVSqVWq/V6Pa1WazKZ\nJicnocXzaTAM0+l0Op3O7XYPBoN6vV6v1+PxOMMwRqPRbDabTCbpVF0OiVar5dZVotFoIBCQ\nwgXNarU2Go1YLLa4uCiF5zu+CILQ6/X5fF4iWTQ4Dzu6ATz77LOXXXaZwWC46KKLXnjhBe7B\nG2+88amnnhpmbOJUKBTUarWkOtyPo16vl0wmPR6PRKZ5Wq0Wl6VAZ8/XqdvtZjKZ48ePr6ys\ntNttl8u1e/fuhYUFt9sNWcrW5HK51WoNBoNvfOMbp6enZTJZIpE4duzY+vp6rVZjWZbvAMcY\nl6twSSDfsYyI3+8fDAb5fJ7vQMA2nE5npVKBjQPgbLYvjD569Oh1112nUqmuv/76n/70p9yD\nxWLxxRdf3Ldv369//etLL710yEGKB8MwpVLJ5/PxHQjYRiwW02g0Eilxbrfb4XDYbDZDlnLe\naJquVCqlUqndbms0GpvNZrFY4PCZ84NhGFcAxjBMo9GoVCrRaBTHcavVarPZoM3x+dFqtbOz\ns6urq6lUSgr3IJlM5vV6k8mk1WqVbJnlWOAq4cvlMpQcg01tn6jcc889Lpfr+eefl8vlG79G\ndrv92LFjl19++b333vujH/1oyEGKR7lcxjDMYrHwHQjYSq1Wazabu3bt4juQUeDOS+EKk/iO\nZSy12+1SqVSpVDAMs9lsgUBAIqtwI4DjuMlkMplMNE1Xq9VSqZTP53U6nc1mM5vNUBJ2rrRa\n7fT0dDgcVqlUUjhOwGazlUqlVCoFR70JnMViqVQqkKiATW1/oX90IWRWAAAgAElEQVThhRdu\nu+22MydgHA7Hrbfe+txzzw0nMHEqFovQlVjgWJZNp9MOh0MK3Q5omo5EIgRBQJZyrliWrVQq\nKysry8vL3W7X7/e/4Q1v8Hq9kKUMg0wms9ls8/Pzi4uLGo0mmUz+7ne/y2Qy/X6f79DGjF6v\nn5ycTCaTjUaD71hGwe/3V6tVkiT5DgRsxWKxcCcv8R0IEKLtV1Tq9frZCkLcbnez2bzQIYlW\ns9nsdrvQhk/gisViv993uVx8BzIK0WgUITQ1NQX7TXeOYZhyuZzP5/v9PreEAsVII6PRaPx+\nv8/nK5fLhUIhl8tZrVbuZEy+QxsbVquVoqj19fW5uTnR/9y0Wq3FYkkmkwsLC3CVEyyVSqXV\naqvVquh/IcF52D5Rcblcy8vLm37queeegwZBO1etVnU6HZStCxlN09ls1u12i/5cC4RQKpVq\nNpsLCwvQB3aHaJouFAqFQgEh5HA47Ha7FH5PBAjHcbvdbrfba7VaoVBYWloyGo0ejwfaFeyQ\nx+Phaj7n5+dFf0vyer0nTpwolUpSqHYbX2azuVwuw5ASnGn7GqR9+/YdPnz4t7/97akPVqvV\nT3ziE48++ugNN9wwtNjEpl6vb9rZGQhHNpuVyWQOh4PvQIaOm5AOBoNSqHB7/RiGyeVyx48f\nL5VKHo9n9+7dEslmBc5kMs3Ozs7PzyOElpeX19bWxrR6pN9H2SyKxVC7PaLvODk5qVKp1tbW\nGIYZ0bfkCXcWVjqdHgwGfMcCzspsNne73fbI3gBgfGx/o/30pz995MiRN7/5zW94wxsQQh/7\n2Mc+9rGPLS8vUxTl9/vvuuuu4QcpBp1Oh6Ioo9HIdyDgrHq9XqFQkEIdVKvVisfjPp/PYDDw\nHYvQsSxbKpWy2SxCyOPx2Gw20f96jB2CIEKhUKvVymQyS0tLZrPZ6/WOSwZOUehnP0OvvooY\nBslkiKbRxAS64QY07I6DOI5PT08vLy8nk0nRb1FzOBzlcjmTyfj9fr5jAZtTqVQEQVSrVVgX\nBafZfkXF5XK99NJLBw8e5Pqvv/rqq6+++qper7/ttttefPFFifRvff1qtZpGoxmXe6c0pdNp\nrVZrNpv5DmS4BoPB2toaV9nPdyxCV6/XT5w4wTVXuOiii+x2O2QpgkUQxMzMzNzcXL/fX1p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K6nA4CoVCo9GQ8r4vcTeKJQginU7zHQXY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\nbvZDolAorFYr9/bv9XrcwkK5XE6lUhiGqdVqrVar0Wi0Wq1Wq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pM5duzY0tKSWq2enp6emppCStlRMplcXV31+XwjIyNIKYpWKBQymczo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\nViqVZrOp0WgsFovL5RoeHjYajb1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0Ot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\nKq1We9lll91yyy233HKLWq2WsUgAAAAAAKUol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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_3_3.png" } }, "output_type": "display_data" } ], "source": [ "a <- 3.5 # average morning wait time\n", "b <- (-1) # average difference afternoon wait time\n", "sigma_a <- 1 # std dev in intercepts\n", "sigma_b <- 0.5 # std dev in slopes\n", "rho <- (-0.0) # correlation between intercepts and slopes\n", "\n", "Mu <- c(a, b)\n", "\n", "sigmas <- c(sigma_a, sigma_b) # standard deviations\n", "Rho <- matrix(c(1, rho, rho, 1), nrow = 2) # correlation matrix\n", "Sigma <- diag(sigmas) %*% Rho %*% diag(sigmas)\n", "\n", "N_cafes <- 20\n", "\n", "library(MASS)\n", "set.seed(5) # used to replicate example\n", "vary_effects <- mvrnorm(N_cafes, Mu, Sigma)\n", "\n", "a_cafe <- vary_effects[, 1]\n", "b_cafe <- vary_effects[, 2]\n", "\n", "iplot(function() {\n", " plot(a_cafe, b_cafe,\n", " col = rangi2,\n", " xlab = \"intercepts (a_cafe)\", ylab = \"slopes (b_cafe)\",\n", " main = \"Figure 14.2 (updated simulation)\"\n", " )\n", "\n", " library(ellipse)\n", " for (l in c(0.1, 0.3, 0.5, 0.8, 0.99)) {\n", " lines(ellipse(Sigma, centre = Mu, level = l), col = col.alpha(\"black\", 0.2))\n", " }\n", "})\n", "\n", "set.seed(22)\n", "N_visits <- 10\n", "afternoon <- rep(0:1, N_visits * N_cafes / 2)\n", "cafe_id <- rep(1:N_cafes, each = N_visits)\n", "mu <- a_cafe[cafe_id] + b_cafe[cafe_id] * afternoon\n", "sigma <- 0.5 # std dev within cafes\n", "wait <- rnorm(N_visits * N_cafes, mu, sigma)\n", "d <- data.frame(cafe = cafe_id, afternoon = afternoon, wait = wait)" ] }, { "cell_type": "markdown", "id": "7b78e0cc", "metadata": {}, "source": [ "Refit the model:" ] }, { "cell_type": "code", "execution_count": 3, "id": "e664520f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "b_cafe[1] -0.97493827 2.706508e-01 -1.4053396 -0.5321296 2558.033 0.9985400\n", "b_cafe[2] -1.57678103 2.754448e-01 -2.0302763 -1.1429525 2258.533 0.9987245\n", "b_cafe[3] -1.75208873 2.937009e-01 -2.2155046 -1.2700634 2475.211 1.0004769\n", "b_cafe[4] -1.38179526 2.640233e-01 -1.7984554 -0.9628625 2678.364 0.9997784\n", "b_cafe[5] -0.85552684 2.673436e-01 -1.2846377 -0.4451974 2146.033 0.9990816\n", "b_cafe[6] -1.03052158 2.727011e-01 -1.4647225 -0.5959246 2341.112 1.0009258\n", "b_cafe[7] -1.07318113 2.612501e-01 -1.5018916 -0.6632712 2523.437 0.9998771\n", "b_cafe[8] -1.66622936 2.724191e-01 -2.1166805 -1.2528713 2411.146 1.0007548\n", "b_cafe[9] -1.09643654 2.628003e-01 -1.5073631 -0.6833408 2509.108 0.9986496\n", "b_cafe[10] -0.85150181 2.644251e-01 -1.2527569 -0.4179187 2583.283 0.9994003\n", "b_cafe[11] -0.94436493 2.765405e-01 -1.3854714 -0.4974285 2568.146 0.9985809\n", "b_cafe[12] -1.08532110 2.689619e-01 -1.5141136 -0.6673375 2766.285 1.0006618\n", "b_cafe[13] -1.82885505 2.764952e-01 -2.2718830 -1.3952793 2499.467 0.9990739\n", "b_cafe[14] -1.09088505 2.773739e-01 -1.5262770 -0.6556258 2419.601 0.9986678\n", "b_cafe[15] -2.08013935 2.922605e-01 -2.5285539 -1.6230970 2367.273 1.0003216\n", "b_cafe[16] -1.13964911 2.668720e-01 -1.5497444 -0.7027246 2683.230 0.9985100\n", "b_cafe[17] -0.84962462 2.791103e-01 -1.2910448 -0.4098209 2627.050 1.0004932\n", "b_cafe[18] 0.13329806 2.973738e-01 -0.3546918 0.6137691 2271.025 0.9996235\n", "b_cafe[19] -0.05123218 2.914838e-01 -0.5206416 0.4161668 2227.332 0.9997787\n", "b_cafe[20] -0.94603730 2.643219e-01 -1.3730128 -0.5212390 2253.346 0.9992708\n", "a_cafe[1] 4.32822010 2.020550e-01 3.9961308 4.6447876 2655.898 0.9990083\n", "a_cafe[2] 2.23007232 2.012716e-01 1.9124224 2.5524646 2430.606 0.9988290\n", "a_cafe[3] 4.55863435 2.128146e-01 4.2177601 4.8939822 2441.837 1.0012199\n", "a_cafe[4] 3.31432538 1.956863e-01 2.9999354 3.6215312 2700.695 0.9993147\n", "a_cafe[5] 1.92490907 1.986681e-01 1.6207611 2.2437742 2374.147 0.9986663\n", "a_cafe[6] 4.24067936 1.990592e-01 3.9296951 4.5483649 2351.843 0.9995529\n", "a_cafe[7] 3.77722779 1.908971e-01 3.4746905 4.0842010 2392.385 0.9998529\n", "a_cafe[8] 4.12167102 2.033142e-01 3.8058353 4.4586906 2764.740 1.0017864\n", "a_cafe[9] 3.91765196 1.923953e-01 3.6088796 4.2293424 2563.342 0.9989676\n", "a_cafe[10] 3.46479236 2.000028e-01 3.1430532 3.7814975 2343.924 0.9993257\n", "a_cafe[11] 1.95604246 2.003907e-01 1.6292569 2.2770210 2497.175 0.9988287\n", "a_cafe[12] 3.98535177 1.923491e-01 3.6838910 4.2991258 2487.950 0.9997389\n", "a_cafe[13] 4.14900451 2.017190e-01 3.8299155 4.4610220 2534.936 0.9989087\n", "a_cafe[14] 3.31122820 2.030783e-01 2.9852590 3.6312353 2594.142 0.9994834\n", "a_cafe[15] 4.62640653 2.048657e-01 4.3016374 4.9457133 2585.030 1.0030749\n", "a_cafe[16] 3.48916086 1.981373e-01 3.1825172 3.8082679 2782.811 1.0004568\n", "a_cafe[17] 4.13659311 2.049720e-01 3.8173995 4.4642264 2521.503 0.9996007\n", "a_cafe[18] 5.57907198 2.139529e-01 5.2380410 5.9266490 2419.397 0.9987837\n", "a_cafe[19] 3.07139300 2.068774e-01 2.7288774 3.4107189 2409.187 0.9994801\n", "a_cafe[20] 3.72791143 1.933597e-01 3.4257859 4.0296822 2214.056 0.9992702\n", "a 3.70381547 2.298564e-01 3.3455440 4.0634464 2344.457 1.0003163\n", "b -1.09575262 1.568141e-01 -1.3393037 -0.8450130 2020.744 0.9996859\n", "sigma_cafe[1] 0.98523622 1.841260e-01 0.7384284 1.3121756 2191.504 1.0001043\n", "sigma_cafe[2] 0.63873123 1.387958e-01 0.4412895 0.8792464 1888.167 0.9996571\n", "sigma 0.47388432 2.663314e-02 0.4333083 0.5167588 2110.001 0.9995346\n", "Rho[1,1] 1.00000000 0.000000e+00 1.0000000 1.0000000 NaN NaN\n", "Rho[1,2] -0.04711170 2.294524e-01 -0.4003752 0.3325041 1973.052 0.9995424\n", "Rho[2,1] -0.04711170 2.294524e-01 -0.4003752 0.3325041 1973.052 0.9995424\n", "Rho[2,2] 1.00000000 9.264531e-17 1.0000000 1.0000000 1999.376 0.9979980" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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pP5cELsMY6mkg/hozjUNDH/LeoIJOx5sCwTF8QUx7mrjv+yiBwZxaGiq3k+po5A\npFkf6gTgJKY4WBPHf1lEjoziUFGPcmJfMRrN2BrUCcBJTHG0H+v4L4vIkVEc6plr20gdgcp6\n63XqCCBgzlFd+tRm3rMZEsN+oY4AgpTiSHX8l/znLtGnK6I41JB8cvP0umGfUccgVHc4dQIQ\nxBdHau82gnC8NGP1xdYBikNx//aryBgr3ecodRBKuM6NC2KLYyx7UxCetrzSO8R9xTZfUBxK\nmxpWe+r6Y4mBH2houM6NC2KL475nBeG0pbsgdBN7VBvFobD+UXOoI/DggmUbdQQQXxw5ZgjC\nbPabIEzPLXJkFIeypoWtoY7AhwqTqROA+OLI6SiODtEpjr+/0SJHRnEo6lCkmY+IuuremjoB\nSHip0lE4n+MZx8bLFUSOjOJQkv3hJ6gj8OKLgtQJQHxxjGH/K8LWCcJXYQNEjoziUNIPYf9S\nR+DFEXaYOgKILo6krpExzrOOCle9KnJkFIeSHuhJnYAfRcx5YTBfpJ45ukX0e2EoDgX9HIar\nye9p15U6AeCUc31o1pE6AUc+KkOdAEQXh31RsxpVMogcGcWhnP+s66kjcGQPO0UdAcQWxwTG\nomIyiBwZxaGcd8S2tSmk5f6aOgKILY5iTY5JHBnFoRh76YnUEbjS/BXqBCC2OGx/Sh0ZxaGY\nrRYcGnU1sTJ1AhD9GwfmHKXzZn3qBHzZbjlPHcH0xBbHgN5SR0ZxKMVe/EPqCHxJjVlEHcH0\nxBbHzSYdVx04kk7kyCgOpezBkgBumkn+ZwwUJnoJSExWTGb0fdQJeDOxEnUC0xNbHB26dL9L\n5MgoDqXUG0idgDc72RnqCGaHM0e5dzV0HXUE3qTlw7JMxCQUx4398VJGRnEoZFEus66h4tuz\nYn/vBZWILo51tRhbKQjNfxM7MopDIb2aUyfgz8clqBOYndji2BqWs4mjOC4WCtshcmQUh0Iw\nVZ6nf5jUE5lBWaIXnS5+6pzzN44LxVuKHBnFoYwzbA91BA7FzaBOYHJiiyPvWCG9OIQxsSJH\nRnEoY27eNOoIHOqGiUdpiS2O0PmZxTHHJnJkFIcyMDevN9/kTqWOYG6ir1UZmlkcL5YQOTKK\nQxkVplAn4NGlkM3UEcxNbHH0iN3pLI6rQ5jYs31RHIq4YNlOHYFLtUdQJzA3scVxLi60JqtR\nI5wVF3thIopDEVjx0LuhD1InMDfR53FceCUvYyzfKxfEjoziUATWWPZuY4jov4mgAglnjtrP\nH5EyDQKKQxF1R1An4NOdWJx1Tkl0cRyeO3Hqd1JKHsWhhOTwX6gjcKrd89QJTE1kcWytm35F\nvaWl2Nk4UBzK2GIRuwCW2XyVF2/IEhJXHKsiWM3B06b0KcliRL8LhuJQwtSK1Al4ddGKN2QJ\niSqO+AJR36VvpE6zFbwmcmQUhxI6dKFOwK3/DaVOYGaiimMK++Lu5jQ2RuTIKA4llJ1OnYBb\n71enTmBmooqjcbF7l0ukFRf7/jmKQwGXLWIvRjafPewkdQQTE1UcBTtk3dgFK7lpaGU4JvHx\nqfg06gQmJqo4bG9m3TgAkxVraGQd6gQc69OEOoGJiSoONijrxkEoDg21xGKHvq0Ku0EdwbxQ\nHFyL+5w6AceSc2JdJjLiiqPeiHvqoTi0cx6zf/nTthN1AvMSVxzZiBwZxSHfTxE4NurH/Nz4\n30NFVHHMy0bkyCgO+Ubh2Kg/V21rqCOYFhZk4tmzvagT8O2x16gTmBaKg2elZlIn4NuHJezU\nEcwKxcGxeMtW6gh8O2HZTR3BrFAcHPvdeos6AudqvEudwKxQHBybWpk6Ae9G3E+dwKxQHBzr\n2pE6Ae92WXChGw0UB8dqjKdOwDt7HC50o4Hi4NftsF+pI3Cvz+PUCUwKxcGvvUzKrPLm9Kst\nnjqCOaE4+DW/IHWCYEzq0KPvyC+1ejsoJeZbjfYE2aA4+PWWnuabuPnTWw+F/eDYmNDjhWfq\nlf3TsfXnGQ322xarJJBAcfDriQHUCTLZnS8HjrRv12v47L0+HvKeLeLR4SuzX3NW2lJjyFa1\nT+38Kg+WyKSA4uBXQbHXE6oqdVXXgmUcn0/17tH+kZKNHFtnvth46e69aceXj1js+Lzrt0SP\nr7TvGPmApbzKzXHZukHdHYBXKA5uXWC+/nnX0tRiYS0/P5ftpt9LWViOysMdWz+WD2fRD833\n8+Vn1jo+nPs+Qb2A9QYFfgwoDsXBrdWhydQRHNpMuOR5Y+Ke5R873yo++dnKIyLWU1sZHdny\nK7VWpHu/qkoDgz8oDm5NrmG2srAAACAASURBVEIcIPmiUiMlLu+a1zZbqdGy281OqDMw+IPi\n4NaLzwX5hUuebVy3Vi3nYu4bpi7aci7g431YXLJZsF/qxZ3fjjs+nlT+SKa96KeKjwkBoTi4\nVXu0xC+4vXZQvYmOz8v6DB03btxfjq1pVfMyFjXHeZ/UFZr3PRY28LrErwmsZOFhp5Qe86UW\nSo8IgaE4eJUWtVzS4091iQlt8M4B95tv7V9x1vGpRdRD/b7+T/xo40ObHpa0e3HiP6oY2mmf\nsmMuzZGi7IAgAoqDV4fZcUmP39puoZ+zry+vGP5ULBM/RefCHyXtXDz7r48/ouyI121rlR0Q\nREBx8GpJTtFnQOwfeE3Mw+zHHK9XUpu/9Zv/f6HT/hK7X07Uxxuy2kNx8Oq9uiIfuKul5TEJ\n73V++EhojlYLfd6d9EWFnBpcaPK/F+RMpOE8YLP/+R6DPlx5wbE1qoZCoUA8FAev2r0k6mEn\nWlmabpE28rXvuj/h+GT30g9H++fLPeiCtOGCsqFOxMDgrmtNXPZ8kVqOz//07PzkfeHOJ7LF\nEvQ7RxAsFAevKk8V9bBvmwU7ofF3ITV6fb49KdttPevOVPEkT1f2b0vnC2IFxzuvxUS1nn3v\nKG+q8+qYCSzula8OpCkYDgJCcXAqOfQ3lfeQtnHcM3HsBcfW6rZtGt8XrfUaJSlTgzglLKnr\nXI9flG4/WrtlQfaeY+vU9jN4h0UbKA5O7Qk4i0/qp0XWy97NVeeC75t69Bky9XstXqF4Oij6\nEHDy7O0+7vm0qCD85/xN6WXGWK6i3zi2pjZt2/bFnjsdW5f+lXoKC4iA4uDU/HwBHvBb1Zjx\n+l869WZUtXminsWVMYVifZ3YcoT9c3e4fzYuX3DasbFiUJ8e3dr+4dhqy8KrPv/xDSXCQhYU\nB6cGP+r37hvPWl+m+RVBYafezFl0eMCDmzd6RpeY7PvvU0k/UxbfObZqUsdKmL1VYSgOTjV/\n1e/dZzoaZg2z+KmVewR6zKnWi/xd5dK9tYj9JD81Uflz6E0LxcGp0jOoE2hsZPuJq0+735h6\nYH6vmocCfu38fCLeU7GPKxr7Lv5OKgTFwaeEkI2+7tpWz5BrtP/WtZqNRa10bM1/d9y4cR84\nJyxtF87ytZgSeFqSM+LmPEqeUbzQSpkxIQOKg0/b2BXvd5zuEtLGqKuXpfyzyvliYkijWrVq\n1XGenrJplcfvIN6VE3fSi5A4LohzR8ALFAef5hT1fvuk6Fp/aJtEF3q2pE5gNigOPr31hPfb\n+8/BGZJefB0r4X/Lr12wiJNsKA4+Pfmmx012tWbtNICzUiZ2PlapLA/TQOsbioNPcR6nY/9S\npzxFEJ0o+5GEB99sG71EtSQmgeLg0jXLn9lvWNsgtJtRj4kqQdSZHPfYR1vN9m630lAcXNpk\nyX6OdF9rZzVm8jOOr/JLW/jpZ2nzMoI7FAeXZpXM/uedqA3/TrC/qSOYC4qDS6/dW5nAvux1\nyiC6ETdT8pdsO6tCDrNAcXCp0dsZn+3Lqod7vr8CnjpIX7W+c1G8uRI0FAeXMteb3lwrvI/i\n65AY0/RSkr8k+blcq1VIYg4oDh5dYrvSP4/sIWEpFHPby6T/r7IPsH2hQhRTQHHwaJ01kTqC\n3qTFfh3EV30aelTxJOaA4uDRtPKpH5XAoTtJmvYN5qt8XEoIgaA4eNTr8QdzTZN2YoLpjbmf\nOoGpoDg4lFbS2kLk9eRw1x9WUcvZeTpfe4OySUwBxcGhA5Y+1BH0JzEsyHlFU3vbJuG3O6lQ\nHBw6xTwWnYeAHhwR7FfOi26FYx0SoTg4k3ZUEFaG+5uZF7zr3zjoL/27aglMcyINioMv158u\nJgjjq1PH0KPFOYNfeSlplYJBTAHFwZWjlSseFoQunahz6NF5tkfeAPpf3kpDKA6ebMj3pPOt\ngVpjqYPoUqlPZH15aq6emGNNNBQHRxIjezsPbqRG/kSdRJc6Sb/OLZvfKxT8Cm+viITi4MmJ\n9I8Hg7jsAgRhWhmZAySPiqp3TJEoxofi4M+i3Ph3Lxi72Xm5Q5x44TclkpgAioMTCb123N0c\n1oAyiH6l5lqqzEB4azYwFAcfztUuc28u4pa9KZPoWKMBigyzNN/EW4oMZGQoDi7sL1n3wr0/\nlP6UMImevVNPkWFuf1ig0BRUh38oDh6si3k2awKOm77Xmwa/fo5IUWaghPH58/+jzFBGheLg\nwcx3XV5Wb7Zcp0uia/EhW5Qa6tY8fBP8QnFwZ4bcdxXNq/JkRYfb3nQ+ZmLzAcVB7fRBtxt6\nPUuSwwheaqPocJd6xsR0/QUXHHqD4iC2OM9rbrc89B5JECOYXUThARMXNAsbrfCYxoDiIBXf\nNfRdt2s67bm+p8liAAfZCcXHvJ7k+DBi8KobAR9pKigOSqsLl/c4nHeU/UsRxRDs+RaqM/Bn\nDcKt1XvHqzO4LqE4KH3+XpLHbUtz4YTzoAU31bkYievHPX9OEO6M+nwHDpgKKA46J33c/g5O\nOA/e6Joq7yC5bQlmrfBC8FMGGQWKg8TZj6rZLni/q2k/baMYyjqr+ocirv7+0XuOXwqPVW/+\n1mfrTfvqBcVBYEG9kKKDfR3JKPKlplmMJTFMs9Vgk2f0e7JUSHnH1u39JnzHFsWhmfhtqxZM\necP5v3vioE0+L8C8wLCEugx13tV0d0mXHR9WseiGI7eY7JJaFIfKlndsVKN07IeOrV4srFCN\nZoHme1gZjqkvZXjjcYKdXlg+oFZIT4IdE0JxqOTkl91qfOD4/O3LQyfNXuScYSY1QczXjVX7\n8J6xLc5FdNzy/DnHh5Oeb5IZFYpDFZuqsAJtxgczDV277oqHMZNzbCfh3usVnmGWwx0oDlX8\nPf6vIM/GKIXJOGQp9yHhzhNGx1Tx/fNkKCgOhR3rHSfn99Urlu2KRTGlbspe5ybVpa4hE0gD\naAXFoaj/Xgp9QNalJqvCkpXKYk5zChIH+EOzN4RJoTiUtDCy1kp5I4yupUwS0zrKDlNHMAUU\nh5I2fCP3OpNneygSxMSKfkadQBBWyFtTTg9QHHwpMYs6gd515GDh3ZXh/Y1+pSKKQyEbSy9W\nYJTzbLcCo5jarKLUCRzW5HzZ4M2hRHGkbFvr5cILUxWHfVJoDyUm1F8WbZbzAFRzmB2hjuDw\nZ0xPYzeHrOIYtdb5cUYsY6yWx7+UZiqOW+2i5ysy0NsNFRnG1Hg4yCEIm3Mbe30FWcXBBjk+\n/MjCn+lZj8UcdbvTTMXRodRfygz02CBlxjGzzh2oE6Qz9i8cChRHuZgDjo9LLC+63Wmm4jhy\nVZlxUnMtU2YgM5tdwOA/s1yQXRwX2ZD07Vbux6TMVBxK2cvOUkfQv//YHuoImTbvCPwYvZJd\nHP+xeenbw2xud5qlOFZ+pdxYn5RQbizzqjCROkGm9/Mcoo6gGtnFkRozNn27Wx63O01SHHND\nFbyqqmNn5cYyrz5PUSfIlNq0kmEXkpRXHB22H7k0uKzzfciD0c3d7jRHcXxmnabgaCVwaawC\nvo/iZVqMaxVaGnViMHnFkWGxICyIDtnmdqcpimO69XMFRzvF9is4mmndDF9FHeGuA7nGU0dQ\niazimDNlRL8urRqucfwAFf3B/U4zFMfNyLlKDrcg1qj/PmmrkfuqmnRWzaZOoBKFTjm/6fk3\n3gzFIaQoOtor7i/3ICiTy1InMD5cq8KRCpOoExjDP8zYZ23yAMURtMU/KzzgKW5OQNC78jwd\nWdhmyIVylCqOo40aCcL1z2dm6WTw4lgY+rXCI36ZD4c4lPF2XeoELn61rqGOoAKlimM3czx6\nT/nSWfIx9VfjI7REyfM3MjzfXukRzWqr5T/qCC76FblIHUF5ShVH0r59brcY+6XKj2EfKD2k\nvSgm8VGIPe5j6gguku9varyrZ3CMIyhJkcovNbiHnVB8TLN6ox51Alf/RE+njqA4ucVhP7Z6\n6dI13n4xNHRxCCrMiDv6PuXHNKsdlmAWw1LNkjnUCRQnrziu9i+QcfJo8ZGJ7vcZuzhUUH8g\ndQIDuW8kdQKDk1UcZ0uxcl1HjB8/rEMRVt19SgrjFse+XWqMejX0dzWGNamxZY13WIErsoqj\nu21R5lbqdEs/tzsNWxw7Y1X512x+LJapV84ZGzfXq2TYtJk6gbJkFUehblnb7ePc7jRqcezO\n00WV0y1adVFjVNNq24I6QXbj856ijqAoWcVhG521/W6Y250GLY49+TqnqjFuQtRyNYY1rXXW\n49QRsrnzUENDnd4nqzhKtMvablnS7U5jFkdy/o6q9IbwXQ5eJpEwiNo9qRNkdzxmdOAH6Yes\n4uhnmZC5RHLCcOY+P7cxi0P4SZ3eENo8p864prUinKezRx2+tm2ljqAgWcURX5PlbNS1b58u\nDaNYA/eaMGhxqCQ+wmNCE5DFXrNb4Adp6u1FgR+jG/LO40iZXMPqPI3DVneWxz/EBiyOY+qd\n2jkrP95TUdiGEIO9kcEV2aecJx3eufOIt/lsjFcce/KNUm3sh19VbWjT6lQdh41Ug2tVRNuT\nT6Xjog4HLaqcVGZuF4tydnxUEDZzdSa8HCgOsdTsDeH1B1Ub2sTW2xSf+kCmXpWM8kOB4hAp\nXs3eSIydo9rYZrbAOoM6QnbXynSkjqAQFIdIt+ep1xvCp3k9rhEEJXxpe1vFb1sQdkV8Qh1B\nGSgODqSVH0YdwahW5XnsDHWGbGaGG2NBWRSHGBevqTr8sojzqo5vZsfr5uPrXP4B31EnUASK\nQ4TjxcaoObydt7OjDeXOMOtbfL1cMQQUR2CnSz+erOb4P4RhzkA1/ZqnKQ4hKQ3FEdClSg1u\nqTm+vVYPNYcH4VDJx7lqjs0/USeQD8URSGrtWtdV3cE3EZxdjWU8x4s/x9OEYPPC11NHkA3F\nEUjK6+quinG77ABVxweHPdE8re0m9M2n+zNIURzUpua5Qh3BBOaFua/7Q+nOkxUvU2eQCcVB\n7Eoe3k6LNqaWD/A0Adf16k2oI8iE4vDr3d5q76FvBVxPr4UzOb6gjuDq7ELqBDKhOPyZpvpc\n2QdsBjjCrgvvFUmgjmAkKA4/Flvnqr2LJnr/lVU3bhVRfLVfmbzNYqMbKA7f1keMU3sXP1n3\nq70LyDSpoKqn40hXaTh1AhlQHL49ofqsXHcqq34MBe5KyP8RdYTsfg57nzpC8FAcvql/hcNn\nudQ9RwRcjSzD0xsrDsvD3qOOEDQUB6HEOPUmMQUPFyP4uk5WEH4I1+3a2CgO75LmaHCO8vhC\nev5fpD9dG1MncLdat/9yoDi8Sn22hPqnV9zMP0X1fYCL7ZbD1BEMA8XhVY+8B9TfybgiXF2z\naQI13qZO4MUNXZ4BiOLwZkj0FvV3klhgqvo7AVcfF75DHcFT5wf0OP8bisOLBWErNdjLtHyc\nnVdgfFcjVlBH8HShTul/qDNIh+Lw4sDvGuzkTin9vhenW+3aUifw4lbLPOuoM0iG4qDyXZTe\nr6zWoR8i4qkjeJH6OlcX/YuC4nB3VqP91MOEgdq7nf8z6gherdXdYXIUh5u5odq8Zbfd8rcm\n+4Fs+j5KncAgUBzZzbJO12ZH3bk7GckUNlq1+o1SqlsDdXX5AYojm3Ghs7XZ0bXoxdrsCLKx\nl+T1PfDEWmUOUWeQAMXhamL4Eo329HFhXZ72o38D/kedwJeEZnl9/yxyB8XhavNWrfZUfYhW\ne4JstltOUkfwJbVXJG9X4fmG4iCxw3KEOoJZlZlIncC3Ma2pE4iG4rhr1SINd9bnEQ13Bq4G\nPkidwBBQHBmS37BqeKlqcp4vtdsZZLPdgpV6FYDiSLfzvkK/ari7JVE6+n9jNGUmUSfw67U+\nnM1T5h2Kw2m27TlNz/9+ppOWe4NsBjxEncCvrXk6cXgJrwcUh5PGy4dfDdfi6lvw7k8L34t8\n78nfRgdv1aM4tqk/J7G7WQX18G+KUdmLczbbubu/C7Xi/9WKyYsjdVHtMA3m+nLTUPV1F8CP\nNx6mThDAPy35X3TO1MVxY0LpyN7aH2M/a92s+T4hy6aQM9QR9M/UxfFR3PsUFxZNKaHBDOrg\nU1pRjS5kNDKzFseZZXT7rjuAbt/g8FpD6gSBTW3L99KypiyOtJ9ahFbW/phoppOWHVS7hnTr\ndfBa5XDhllw3hxmLY26p8A5r6V4tfFAar1RopRWdRh0hsEN8N4cZi2PkGNIpU2oPptw7OLz2\nCHUCEf4p0oLj8zlMVhynfqNOIBxju6kjmN7GEF7nAXP1z8PnqCP4ZqriuD44sil1BmFMeeoE\nwO88YLphouKwf1Wo1EL6wwv3v0OdAIQBuLZeJhMVR/+oUUnUGQThMNtLHQGEXZZj1BHEWfLE\nFeoI3pmoOI5wcW3T+5WoE4BDxfepE4hzvvp9fB6OMUlx3ODmqqGq71InAIdRejnSFF+vFJcr\ny5qjOBbE8LIYwUGGdZh4cMKynTqCSLda5N1DncELMxTHzRds43j5jePdqtQJIF2D16gTiJX6\nzh/UEbwwQXHsrVh6G3WGeyqMpk4A6T7Lz/N5mfwzQXHUbXONOsI9Oyz/UkeAdDdzaLX2liK2\ncPLDdI8JioOn83b7c7uOmOl0aUadQIo6lbSfb8ovgxfHdV6ObWRIK8b5rHUm8of1FHUECeJb\n5FhAnSEbYxfHklxLqSNk81voeeoIcFflEdQJpLB/ENqNg/MX7zFycdx+wzqKr984utJfKgN3\nTdbZut9bqvN0daSBi+NM/fyraRO4u5Xra+oIcM/VSF0dHuWMgYvjyYd4exE7LyaROgJk6fYI\ndQLpfublGhsDF0c82eSAvjR8hToBuNinwzkcO+WYRR0hg0GLg69DG5mOWvg5EQ0cHu1KnUAy\n+9TIFheoQzgZszi2lZxDtm/fBlejTgDZ/BjGxQXT0hyoVeBP6gyCQYtjRngXDg8mpBT8hDoC\nZGO//w3qCEG4PWYDdQTBkMWR9GL4DJo9+7cg5w3qCJDdghyk01brmQGL4+ViPPwq5+khHBrl\nTWoFva6NNfdb4gAGLI6TfE62tsVykDoCuJsfrdNTeWeH9qE9fc2AxcGp1rq6qMokUqv0oY4Q\npHWFHiZ9mWWs4rCPmaL5PkU6ZF1HHQE8/WDjcmI+EU7VKnGEcPeGKo47XXL8ovU+xercgDoB\nePNYc+oEwUp81fePrvqMVBy3mhbg9lTAg9a11BHAm79Cf6SOoEsGKo6EBqUOa7tHCVo9Sp0A\nvHu9DIfn/Ih2iWrHBiqOY0+f0XaHEvwesos6Anh3vZhe35J1SAwfQ7RnAxUHx25Xe5E6Aviy\nIlTHlxAtCxtBs2MUhxbG5sUZivzqXOEWdYTg/RROs8KXQYojqdUP2u1MsgORX1JHAN/i4/R8\nTu+PYdModmuM4kh9Nu60ZjuTLOV+3b7lZw5/hH5HHUGGVSSrFBqjOHrn5Wzy+Gz6FsILFb6N\nijlEHUFvDFEckyIoT4U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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_5_1.png" } }, "output_type": "display_data" } ], "source": [ "set.seed(867530)\n", "m_cafe_rho_zero <- ulam(\n", " alist(\n", " wait ~ normal(mu, sigma),\n", " mu <- a_cafe[cafe] + b_cafe[cafe] * afternoon,\n", " c(a_cafe, b_cafe)[cafe] ~ multi_normal(c(a, b), Rho, sigma_cafe),\n", " a ~ normal(5, 2),\n", " b ~ normal(-1, 0.5),\n", " sigma_cafe ~ exponential(1),\n", " sigma ~ exponential(1),\n", " Rho ~ lkj_corr(2)\n", " ),\n", " data = d, chains = 4, cores = 4\n", ")\n", "display(precis(m_cafe_rho_zero, depth = 3), mimetypes=\"text/plain\")\n", "\n", "post <- extract.samples(m_cafe_rho_zero) # posterior\n", "R <- rlkjcorr(1e4, K = 2, eta = 2) # prior\n", "\n", "iplot(function() {\n", " dens(postRho[, 1, 2], xlim = c(-1, 1))\n", " dens(R[, 1, 2], add = TRUE, lty = 2)\n", "})" ] }, { "cell_type": "markdown", "id": "338281d3", "metadata": {}, "source": [ "The model has inferred rho is zero, as expected.\n", "\n", "**14M2.** Fit this multilevel model to the simulated café data:\n", "\n", "\n", "\\begin{align}\n", "W_i & \\sim Normal(\\mu_i, \\sigma) \\\\\n", "\\mu_i & = \\alpha_{CAFE[j]} + \\beta_{CAFE[j]} A_i \\\\\n", "\\alpha_{CAFE} & \\sim Normal(\\alpha, \\sigma_{\\alpha}) \\\\\n", "\\beta_{CAFE} & \\sim Normal(\\beta, \\sigma_{\\beta}) \\\\\n", "\\alpha & \\sim Normal(0, 10) \\\\\n", "\\sigma, \\sigma_{\\alpha}, \\sigma_{\\beta} & \\sim Exponential(1)\n", "\\end{align}\n", "\n", "\n", "Use WAIC to compare this model to the model from the chapter, the one that uses a multi-variate\n", "Gaussian prior. Explain the result." ] }, { "cell_type": "code", "execution_count": 4, "id": "1f6e19c6", "metadata": {}, "outputs": [], "source": [ "a <- 3.5 # average morning wait time\n", "b <- (-1) # average difference afternoon wait time\n", "sigma_a <- 1 # std dev in intercepts\n", "sigma_b <- 0.5 # std dev in slopes\n", "rho <- (-0.7) # correlation between intercepts and slopes\n", "\n", "Mu <- c(a, b)\n", "\n", "sigmas <- c(sigma_a, sigma_b) # standard deviations\n", "Rho <- matrix(c(1, rho, rho, 1), nrow = 2) # correlation matrix\n", "Sigma <- diag(sigmas) %*% Rho %*% diag(sigmas)\n", "\n", "N_cafes <- 20\n", "\n", "library(MASS)\n", "set.seed(5) # used to replicate example\n", "vary_effects <- mvrnorm(N_cafes, Mu, Sigma)\n", "\n", "a_cafe <- vary_effects[, 1]\n", "b_cafe <- vary_effects[, 2]\n", "\n", "set.seed(22)\n", "N_visits <- 10\n", "afternoon <- rep(0:1, N_visits * N_cafes / 2)\n", "cafe_id <- rep(1:N_cafes, each = N_visits)\n", "mu <- a_cafe[cafe_id] + b_cafe[cafe_id] * afternoon\n", "sigma <- 0.5 # std dev within cafes\n", "wait <- rnorm(N_visits * N_cafes, mu, sigma)\n", "d <- data.frame(cafe = cafe_id, afternoon = afternoon, wait = wait)\n", "\n", "m_cafe_separate_variation <- ulam(\n", " alist(\n", " wait ~ normal(mu, sigma),\n", " mu <- a_cafe[cafe] + b_cafe[cafe] * afternoon,\n", " a_cafe[cafe] ~ normal(a, sigma_a),\n", " b_cafe[cafe] ~ normal(b, sigma_b),\n", " a ~ normal(5, 2),\n", " b ~ normal(-1, 0.5),\n", " sigma ~ exponential(1),\n", " sigma_a ~ exponential(1),\n", " sigma_b ~ exponential(1)\n", " ),\n", " data = d, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "\n", "m14.1 <- ulam(\n", " alist(\n", " wait ~ normal(mu, sigma),\n", " mu <- a_cafe[cafe] + b_cafe[cafe] * afternoon,\n", " c(a_cafe, b_cafe)[cafe] ~ multi_normal(c(a, b), Rho, sigma_cafe),\n", " a ~ normal(5, 2),\n", " b ~ normal(-1, 0.5),\n", " sigma_cafe ~ exponential(1),\n", " sigma ~ exponential(1),\n", " Rho ~ lkj_corr(2)\n", " ),\n", " data = d, chains = 4, cores = 4, log_lik = TRUE\n", ")" ] }, { "cell_type": "markdown", "id": "5499fb22", "metadata": {}, "source": [ "**Answer.** A compare plot with its associated raw data:" ] }, { "cell_type": "code", "execution_count": 5, "id": "3eecb722", "metadata": {}, "outputs": [ { "data": { "image/png": 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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_9_0.png" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "Raw data (preceding plot):" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " WAIC SE dWAIC dSE pWAIC weight \n", "m14.1 303.9898 17.71746 0.000000 NA 32.61315 0.731242\n", "m_cafe_separate_variation 305.9916 18.16013 2.001866 2.29854 32.59902 0.268758" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "iplot(function() {\n", " plot(compare(m14.1, m_cafe_separate_variation))\n", "}, ar=4.5)\n", "display_markdown(\"Raw data (preceding plot):\")\n", "display(compare(m14.1, m_cafe_separate_variation), mimetypes=\"text/plain\")" ] }, { "cell_type": "markdown", "id": "c23dbaea", "metadata": {}, "source": [ "The new model fits the training data worse (as expected, having fewer parameters). It doesn't make\n", "up for this in the penalty term, though, because it also does less parameter sharing.\n", "\n", "**14M3.** Re-estimate the varying slopes model for the UCBadmit data, now using a non-centered\n", "parameterization. Compare the efficiency of the forms of the model, using n_eff. Which is better?\n", "Which chain sampled faster?\n", "\n", "**ERROR.** There is no varying slopes model for UCBadmit data. This is the first chapter on\n", "varying slopes, and no model in this chapter is based on that dataset.\n", "\n", "It's likely the non-centered parameterization does better, if we had what model the author is\n", "referring to.\n", "\n", "**14M4.** Use WAIC to compare the Gaussian process model of Oceanic tools to the models fit to the\n", "same data in Chapter 11. Pay special attention to the effective numbers of parameters, as estimated\n", "by WAIC.\n", "\n", "**Answer.** Let's reproduce results from the two chapters:" ] }, { "cell_type": "code", "execution_count": 6, "id": "85e41f56", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "SAMPLING FOR MODEL 'ea958e18e4c604fc5bca60c02cb71b9a' NOW (CHAIN 1).\n", "Chain 1: \n", "Chain 1: Gradient evaluation took 8e-06 seconds\n", "Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 0.08 seconds.\n", "Chain 1: Adjust your expectations accordingly!\n", "Chain 1: \n", "Chain 1: \n", "Chain 1: Iteration: 1 / 1000 [ 0%] (Warmup)\n", "Chain 1: Iteration: 100 / 1000 [ 10%] (Warmup)\n", "Chain 1: Iteration: 200 / 1000 [ 20%] (Warmup)\n", "Chain 1: Iteration: 300 / 1000 [ 30%] (Warmup)\n", "Chain 1: Iteration: 400 / 1000 [ 40%] (Warmup)\n", "Chain 1: Iteration: 500 / 1000 [ 50%] (Warmup)\n", "Chain 1: Iteration: 501 / 1000 [ 50%] (Sampling)\n", 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leapfrog steps per transition would take 0.07 seconds.\n", "Chain 4: Adjust your expectations accordingly!\n", "Chain 4: \n", "Chain 4: \n", "Chain 4: Iteration: 1 / 1000 [ 0%] (Warmup)\n", "Chain 4: Iteration: 100 / 1000 [ 10%] (Warmup)\n", "Chain 4: Iteration: 200 / 1000 [ 20%] (Warmup)\n", "Chain 4: Iteration: 300 / 1000 [ 30%] (Warmup)\n", "Chain 4: Iteration: 400 / 1000 [ 40%] (Warmup)\n", "Chain 4: Iteration: 500 / 1000 [ 50%] (Warmup)\n", "Chain 4: Iteration: 501 / 1000 [ 50%] (Sampling)\n", "Chain 4: Iteration: 600 / 1000 [ 60%] (Sampling)\n", "Chain 4: Iteration: 700 / 1000 [ 70%] (Sampling)\n", "Chain 4: Iteration: 800 / 1000 [ 80%] (Sampling)\n", "Chain 4: Iteration: 900 / 1000 [ 90%] (Sampling)\n", "Chain 4: Iteration: 1000 / 1000 [100%] (Sampling)\n", "Chain 4: \n", "Chain 4: Elapsed Time: 0.251119 seconds (Warm-up)\n", "Chain 4: 0.193643 seconds (Sampling)\n", "Chain 4: 0.444762 seconds (Total)\n", "Chain 4: \n" ] }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a[1] 0.8800983 0.65054147 -0.1834540 1.9201282 565.6799 1.002317\n", "a[2] 0.9746582 0.86439910 -0.4510622 2.3074925 757.6732 1.003718\n", "b[1] 0.2605599 0.03195418 0.2106948 0.3090734 1138.3743 1.001765\n", "b[2] 0.2831560 0.10590607 0.1137215 0.4526956 622.2586 1.003477\n", "g 1.1062560 0.70797752 0.3024785 2.3540911 629.3185 1.000265" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "k[1] -0.17161009 0.30414571 -0.66143815 3.048374e-01 926.5023 1.003528\n", "k[2] -0.02551078 0.29169884 -0.47878031 4.402735e-01 753.3845 1.002713\n", "k[3] -0.07561711 0.27855221 -0.52055453 3.612202e-01 739.4431 1.001865\n", "k[4] 0.35279917 0.25374071 -0.02367141 7.671806e-01 847.3504 1.001366\n", "k[5] 0.07363948 0.25145421 -0.31178870 4.764131e-01 870.9978 1.002235\n", "k[6] -0.39117077 0.26439183 -0.82002894 8.650118e-05 981.1092 1.001846\n", "k[7] 0.14151847 0.25239664 -0.25475289 5.382755e-01 968.6247 1.000769\n", "k[8] -0.21500487 0.25418783 -0.62187831 1.696835e-01 897.9545 1.002621\n", "k[9] 0.26435768 0.24242971 -0.09946002 6.444307e-01 989.3732 1.000838\n", "k[10] -0.16908003 0.35172372 -0.73773516 3.745784e-01 1123.8908 1.001359\n", "g 0.61245312 0.59785004 0.07536022 1.714195e+00 1780.2318 1.000548\n", "b 0.27736210 0.08869417 0.13684643 4.203858e-01 993.4723 1.002699\n", "a 1.41967173 1.04841388 0.24911481 3.314933e+00 2475.3185 1.000052\n", "etasq 0.19754352 0.19657566 0.03282469 5.615212e-01 1216.1342 1.000394\n", "rhosq 1.33530555 1.70140632 0.08355641 4.533764e+00 2029.9101 1.000207" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data(islandsDistMatrix)\n", "data(Kline2) # load the ordinary data, now with coordinates\n", "d <- Kline2\n", "dP <- scale(log(d$population))\n", "d$contact_id <- ifelse(d$contact == \"high\", 2, 1)\n", "\n", "dat <- list(\n", " T = d$total_tools,\n", " P = d$P,\n", " cid = d$contact_id\n", ")\n", "\n", "# intercept only\n", "m11.9 <- ulam(\n", " alist(\n", " T ~ dpois(lambda),\n", " log(lambda) <- a,\n", " a ~ dnorm(3, 0.5)\n", " ),\n", " data = dat, chains = 4, log_lik = TRUE\n", ")\n", "\n", "# interaction model\n", "m11.10 <- ulam(\n", " alist(\n", " T ~ dpois(lambda),\n", " log(lambda) <- a[cid] + b[cid] * P,\n", " a[cid] ~ dnorm(3, 0.5),\n", " b[cid] ~ dnorm(0, 0.2)\n", " ),\n", " data = dat, chains = 4, log_lik = TRUE\n", ")\n", "\n", "dat2 <- list(T = d$total_tools, P = d$population, cid = d$contact_id)\n", "m11.11 <- ulam(\n", " alist(\n", " T ~ dpois(lambda),\n", " lambda <- exp(a[cid]) * P^b[cid] / g,\n", " a[cid] ~ dnorm(1, 1),\n", " b[cid] ~ dexp(1),\n", " g ~ dexp(1)\n", " ),\n", " data = dat2, chains = 4, log_lik = TRUE\n", ")\n", "flush.console()\n", "display(precis(m11.11, depth=2), mimetypes=\"text/plain\")\n", "flush.console()\n", "\n", "d$society <- 1:10 # index observations\n", "dat_list <- list(\n", " T = d$total_tools,\n", " P = d$population,\n", " society = d$society,\n", " Dmat = islandsDistMatrix\n", ")\n", "m14.8 <- ulam(\n", " alist(\n", " T ~ dpois(lambda),\n", " lambda <- (a * P^b / g) * exp(k[society]),\n", " vector[10]:k ~ multi_normal(0, SIGMA),\n", " matrix[10, 10]:SIGMA <- cov_GPL2(Dmat, etasq, rhosq, 0.01),\n", " c(a, b, g) ~ dexp(1),\n", " etasq ~ dexp(2),\n", " rhosq ~ dexp(0.5)\n", " ),\n", " data = dat_list, chains = 4, cores = 4, iter = 2000, log_lik = TRUE\n", ")\n", "flush.console()\n", "display(precis(m14.8, depth=2), mimetypes=\"text/plain\")\n", "flush.console()" ] }, { "cell_type": "markdown", "id": "7ed8336a", "metadata": {}, "source": [ "A compare plot with its associated raw data:" ] }, { "cell_type": "code", "execution_count": 7, "id": "fff8b29e", "metadata": {}, "outputs": [ { "data": { "image/png": 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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_13_0.png" } }, "output_type": "display_data" }, { "data": { "text/markdown": [ "Raw data (preceding plot):" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " WAIC SE dWAIC dSE pWAIC weight \n", "m14.8 67.37541 2.22661 0.00000 NA 4.011871 9.980596e-01\n", "m11.11 80.20808 11.40787 12.83267 11.55343 4.972381 1.631467e-03\n", "m11.10 83.53601 12.13926 16.16060 12.13169 6.100473 3.089778e-04\n", "m11.9 141.15520 31.71029 73.77979 32.71638 7.945491 9.507763e-17" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "iplot(function() {\n", " plot(compare(m11.9, m11.10, m11.11, m14.8))\n", "}, ar=4.5)\n", "display_markdown(\"Raw data (preceding plot):\")\n", "display(compare(m11.9, m11.10, m11.11, m14.8), mimetypes=\"text/plain\")" ] }, { "cell_type": "markdown", "id": "9d94da0f", "metadata": {}, "source": [ "The new model does better overall relative to m11.1 because it presumably has a more accurate\n", "method of estimating the contact between islands. See the first section of **14.5.1** for how the\n", "new model improves upon the old low/high contact indicator.\n", "\n", "The new model also has the lowest penalty term (effective number of parameters). Notice in the\n", "precis output above it has 10 intercept terms, and 5 other terms. This is much more than the 5\n", "parameters in m11.1, also above. It achieves this relative to m11.1 because of the significant\n", "regularization provided by parameter sharing.\n", "\n", "**14M5.** Modify the phylogenetic distance example to use group size as the outcome and brain size\n", "as a predictor. Assuming brain size influences group size, what is your estimate of the effect? How\n", "does phylogeny influence the estimate?\n", "\n", "**Answer.** First, let's reproduce the results from the chapter:" ] }, { "cell_type": "code", "execution_count": 8, "id": "f38be537", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a -0.0001731167 0.017310086 -0.02790983 0.02609835 1939.636 0.9986765\n", "bG 0.1230980344 0.023572481 0.08502910 0.16036884 1088.188 1.0011412\n", "bM 0.8930430495 0.023047869 0.85791614 0.93003799 1069.554 1.0030455\n", "sigma_sq 0.0473859234 0.005699073 0.03923401 0.05715970 1300.850 1.0026744" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ "Warning message in Initialize.corPhyl(phy, dummy.df):\n", "“No covariate specified, species will be taken as ordered in the data frame. To avoid this message, specify a covariate containing the species names with the 'form' argument.”\n" ] }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a -0.18873820 0.16496198 -0.44557098 0.07618946 2216.384 1.0027970\n", "bG -0.01217738 0.01971775 -0.04277674 0.01980523 2350.256 0.9990575\n", "bM 0.70105765 0.03861462 0.63972330 0.76345226 1776.208 1.0010190\n", "sigma_sq 0.16148768 0.01875378 0.13339710 0.19432609 2409.753 1.0005959" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a -0.06587284 0.076292599 -0.18646383 0.05812055 2012.089 0.9999619\n", "bG 0.04981556 0.023797105 0.01034797 0.08758256 2213.185 1.0003827\n", "bM 0.83321792 0.030898044 0.78324467 0.88101712 2727.300 0.9988425\n", "etasq 0.03494790 0.006854313 0.02494174 0.04695430 1937.816 0.9993151\n", "rhosq 2.79131896 0.250754096 2.39426624 3.20118552 2170.700 0.9996398" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data(Primates301)\n", "data(Primates301_nex)\n", "\n", "d <- Primates301\n", "d$name <- as.character(d$name)\n", "dstan <- d[complete.cases(d$group_size, d$body, d$brain), ]\n", "spp_obs <- dstan$name\n", "\n", "dat_list <- list(\n", " N_spp = nrow(dstan),\n", " M = standardize(log(dstan$body)),\n", " B = standardize(log(dstan$brain)),\n", " G = standardize(log(dstan$group_size)),\n", " Imat = diag(nrow(dstan))\n", ")\n", "m14.9 <- ulam(\n", " alist(\n", " B ~ multi_normal(mu, SIGMA),\n", " mu <- a + bM * M + bG * G,\n", " matrix[N_spp, N_spp]:SIGMA <- Imat * sigma_sq,\n", " a ~ normal(0, 1),\n", " c(bM, bG) ~ normal(0, 0.5),\n", " sigma_sq ~ exponential(1)\n", " ),\n", " data = dat_list, chains = 4, cores = 4\n", ")\n", "display(precis(m14.9, depth=2), mimetypes=\"text/plain\")\n", "\n", "library(ape)\n", "tree_trimmed <- keep.tip(Primates301_nex, spp_obs)\n", "Rbm <- corBrownian(phy = tree_trimmed)\n", "V <- vcv(Rbm)\n", "\n", "# put species in right order\n", "dat_list$V <- V[spp_obs, spp_obs]\n", "# convert to correlation matrix\n", "dat_list$R <- dat_list$V / max(V)\n", "\n", "m14.10 <- ulam(\n", " alist(\n", " B ~ multi_normal(mu, SIGMA),\n", " mu <- a + bM * M + bG * G,\n", " matrix[N_spp, N_spp]:SIGMA <- R * sigma_sq,\n", " a ~ normal(0, 1),\n", " c(bM, bG) ~ normal(0, 0.5),\n", " sigma_sq ~ exponential(1)\n", " ),\n", " data = dat_list, chains = 4, cores = 4\n", ")\n", "display(precis(m14.10, depth=2), mimetypes=\"text/plain\")\n", "\n", "Dmat <- cophenetic(tree_trimmed)\n", "# add scaled and reordered distance matrix\n", "dat_list$Dmat <- Dmat[spp_obs, spp_obs] / max(Dmat)\n", "\n", "m14.11 <- ulam(\n", " alist(\n", " B ~ multi_normal(mu, SIGMA),\n", " mu <- a + bM * M + bG * G,\n", " matrix[N_spp, N_spp]:SIGMA <- cov_GPL1(Dmat, etasq, rhosq, 0.01),\n", " a ~ normal(0, 1),\n", " c(bM, bG) ~ normal(0, 0.5),\n", " etasq ~ half_normal(1, 0.25),\n", " rhosq ~ half_normal(3, 0.25)\n", " ),\n", " data = dat_list, chains = 4, cores = 4\n", ")\n", "display(precis(m14.11, depth=2), mimetypes=\"text/plain\")" ] }, { "cell_type": "markdown", "id": "1ffc06cc", "metadata": {}, "source": [ "Reversing the prediction problem:" ] }, { "cell_type": "code", "execution_count": 9, "id": "0a2c768a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a -0.001417642 0.05685219 -0.09147605 0.08793679 1327.7488 0.9992159\n", "bB 1.004936856 0.20442226 0.68104136 1.34138179 854.5307 1.0005631\n", "bM -0.337334331 0.20456292 -0.67326748 -0.01079579 828.9535 1.0016998\n", "sigma_sq 0.519471576 0.06055068 0.42832399 0.61695123 1429.3501 1.0018326" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a -0.47774105 0.5678362 -1.359264822 0.4414133 1496.797 1.000575\n", "bB -0.07150671 0.2583164 -0.476816067 0.3477977 1091.952 1.000832\n", "bM 0.34676958 0.2160707 0.001476129 0.6938241 1003.165 1.001472\n", "sigma_sq 2.68982107 0.3120843 2.234004692 3.2161848 1479.938 1.003012" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% n_eff Rhat4 \n", "a -0.5021950 0.3442075 -1.0440793 0.03602275 1511.5889 1.000513\n", "bB 0.1850170 0.2626387 -0.2375381 0.60738516 968.2030 1.000422\n", "bM 0.1880509 0.2259942 -0.1873261 0.54406083 989.1999 1.000826\n", "etasq 0.9309690 0.1206105 0.7537561 1.14232420 1593.3978 1.000191\n", "rhosq 3.0219251 0.2384142 2.6610231 3.40037960 1592.1098 1.003639" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dat_list <- list(\n", " N_spp = nrow(dstan),\n", " M = standardize(log(dstan$body)),\n", " B = standardize(log(dstan$brain)),\n", " G = standardize(log(dstan$group_size)),\n", " Imat = diag(nrow(dstan))\n", ")\n", "m14.9_reversed <- ulam(\n", " alist(\n", " G ~ multi_normal(mu, SIGMA),\n", " mu <- a + bM * M + bB * B,\n", " matrix[N_spp, N_spp]:SIGMA <- Imat * sigma_sq,\n", " a ~ normal(0, 1),\n", " c(bM, bB) ~ normal(0, 0.5),\n", " sigma_sq ~ exponential(1)\n", " ),\n", " data = dat_list, chains = 4, cores = 4\n", ")\n", "display(precis(m14.9_reversed, depth=2), mimetypes=\"text/plain\")\n", "\n", "# put species in right order\n", "dat_list$V <- V[spp_obs, spp_obs]\n", "# convert to correlation matrix\n", "dat_list$R <- dat_list$V / max(V)\n", "\n", "m14.10_reversed <- ulam(\n", " alist(\n", " G ~ multi_normal(mu, SIGMA),\n", " mu <- a + bM * M + bB * B,\n", " matrix[N_spp, N_spp]:SIGMA <- R * sigma_sq,\n", " a ~ normal(0, 1),\n", " c(bM, bB) ~ normal(0, 0.5),\n", " sigma_sq ~ exponential(1)\n", " ),\n", " data = dat_list, chains = 4, cores = 4\n", ")\n", "display(precis(m14.10_reversed, depth=2), mimetypes=\"text/plain\")\n", "\n", "# add scaled and reordered distance matrix\n", "dat_list$Dmat <- Dmat[spp_obs, spp_obs] / max(Dmat)\n", "\n", "m14.11_reversed <- ulam(\n", " alist(\n", " G ~ multi_normal(mu, SIGMA),\n", " mu <- a + bM * M + bB * B,\n", " matrix[N_spp, N_spp]:SIGMA <- cov_GPL1(Dmat, etasq, rhosq, 0.01),\n", " a ~ normal(0, 1),\n", " c(bM, bB) ~ normal(0, 0.5),\n", " etasq ~ half_normal(1, 0.25),\n", " rhosq ~ half_normal(3, 0.25)\n", " ),\n", " data = dat_list, chains = 4, cores = 4\n", ")\n", "display(precis(m14.11_reversed, depth=2), mimetypes=\"text/plain\")" ] }, { "cell_type": "markdown", "id": "ec9958fa", "metadata": {}, "source": [ "Interestingly, the ordinary regression model makes an even more extreme prediction about how group\n", "size influences brain size than the reverse. Still, the uncertainties are large.\n", "\n", "The addition of phylogeny once again removes the presumed effect. The uncertainties are so large in\n", "these latter two models that they really say almost nothing about an association.\n", "\n", "**14H1.** Let’s revisit the Bangladesh fertility data, data(bangladesh), from the practice\n", "problems for Chapter 13. Fit a model with both varying intercepts by district_id and varying\n", "slopes of urban by district_id. You are still predicting use.contraception. Inspect the\n", "correlation between the intercepts and slopes. Can you interpret this correlation, in terms of what\n", "it tells you about the pattern of contraceptive use in the sample? It might help to plot the mean\n", "(or median) varying effect estimates for both the intercepts and slopes, by district. Then you can\n", "visualize the correlation and maybe more easily think through what it means to have a particular\n", "correlation. Plotting predicted proportion of women using contraception, with urban women on one\n", "axis and rural on the other, might also help.\n", "\n", "**Answer.** To review, the help for the bangladesh data.frame:" ] }, { "cell_type": "code", "execution_count": 10, "id": "cb4c22ab", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "  bangladesh {rethinking} R Documentation \n", "\n", " ## Bangladesh contraceptive use data \n", "\n", " ### Description \n", "\n", " Contraceptive use data from 1934 Bangladeshi women.\n", " \n", "\n", "\n", " ### Usage \n", "\n", " \n", "data(bangladesh)\n", " \n", "\n", "\n", " ### Format \n", "\n", "\n", " \n", " 1. woman : ID number for each woman in sample\n", " \n", " 2. \n", " 3. district : Number for each district\n", " \n", " 4. \n", " 5. use.contraception : 0/1 indicator of contraceptive use\n", " \n", " 6. \n", " 7. living.children : Number of living children\n", " \n", " 8. \n", " 9. age.centered : Centered age\n", " \n", " 10. \n", " 11. urban : 0/1 indicator of urban context\n", " \n", " \n", "\n", "\n", "\n", " ### References \n", "\n", " Bangladesh Fertility Survey, 1989 \n", "\n", " [Package rethinking version 2.13 ] " ], "text/latex": [ "\\inputencoding{utf8}\n", "\\HeaderA{bangladesh}{Bangladesh contraceptive use data}{bangladesh}\n", "%\n", "\\begin{Description}\\relax\n", "Contraceptive use data from 1934 Bangladeshi women.\n", "\\end{Description}\n", "%\n", "\\begin{Usage}\n", "\\begin{verbatim}\n", "data(bangladesh)\n", "\\end{verbatim}\n", "\\end{Usage}\n", "%\n", "\\begin{Format}\n", "\\begin{enumerate}\n", "\n", "\\item{} woman : ID number for each woman in sample\n", "\\item{} district : Number for each district\n", "\\item{} use.contraception : 0/1 indicator of contraceptive use\n", "\\item{} living.children : Number of living children\n", "\\item{} age.centered : Centered age\n", "\\item{} urban : 0/1 indicator of urban context\n", "\n", "\\end{enumerate}\n", "\n", "\\end{Format}\n", "%\n", "\\begin{References}\\relax\n", "Bangladesh Fertility Survey, 1989\n", "\\end{References}" ], "text/plain": [ "bangladesh package:rethinking R Documentation\n", "\n", "_\bB_\ba_\bn_\bg_\bl_\ba_\bd_\be_\bs_\bh _\bc_\bo_\bn_\bt_\br_\ba_\bc_\be_\bp_\bt_\bi_\bv_\be _\bu_\bs_\be _\bd_\ba_\bt_\ba\n", "\n", "_\bD_\be_\bs_\bc_\br_\bi_\bp_\bt_\bi_\bo_\bn:\n", "\n", " Contraceptive use data from 1934 Bangladeshi women.\n", "\n", "_\bU_\bs_\ba_\bg_\be:\n", "\n", " data(bangladesh)\n", " \n", "_\bF_\bo_\br_\bm_\ba_\bt:\n", "\n", " 1. woman : ID number for each woman in sample\n", "\n", " 2. district : Number for each district\n", "\n", " 3. use.contraception : 0/1 indicator of contraceptive use\n", "\n", " 4. living.children : Number of living children\n", "\n", " 5. age.centered : Centered age\n", "\n", " 6. urban : 0/1 indicator of urban context\n", "\n", "_\bR_\be_\bf_\be_\br_\be_\bn_\bc_\be_\bs:\n", "\n", " Bangladesh Fertility Survey, 1989\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data(bangladesh)\n", "display(help(bangladesh))\n", "\n", "bc_df <- bangladesh\n", "bc_df$district_id <- as.integer(as.factor(bc_df$district))" ] }, { "cell_type": "markdown", "id": "3f62659d", "metadata": {}, "source": [ "A head and summary of the bangladesh data.frame, with the new variable suggested by the author\n", "in question 13H1:" ] }, { "cell_type": "code", "execution_count": 11, "id": "98b78105", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", " A data.frame: 6 × 7 womandistrictuse.contraceptionliving.childrenage.centeredurbandistrict_id <int><int><int><int><dbl><int><int> 11104 18.440011 22101 -5.559911 33103 1.440011 44104 8.440011 55101-13.559011 66101-11.560011 \n" ], "text/latex": [ "A data.frame: 6 × 7\n", "\\begin{tabular}{r|lllllll}\n", " & woman & district & use.contraception & living.children & age.centered & urban & district\\_id\\\\\n", " & & & & & & & \\\\\n", "\\hline\n", "\t1 & 1 & 1 & 0 & 4 & 18.4400 & 1 & 1\\\\\n", "\t2 & 2 & 1 & 0 & 1 & -5.5599 & 1 & 1\\\\\n", "\t3 & 3 & 1 & 0 & 3 & 1.4400 & 1 & 1\\\\\n", "\t4 & 4 & 1 & 0 & 4 & 8.4400 & 1 & 1\\\\\n", "\t5 & 5 & 1 & 0 & 1 & -13.5590 & 1 & 1\\\\\n", "\t6 & 6 & 1 & 0 & 1 & -11.5600 & 1 & 1\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 6 × 7\n", "\n", "| | woman <int> | district <int> | use.contraception <int> | living.children <int> | age.centered <dbl> | urban <int> | district_id <int> |\n", "|---|---|---|---|---|---|---|---|\n", "| 1 | 1 | 1 | 0 | 4 | 18.4400 | 1 | 1 |\n", "| 2 | 2 | 1 | 0 | 1 | -5.5599 | 1 | 1 |\n", "| 3 | 3 | 1 | 0 | 3 | 1.4400 | 1 | 1 |\n", "| 4 | 4 | 1 | 0 | 4 | 8.4400 | 1 | 1 |\n", "| 5 | 5 | 1 | 0 | 1 | -13.5590 | 1 | 1 |\n", "| 6 | 6 | 1 | 0 | 1 | -11.5600 | 1 | 1 |\n", "\n" ], "text/plain": [ " woman district use.contraception living.children age.centered urban\n", "1 1 1 0 4 18.4400 1 \n", "2 2 1 0 1 -5.5599 1 \n", "3 3 1 0 3 1.4400 1 \n", "4 4 1 0 4 8.4400 1 \n", "5 5 1 0 1 -13.5590 1 \n", "6 6 1 0 1 -11.5600 1 \n", " district_id\n", "1 1 \n", "2 1 \n", "3 1 \n", "4 1 \n", "5 1 \n", "6 1 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " woman district use.contraception living.children\n", " Min. : 1.0 Min. : 1.00 Min. :0.0000 Min. :1.000 \n", " 1st Qu.: 484.2 1st Qu.:14.00 1st Qu.:0.0000 1st Qu.:1.000 \n", " Median : 967.5 Median :29.00 Median :0.0000 Median :3.000 \n", " Mean : 967.5 Mean :29.35 Mean :0.3925 Mean :2.652 \n", " 3rd Qu.:1450.8 3rd Qu.:45.00 3rd Qu.:1.0000 3rd Qu.:4.000 \n", " Max. :1934.0 Max. :61.00 Max. :1.0000 Max. :4.000 \n", " age.centered urban district_id \n", " Min. :-13.560000 Min. :0.0000 Min. : 1.00 \n", " 1st Qu.: -7.559900 1st Qu.:0.0000 1st Qu.:14.00 \n", " Median : -1.559900 Median :0.0000 Median :29.00 \n", " Mean : 0.002198 Mean :0.2906 Mean :29.25 \n", " 3rd Qu.: 6.440000 3rd Qu.:1.0000 3rd Qu.:45.00 \n", " Max. : 19.440000 Max. :1.0000 Max. :60.00 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(head(bc_df))\n", "display(summary(bc_df))" ] }, { "cell_type": "markdown", "id": "d2ae5599", "metadata": {}, "source": [ "Sampling from the varying intercepts model:" ] }, { "cell_type": "code", "execution_count": 12, "id": "12fe644d", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#bulk-ess”\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#tail-ess”\n" ] }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% \n", "b_district[1] 1.0670860 0.3782827 0.4859153953 1.6648881 \n", "b_district[2] 0.5967072 0.6645532 -0.4330004363 1.6322922 \n", "b_district[3] 0.8848223 0.8057362 -0.3856858371 2.2487559 \n", "b_district[4] 1.5814457 0.6347096 0.6560098348 2.6659842 \n", "b_district[5] 0.6113797 0.5942621 -0.3188659912 1.5578244 \n", "b_district[6] 1.2810511 0.5527699 0.4667433362 2.2225933 \n", "b_district[7] 0.7745289 0.6689434 -0.2951438126 1.8745062 \n", "b_district[8] 0.9065896 0.6014774 0.0002929298 1.8780210 \n", "b_district[9] 0.9863604 0.6166353 0.0425672943 1.9837517 \n", "b_district[10] 1.1954027 0.7592615 0.0276866328 2.4434961 \n", "b_district[11] 1.5756218 0.8116946 0.4444062308 2.9595681 \n", "b_district[12] 0.4322015 0.5665931 -0.4999139671 1.3354042 \n", "b_district[13] 0.2684581 0.5874672 -0.6925710533 1.2110490 \n", "b_district[14] 1.2110843 0.4319248 0.5424204957 1.9125391 \n", "b_district[15] 0.4493872 0.5861374 -0.4998182743 1.3609454 \n", "b_district[16] 0.5669155 0.6321994 -0.4256460915 1.5818233 \n", "b_district[17] 0.7624304 0.6745130 -0.3045817881 1.8874580 \n", "b_district[18] 0.8479431 0.4911165 0.0857845437 1.6496457 \n", "b_district[19] 0.9680160 0.6254921 0.0303852148 2.0321759 \n", "b_district[20] 0.5403988 0.6952316 -0.5619983408 1.6191578 \n", "b_district[21] -0.3209662 0.6859289 -1.4403290374 0.7075015 \n", "b_district[22] 0.9749350 0.6772639 -0.0584712608 2.1394007 \n", "b_district[23] 0.8028469 0.6992094 -0.2879172061 1.9132030 \n", "b_district[24] 1.2329838 0.7372550 0.1094543016 2.4527721 \n", "b_district[25] 0.1879679 0.4248847 -0.5040083386 0.8567129 \n", "b_district[26] 0.5668825 0.7233731 -0.5650370280 1.7357724 \n", "b_district[27] 1.1476359 0.6180868 0.2054302074 2.1557858 \n", "b_district[28] 0.7334328 0.6005227 -0.2234647593 1.6730947 \n", "b_district[29] 1.1410977 0.5579254 0.2976138234 2.0465502 \n", "b_district[30] 1.0106844 0.5002790 0.2772004374 1.8338426 \n", "⋮ ⋮ ⋮ ⋮ ⋮ \n", "a_district[39] -0.24878952 3.446544e-01 -0.8001652 0.30037495\n", "a_district[40] -0.53367224 4.056508e-01 -1.1726077 0.11575554\n", "a_district[41] -0.08785561 3.647116e-01 -0.6613238 0.48234779\n", "a_district[42] -0.05918072 5.055008e-01 -0.8316718 0.77688896\n", "a_district[43] -0.22036656 3.018605e-01 -0.6984655 0.24937437\n", "a_district[44] -1.05308364 3.537547e-01 -1.6495761 -0.50317067\n", "a_district[45] -0.91672877 3.193301e-01 -1.4355843 -0.41527769\n", "a_district[46] -0.09571376 2.228935e-01 -0.4450982 0.26582506\n", "a_district[47] -0.51778990 4.465133e-01 -1.2312732 0.21138532\n", "a_district[48] -0.22569530 3.243286e-01 -0.7331933 0.30002079\n", "a_district[49] -1.04824482 5.298423e-01 -1.9150630 -0.27016833\n", "a_district[50] -0.67188490 4.024037e-01 -1.3064462 -0.02679504\n", "a_district[51] -0.64603156 3.617746e-01 -1.2429197 -0.06510586\n", "a_district[52] -0.11721394 2.784987e-01 -0.5601760 0.32948042\n", "a_district[53] -0.70873036 5.682276e-01 -1.5958060 0.20074087\n", "a_district[54] -0.75671498 6.164120e-01 -1.7673297 0.23632531\n", "a_district[55] -0.10909625 3.251141e-01 -0.6168951 0.42430576\n", "a_district[56] -1.17789470 3.753756e-01 -1.7906242 -0.60817455\n", "a_district[57] -0.17468722 3.562620e-01 -0.7293605 0.39079686\n", "a_district[58] -1.17842367 4.955465e-01 -2.0236499 -0.42535810\n", "a_district[59] -1.15104807 3.848318e-01 -1.7852631 -0.56316102\n", "a_district[60] -1.17134926 3.309090e-01 -1.7302584 -0.68202729\n", "a -0.68697115 9.680213e-02 -0.8431896 -0.53422309\n", "b 0.64241389 1.533845e-01 0.3911194 0.89095418\n", "sigma_intercepts_slopes[1] 0.57516450 9.473592e-02 0.4356859 0.73634803\n", "sigma_intercepts_slopes[2] 0.76059552 1.976562e-01 0.4589757 1.08665688\n", "Rho[1,1] 1.00000000 0.000000e+00 1.0000000 1.00000000\n", "Rho[1,2] -0.65363331 1.671887e-01 -0.8613258 -0.34409840\n", "Rho[2,1] -0.65363331 1.671887e-01 -0.8613258 -0.34409840\n", "Rho[2,2] 1.00000000 6.272117e-17 1.0000000 1.00000000\n", " n_eff Rhat4 \n", "b_district[1] 1831.8290 1.0012389\n", "b_district[2] 2883.8034 0.9994656\n", "b_district[3] 2096.1790 0.9996167\n", "b_district[4] 742.8528 1.0039141\n", "b_district[5] 2158.3104 0.9983583\n", "b_district[6] 1916.0610 0.9987753\n", "b_district[7] 2448.2445 0.9993163\n", "b_district[8] 1779.2636 1.0011896\n", "b_district[9] 2200.3913 0.9991816\n", "b_district[10] 1714.6876 1.0003149\n", "b_district[11] 1021.2957 1.0014837\n", "b_district[12] 3222.1393 1.0006625\n", "b_district[13] 2065.5455 0.9998587\n", "b_district[14] 1408.5814 1.0017142\n", "b_district[15] 2473.9455 0.9988708\n", "b_district[16] 1695.4276 1.0019869\n", "b_district[17] 2690.2394 0.9987431\n", "b_district[18] 2195.1137 0.9999696\n", "b_district[19] 1638.6104 1.0022221\n", "b_district[20] 2519.0662 0.9989753\n", "b_district[21] 921.4559 1.0005069\n", "b_district[22] 2082.2386 1.0003840\n", "b_district[23] 2111.5169 1.0019826\n", "b_district[24] 1380.2483 1.0008525\n", "b_district[25] 1650.5842 1.0014639\n", "b_district[26] 2522.6748 1.0012108\n", "b_district[27] 1632.7972 1.0001834\n", "b_district[28] 3012.6085 0.9992483\n", "b_district[29] 1858.0194 0.9996650\n", "b_district[30] 1301.2451 1.0008541\n", "⋮ ⋮ ⋮ \n", "a_district[39] 2481.3080 1.0003322\n", "a_district[40] 1950.4880 1.0025755\n", "a_district[41] 2499.2493 0.9988345\n", "a_district[42] 1573.8640 1.0001231\n", "a_district[43] 2089.1375 0.9988561\n", "a_district[44] 2712.3422 0.9987354\n", "a_district[45] 2734.5355 1.0001725\n", "a_district[46] 2624.5404 0.9995971\n", "a_district[47] 2193.7884 0.9993473\n", "a_district[48] 1930.0847 0.9995102\n", "a_district[49] 2290.7133 0.9989410\n", "a_district[50] 2363.4590 0.9991670\n", "a_district[51] 2288.5704 0.9997117\n", "a_district[52] 1992.2301 0.9997977\n", "a_district[53] 2065.2941 0.9997024\n", "a_district[54] 1532.5275 0.9999255\n", "a_district[55] 2246.6413 0.9994746\n", "a_district[56] 2510.3441 0.9997795\n", "a_district[57] 1348.0636 0.9997778\n", "a_district[58] 2411.5027 0.9985544\n", "a_district[59] 2692.0315 0.9991757\n", "a_district[60] 2315.3140 0.9989207\n", "a 1699.3030 0.9988051\n", "b 1236.1160 1.0003488\n", "sigma_intercepts_slopes[1] 604.1727 1.0028934\n", "sigma_intercepts_slopes[2] 263.0453 1.0080110\n", "Rho[1,1] NaN NaN\n", "Rho[1,2] 379.9839 1.0097282\n", "Rho[2,1] 379.9839 1.0097282\n", "Rho[2,2] 1937.6490 0.9979980" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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29jXaf1cdxsfu+AOLSFrDgMDp5XPQLF0MkcnVlwNNhY7uy4eFetESfMF0Ac2kJZ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\nM71S/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I2V+QRH7m84DJKRhMiJolsA4ErzS5V2tvOZHNN7vvW412OP1q1rs92cMyvFqzyC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\nCr0VMScXVqFW2r31UW1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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_23_4.png" } }, "output_type": "display_data" } ], "source": [ "# If you want to reproduce results from the previous chapter:\n", "#\n", "# bc_dat <- list(\n", "# UseContraception = bc_df$use.contraception,\n", "# DistrictId = bc_df$district_id\n", "# )\n", "# m_bc_ve <- ulam(\n", "# alist(\n", "# UseContraception ~ dbinom(1, p),\n", "# logit(p) <- a[DistrictId],\n", "# a[DistrictId] ~ dnorm(a_bar, sigma),\n", "# a_bar ~ dnorm(0, 1.5),\n", "# sigma ~ dexp(1)\n", "# ),\n", "# data = bc_dat, chains = 4, cores = 4, log_lik = TRUE\n", "# )\n", "\n", "bc_dat <- list(\n", " UseContraception = bc_df$use.contraception,\n", " DistrictId = bc_df$district_id,\n", " Urban = bc_df$urban\n", ")\n", "m_bc_vis <- ulam(\n", " alist(\n", " UseContraception ~ dbinom(1, p),\n", " logit(p) <- a_district[DistrictId] + b_district[DistrictId] * Urban,\n", " c(a_district, b_district)[DistrictId] ~ multi_normal(c(a, b), Rho, sigma_intercepts_slopes),\n", " a ~ normal(0, 2),\n", " b ~ normal(0, 0.5),\n", " sigma_intercepts_slopes ~ exponential(1),\n", " Rho ~ lkj_corr(2)\n", " ),\n", " data = bc_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "display(precis(m_bc_vis, depth=3), mimetypes=\"text/plain\")\n", "iplot(function() {\n", " plot(precis(m_bc_vis, depth=3), main=\"m_bc_vis\")\n", "}, ar=0.4)\n", "\n", "post <- extract.samples(m_bc_vis) # posterior\n", "R <- rlkjcorr(1e4, K = 2, eta = 2) # prior\n", "\n", "iplot(function() {\n", " dens(post$Rho[, 1, 2], xlim = c(-1, 1))\n", " dens(R[, 1, 2], add = TRUE, lty = 2)\n", "})" ] }, { "cell_type": "markdown", "id": "eb470ee1", "metadata": {}, "source": [ "Not surprisingly, the b slope parameter and most of the b_district are positive. Normally,\n", "living in an urban area makes one more open to ideas like contraception. The a parameters are\n", "likely negative because in general many women do not use contraception.\n", "\n", "The correlation is negative, because a is typically negative and b is typically positive. It is\n", "also relatively large in absolute magnitude, implying that a more negative intercept is associated\n", "with a more positive slope (and vice versa). We can see this in a plot of mean intercepts vs. mean\n", "slopes:" ] }, { "cell_type": "code", "execution_count": 13, "id": "4695e718", "metadata": {}, "outputs": [ { "data": { "image/png": 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/3oS4HrsSzLsmy/3y+VSoVCIZvN6nQ6s9l86x4/mDS5XL68vFwsFlOpFNe1ghG6\ncAEkEsnS0lIqldra2vJ6vUajke+KAE4AQQWOS6VSYUVFODqdTjwen5ub0+l0fNcCQiSVSu12\nu81mq9frxWJxd3dXLpebTCaz2Yz1Nx6ZzWatVptIJDY3N9G1AheDYRiPx6NQKLjp9U6nk++K\nAI4Lb1dwXCqVqlQq8V0FEBENh8NoNKrVaufm5viuBQSNYRhugaXX65XLZSywCAGWVoAXVqtV\noVDEYrFut+v1ekUibP6HKYAvUzgulUo1GAzQkCcE8XiciLxeL891wPSQyWR2u311ddXr9Q6H\nw52dnXA4XCwWMTWSL+hagYvHsmwgEGg2m9vb25iNBlMBQQWOS6FQiMVi7P7iXaVSqVarPp8P\nx03CSTEMYzAYlpaWVldXWZZNp9Nra2uZTAa3LLzgllZwIBhcJKVSGQqFGIYJh8N4QwfhQ1CB\nE+D66fmu4lIbjUb7+/s2m02pVPJdC0wxuVzOHRHmcrkODw/X1tZisRgOBeIFllbggkkkkuXl\nZa1Wu7W1dXh4yHc5ALeCHhU4AfTT8+7g4GA0Gtntdr4LgVnAMAw3ILJWq+Xz+UgkolKprFar\n0WhkGIbv6i4RdK3ABWMYZmFhIZfLxWIxu93ucDj4rgjg5hBU4ARUKlWlUuG7isur3+8fHBy4\nXC5s+oLzxTXcdzqdQqGQTCaz2azZbLZYLPhKu0g4EAwumN1ul8vl8Xi83+97PB48ngABQlCB\nE1CpVP1+v9/vYwg6L9LptFwux+0LTIhCoXC73Q6Ho1QqHRwc5HI5g8Fgs9kUCgXfpV0WWFqB\nC2YwGGQyWTQa3d7exuxgECD0qMAJKBQKkUiE3V+8aLVapVLJ7XbzXQjMOLFYbLVaV1dX5+fn\n2+32xsbG7u5urVbju65LBF0rcJHUanUoFBqNRpFIpNPp8F0OwIsgqMAJMAyDfnq+pFIpg8Gg\n0Wj4LgQuBe58sGAwGAgEGIbZ3d2NRCLou70w3NKKw+HgDgTDsWwwUVKpNBAIKJXKSCRSr9f5\nLgfgBQgqcDJqtbrRaPBdxaXTbrcbjQbGO8LF02g0fr9/ZWVFpVLFYrHNzc1yuTwej/mu61Kw\nWq1XrlwZDoebm5tIiTBRIpHI7/dbrdadnZ1CocB3OQDPQ1CBk2FZtl6vY0jcBSsWixqNBkcS\nA1/kcrnH47l27Zper08mk+vr6/l8Hq8DF0AulwcCAZvNFovF4vH4cDjkuyKYZc5gm/4AACAA\nSURBVA6Hw+PxpFKpRCKB5xEgBAgqcDJarZZhGCwNX6TRaFQqldBDD7yTSCQOh+Pq1asWiyWb\nzXLDInHrPGkMw9jt9kAg0Gg0Njc3saYNE2U2m5eXlw8PD3d3d/HdDbxDUIGTEYlEGo0GnbUX\niTsS2mAw8F0IABGRWCy22+1Xr16dm5srFotra2vpdHowGPBd14zjOp5Zlt3e3k6n03jaDZOj\n0WiCwWCv19va2ur1enyXA5caggqcGMuy1WqV7youkWKxaDKZRCJ8t4KAiEQiq9V69epVt9vN\nzbZPpVLo+Z4osVg8Pz/v8/mKxeLW1la32+W7IphZcrk8GAzKZLJwOIxFPOARbn3gxHQ6Xbfb\nxXvkxeh0Oo1Gw2Qy8V0IwE1ws+1XVlZ8Pl+j0VhbW4vH4zjhdKL0ev2VK1ckEkk4HMbhxTA5\nYrHY7/cbjcbt7e1SqcR3OXBJYbIPnJhCoZDL5bVazWKx8F3L7CsWi2q1WqVS8V0IwK3odDqd\nTnd4eJjL5TY3N41G49zcnFwu57uu2SSVShcXF7m5kNVqdX5+HnP6YBIYhnG73XK5PJFI9Ho9\nnDwJFw8rKnAa2P11YarVqtFo5LsKgGPR6/XBYHBxcbHT6WxsbCSTSWxwnxyz2cw1EmxubuIF\nGSbHarX6fL5cLoejwODiIajAaXCHFOMFa9L6/X6n09FqtXwXAnACLMtycaXZbK6vrycSCfSu\nTIhSqQwEAiaTKRqNJhIJHBgNE6LX67mjwKLRKL7M4CIhqMBpaLXa8XiMQ4onrV6vSyQSjE+B\nacSybCgUWlxcbLVaa2triCsTIhKJnE7n4uJitVqNRCKtVovvimA2qdXqYDDY6XS2t7dxyh9c\nGAQVOA2xWIxDii9Ao9HQaDR8VwFwelxcWVhYaDQa6+vr6XQakxkmgWXZlZUVpVK5tbWVy+X4\nLgdmEzd+dDweRyIRHKgDFwPtd3BKLMuWy2W+q5hx9Xodcx7PS6lE8TiVy8Sy5HSSy8V3QZeJ\nwWAwGAyVSiWdThcKBYvFYrfbxWIx33XNFLFYvLCwUCqVkslkvV73er1SqZTvomDWSKXSQCAQ\njUa3trYWFxdx0AtMGoIKnBLLsul0utfryWQyvmuZTYPBAA0q52I0ou9+l37+czIYyGSiWIy+\n/31aWKD3v5/wJnuRDAaDXq8vl8vZbLZYLFosFpvNhrhyvkwmk1ar3dvb29jY8Hg8OIoDzp1I\nJFpcXIzH41tbW36/n2VZviuCWYagAqekUqmkUmmtVsMj/wmp1+tisRgNKmf3/e9TOEwf/zh5\nvc9fKZfpoYfoi1+kT3yCGIbP2i4bbu6K0WgsFAq5XK5YLNrtdrPZjHmm50gmky0vLx8cHMTj\n8Vqt5vF48L8XzhfDMAsLC5lMZnd31+v1Ig/D5ODFC04PhxRPFNegwuA++mwOD+npp+n9738h\npRCR0Ugf/SgVCrS5yVthlxnDMFardXV11WazZbPZjY0N7CM9XwzD2O325eXlRqOxubnZbDb5\nrghmkMPhcLlc8Xg8k8nwXQvMLKyowOnpdDruQEw8rpuEbrerUCj4rmLqRaOk09HCAhFRv9/v\n9XpHPxoMgyefHCuVo9FoNB6PR79CRCKRiGEYblfS0Y8Mw0ilUolEcvSjVCrFF/+piUQim81m\nNpsPDg4SicTBwYHL5cJex3Ok0WhCoVAqldra2nK5XFarle+KYNZYrVaZTLa3tzccDt1uN9/l\nwAxCUIHT0+l04/G4Wq0aDAa+a5lB3W4Xe39PbTQatdvtdrsdjbba7fbaWq/f73OTf8RisVQq\nlclkKpX48FAsFou5AepcIOEmfA+HQy66HAWY8Xg8GAza7fZgMOj3+0dHV4lEIi6xyOVyuVyu\nUCi4n6D14pjEYrHD4bBYLJlMZmdnR6vVulwu7Hg8L2Kx2Ov1arVarsMeM+zh3HEjVnZ3d3u9\n3sLCAp7dwPnCCxacnkgkMhgM5XIZQWUS+v2+MA8qGI1oPCYB3oe32+16vd5sNtvtdqfTGY/H\ncrlcKlUOh6zDIZPJZFw+OXofXV8nrZbm50/zd43H436/z4WWwWDQ6/W63W61Ws3n89yEAYlE\nwoUWhUKhVCq5nq5z/I+dMVKpdH5+3mazZTKZzc1Nk8nkdDrxf+y8mEwmtVodi8XC4fDCwgIO\nPYfzpVaruayyvb29uLiIMAznCF9McCZGo3F3d3cwGOCF6XwNBoPhcCiooDIe089/Tr/4BeXz\nNBqR0UgrK/T61xO/N5Oj0ahWq9VqtWq12uv1FAqFWq02m81cNhCLxXNz9Nxz1OmQyfSiT+x0\naHubfuM3Tvn3Mgwjk8lu+g80HA673W6n0+l2u91u9/DwMJvNjkYjqVTKVcXhlnHgegqFwufz\n1ev1/f399fV1q9WKU4zPi0KhCAaD6XR6e3vbbrc7HA6+K4KZolQqg8Hgzs4Ol1UE9eYFUw03\nl3AmLMtKJJJKpWKxWPiuZab0ej0iEs5r/XhMDz1E0Si97nX0679OEglls/STn9D2Nv3Wb9HF\nt9KMRqNyuVypVOr1OsMwWq3WbrezLPvSu3+TiW67jb7yFfrIR8hme/5is0lf+QqxLF29ev61\nicViLoocXRmPx51Op91ut1qtZrNZKBSGwyF3pJtardZoNBqNBlH/iFarDYVC3NCVYrE4Nzdn\nsVhwqsTZiUQit9utUqmSyWSr1fJ6vfiqg3PEjVjZ3d2NRCJLS0vYwAnnAi9ScFZGo7FUKiGo\nnK9erycSiYRzG/GLX1A0Sp/4BB39O3s8dO0aPfggPfIIvetdF1dJu90uFArlcplhGKPRaLPZ\nNBrNrXdFv+td9K//Sn/3d+R0kslEtRrt75PZTB/9KF3MbmqGYZRKpVKpPDrEs9vtcrml0WgU\nCoXRaKRUKjW/IpyAyiNu6EqhUMhkMoVCweFwYIvpucA2MJgcsVi8vLy8t7fHjYPEVxecnVBu\ng2B6mUymg4ODTqeDI6rO0ctN0ozHaWeHikVSKmlujq5do4t5aPXzn9Ndd9ENaVSppDe/mb76\nVfqN36BJR6rxeFwulwuFQrPZ1Gg0Ho/HYDAc8ym7REIf/CDt71M8TqUSud302tfS0hKfE1S4\nhnu9Xk9E4/GYSyyNRiOVSg0GA5lMptFotFqtVqu9zDvEuFOMjUbjwcHB3t4edywYbn3ODtvA\nYHIYhvH5fPv7+9vb2wsLC3i+AGeEoAJnxT0qLpfLeLc7Ry/tpB+N6Gtfo40NWlggq5Xabfrp\nT+nHP6YPfvBFE0ImYTymfJ7e/Oab/JbHQ/0+lcs00YNPy+VyOp0eDocmk8nr9Z4uErtc5HKd\ne2nngGEYtVqtVqttNhsRtdttLrRks9lEIiGXy1mW1el0Wq32ch6nI5FInE6n2WxOp9NbW1tG\no9HlcqHP/oy4bWBqtTqRSGAbGJw7l8vFHVvc6/VsR5tuAU4OL0xwDrg50wgq54jrYbj+yiOP\n0N4ePfDAC40WoxE9/DD90z/R7/8+TXr4xHh88/WHSS9K1Gq1dDrd6XQuT181l/y5vZTdbrde\nr9dqtb29vdFopFardTody7LXN8BcEnK53OfzcYtO6+vrc3NzNpsNjStnZDQaVSoVtoHBJFit\nVolEEo/He70eRqzAqSGowDkwmUyZTIabpM53LbOp06GnnqIPfICufzIlEtHb3kbJJP30p/SW\nt0zwb2cYMpspnSaf78bf2t8nsZgmsbbfbrf39/fr9brJZFpcXLycT9C5HWJms3k0GjUajWq1\nWiqV0um0TCbjlllYlr1UyyzcBMNSqbS/v18sFt1ut06n47uo6YZtYDA5RqNRKpVGo9HhcDg/\nP48nC3AKCCpwDqRSqUajKZfLCCoTsr9PDEPLyzdeZxi6coXC4YkX8KpX0f/7f3TtGl1/W9jv\n06OP0srK+Z9QnM/n0+m0Vqu9cuWKYHufxmNqNkmtvoheF5FIxLIsNwC01+tVq1VumYWIdDqd\nwWDQ6XSXJ7GYTCa9Xp/L5Z59NkqkXVlxm80C/SKZCtgGBpOj1WoDgcDOzs7Ozo7f778Mq+Jw\nvvBiBOfDZDKlUim3241HJufl+v+TnQ4pFDc/okqlok5n4sXceSft7NDf/z3dey+53SSVUiZD\njz9OgwG99a3n+RcNBoN4PF6v151Op3WijS9nsL9Pjz1GqRT1+ySVktNJb3oTeTyv8FmdDhWL\nJJGQxXKmcZkymcxisVgsltFoVK/XK5VKIpEYj8darVav1+v1+pm/yxyP6Ze/FP/oR87DQ1O1\nmvrSlzadTssHPuAIhXAPdHrYBgYTolQquWOLt7a2lpaWLufyOJzajL+fwYUxGAzJZLJarXIH\nGcH50mqp1aJul156BFS5TCw78QLEYvroR+mJJ+iJJ6haJSJSKmllhe6//zyPHavVavF4XCqV\nhkIhwS6khMP00EO0skIf+hDp9VSt0toa/eM/0nvf+7JTWYpF+s53aG+PGIbGYxKL6VWvol//\n9Zv8a56ISCTS6XQ6nW48HtdqNW7wSDKZ1Gq13Nm+s5pYHn2UfvYzetObKBRSsOxSPF595JHk\nf//vlQ99yHnvvaZX/nx4GdgGBhMil8sDgUA0GuWOLRbsyzsI0Gy+jcHFE4lEer2+VCohqEyC\ny0UKBf3853T33S+63u3Sc8/R6173ooujETHM+e9HEovp3nvp3nup06HhkNTqc/7z8/n8/v6+\n1Wp1Op2CXZdrt+kb36D77qN7733+itlMfj/ZbPStb9HCAr30MXShQA8+SB4PfeITZLfTYECJ\nBP3gB/S5z9Fv//b5HOvMMMxRYqnX64eHh5lMJplMsixrNBr1ev0s7Qo7OKAnnqD/8B/I73/+\nis+n++QnV77zndxDDyVZtrC05Faf+1fnpcFtA9NoNIlEotlser1ePP+GcyGRSJaWlmKx2NbW\nlt/vx5IdHBOCCpwbo9EYjUYHg8GsPsflkVhMb30rfeMbJJHQq1/9/MahUom+9jVSKOjOO4mI\nhkP66U9pbY2KRWIYsljo9tvpzjvPP7FM4llYLpfLZDJer/doJKIwhcMkkdDrX3/j9de+lp56\nijY26K67bvyt736XPB76zd98/h9CIqFAgNxu+p//k372M7rnnvMsj2EYrpXF4/HU6/VSqZRM\nJpPJpF6vN5lM2kmfDXch1tbI7X4hpXBEItE73+lYXzfncpnhMGIymVwuF16ITs1gMCiVylgs\nFolEsA0MzotIJPL7/alUamdnx+fz4SQMOA68jsO5YVlWIpFUKhVMqZ+E226j0Yi+/3165BEy\nmajdpmqVfD760IdIIqF+nz7/eSqX6bWvJYeDxmNKpeixxygapQ9/+ILmr59aJpPJ5XI+n0/4\ny3GFAjmdN/n/yTDkclGhcOP1RoP29uh3fufGuKhS0WteQ2tr5xxUrsfNi+T6WEql0s7OjkQi\nMRgMJpNpqk83LpfJbr/JdYYhh0OmUHiXl03cEcYOh8NisQh2dU7guG1gqVRqe3vb6XRiFAac\nC4ZhPB6PTCaLRqNutxt3C/CKEFTg3DAMYzQaS6USXnom5FWvoitXaH+fCoXnJ9MfdZv/+MdU\nrdIDD7wwUMXno6tX6bOfpZ/97Ma9YYKSSqWKxeLi4iJ7Aa02F65SISK66T2ezUaPPz7xAo76\nWAaDQblcLpVK+XxepVKZTCaj0TiNaw4SCQ0GN/+tfp/EYtJqtaFQKJ/PZzKZUqk0Pz8/1cGM\nRyKRaH5+XqvVHm0Dm6U9hMAju90ulUoTiUSv13M6nXyXA4KGFx04TxaLpdlsNhoNvguZemKx\neHCz2zG5nPx+eu1r6bbbXkgp4zH94hd03303jn00Gunuu+mZZyZf7mlls9lSqbS0tDQtKcVq\npXSaRqMbr4/HtL9PLz2ljAsCN72xHgzOdPbXSUkkEqvVGgqFVlZWWJY9ODh47rnn9vb26vX6\nxRVxHubmaG+PxuMbr7fblM3S3BwREcMwNpttZWVFLpdHIpH9/f3RS//N4HiMRmMoFGq32+Fw\nuHMBJwzC5WAymfx+fz6fj8fj45d+PwP8CoIKnCe5XK7T6fL5PN+FTD2pVNrv94/5wfU6tVrk\n9d7kt+bnqVx+2SfQ/KrVatlsdn5+fop2wIdCNBzSj3984/Unn6R2m1ZWbrxusZBUStHoTf6o\naJR4OVRJoVA4nc6rV68uLi6Ox+OdnZ319fVcLnfTYCxAt91G7TY9+uiLsspoRN/8JhmNL5pJ\nKpVKfT6f3++vVCrr6+sVbnkLTo7bBqZQKCKRyOHhId/lwIzQ6XTLy8vVajUajeJRAryc6Vv3\nB4Gz2Ww7Ozvdbld+xrNXLzeZTNbr9Y75wdwd20234nM7NQT4uKrX6+3t7dntdsMkxtpPjEJB\n7343ffnLVCjQ1atkNFKlQhsbtLFB73vfTU5Ck0jo136NfvADcrledIr07i49+yz95m9eZO03\n4tru+/1+qVQqFAqZTEav15vNZoGvbqlU9P7305e/TKkUhUKk01GpRM89R60WffzjN2kf0ul0\nKysruVxub2+vVCpx++P5KHy6icViv9+fy+VisZjNZsN2HTgXarU6GAzu7Oxsb28vLi5O42ZU\nmDR8TcA502q1CoWiUCi4XC6+a5liUql0OByORqPjbArXakkup3SaXtqLnk6TTnf+k+PPaDQa\nRaNRlUo1x+3UmSqBAH3yk/TYY/T1r1OnQ3I5uVz0n/4Tvdyd25vfTPk8/e3f0u23k91O/T4l\nErSxQW94Ay0tXWzpNyOVSu12u91ur9VqxWJxd3dXLpebTCaz2SzYm4bFRfrd36Unn6Rnn6Vq\nlQwGWlyku+9+2SOzRSKRw+EwGAyJRGJjY2Nubs5ms6HJ/hTsdrtSqdzb22u32wsLC5gyDmfH\njVjhxkEuLy/jOGy4gUDfh2CqWa3W/f19h8OBzstT416s+/3+cRamRCK6do1+9CNaXHzRDMFm\nkx5/nF71qsmVeUqpVGo4HC4tLU3pzeLcHH30o0RE7fYrz7uUSuk//kf6xS8oHKaNDZJKyWaj\nj32MFhYuoNIT4BZYer1esVgsFArZbNZoNFqtVuU5TvQ8P0YjvetdJ/sUpVIZDAaLxeL+/n6l\nUvF4PBi3cgo6nS4UCkWj0XA47Pf7hfnlAdNFKpUuLy8fja7Hdgy4HoIKnD+TycSdt4Pjv07t\nREGFiN70JvqHf6C//3t6wxvI5aLRiFIp+vGPSaud4AG4p9NqtYrF4vLysmAf2B/fMW/SGIZe\n/Wp69asnXM15kMlkDodjbm6uWq0eHBxsbm6yLGu1Wmdm4oHZbNbpdOl0emtry2KxOBwOLAuc\nlFwuDwaD8Xg8Eol4vd7p2r0JwiQWi5eWlrjR9UtLSwjAcGTqbxRAgBiGMZvNBwcHCCqn1mgw\n+byEZft+/7GmoCiV9IlP0KOP0ve+R+02EZFaTbffTvfdJ7h9X6lUymAwzMbwwVnFMIxer9fr\n9a1Wq1AoxGIxqVRqtVrNZvMMLJNKpVLu9jqZTHJLK8If4CM0IpHI5/NxnT+tVsvhcEzp6igI\nh0gkWlxc3Nvb297eXlpawqniwEFQgYmwWq25XK5arc7Mg9gLE4vR975HhQKVSjK5vGcy0ete\nR294wyvHFbmc3v52evvbqV4nkehl9+vzq1wuN5vNlZcejwWCpFKp5ufnHQ5HqVTK5XKZTMZk\nMtlsthnoR+ea7LPZbCwWY1kWTfanYLfbVSoVl1UWFhZmYI0U+MUwzMLCQiKR4Hrrp+hASJgc\nvKzAREgkEqPRmM/nEVROZGuLvvxluuMO+vCHqVyWEvWbTfrBD6hUove977h/iGDXKkajUTqd\nttlsp9iCXCrRk09SJkO1GhmN5PXS3Xcfd+cVnBHXcG+1Wsvlcj6fLxQKBoPBZrOd6JHnYEDp\nNBWLz88qFcJ2IZFI5HQ6uSb7zc1Nl8tlNpv5LmrKsCx7fcsKnoLDGTEM4/V6U6nUzs6O3+8X\n+CGEcAEQVGBSrFZrOBxut9vYbHpMwyF961t0zz10//1ERK2WvNvt3H47zc3R//7fdO0aLS7y\nXeLZFIvF8Xhst9tP+onb2/SVr5DLRbfdRiz7/HG0//Zv9Fu/RSbTJCqFmxCJRGaz2Ww212q1\nfD4fDodZlrXb7cfZxbe2Rt/7HnU6ZDRSs0ntNgUC9O//PQnhtlalUgWDwXw+n0qlKpXK/Pw8\nllZORCaTBQKBZDK5tbXl8XhM+J6EM3O73QzD7O7u+nw+7My85BBUYFJUKpVGo8nn8/Pz83zX\nMh3icep06PWvf/6XKpWKG1Fns1EwSOvrsxBUzGbzSXuXGw36l3+hu++mN73phYt3301f/jI9\n9BA98MDNB8jA5HDng7Xb7YODg52dHaVSeet5OOvr9LWv0f330113Ebc5KJejr3+dPvc5+uQn\nSQit7Nwke71ej6WV0xGJRF6vV6PRJBKJRqPh8XjQsgJn5HK5JBJJLBabn59H+r3Mpr4tEoTM\narWWSqVpmXjNu0qFDAY6epirUqn6/T43n95mo3KZz9rOrtFotNvtU9z/PfssabX0xje+6KJY\nTP/u31E+T4nEeRUIJ6NUKr1e78rKikajicfjm5ubpVJp/JLZoqMRfe979MY30j330FELg91O\nH/841ev0i19cdNm3IJfLl5eXXS4Xt+3k+BNXgWM2m7lB49vb29wLF8BZ2O12t9udSCSKxSLf\ntQBvEFRggvR6vUwmKxQKfBcyHSQSuv7NXaFQiESiVqtFRP0+TXufarFYZFn2FJtqMhny+W6y\nbKLRkM1G2ez5lAenI5fL3W736uqqXq9PpVIbGxv5fH40Gh19QCpF7Ta95jU3fqJSSdeuUSRy\nodUeh9lsvnLlyng83tzcxO3RSWk0mmAwOB6PI5FIs9nkuxyYehaLZX5+PplMHhwc8F0L8ANB\nBSaIYRiLxVIoFF76nBVeyuGgw0MqlZ7/JcMwSqWSCyrRKDkcfNZ2RsPhsFKpnO646uHwZUOa\nREJYrhMCqVTqcDhWV1eNRmMmk7k+rtRqpFbTTU9PMJmoVrvoUo8DSytnwbWssCy7tbWFpAdn\nZzKZvF5vOp1Op9N81wI8QFCByTKbzdxNKt+FTAGrlRYW6BvfoKP7IpVK1Wq1nnyS8nm64w5e\nizubSqUiFotPdwSc0Ug3fZQ2GlGhQEbjWWuD8yKRSBwOx9WrVy0WSy6XW19fz+fzUumo26Wb\nPqlotW4eYATi+qWVfD7PdznThGGY+fl5t9udTCaTySQeVMEZGY1Gv9+fz+eRVS4hBBWYLLFY\nzA1/5LuQ6fDe91KzSf/jf9Bjj9HaGm1sqP75n1uPPkrveQ9N9cEn9XqdZdnT9deurtLe3k16\nUX7yEyKa+gMGZo9YLLbb7VevXnU4HLlcrlZbOzzMbW+Pbviw8ZgiEfJ4eKnxuI6WVrhJ9t1u\nl++KponFYlleXj48PNzZ2UGnIpyRTqdbXFwsFArJZJLvWuBCIajAxNlstna7fXh4yHchU0Cr\npQceoFe/mlIpevhhikZVSmXvE58YTPuAxHq9furRXU4nveY19MUv0lNPUbVKoxEVi/Tww/TD\nH9I73ynoR/KXGcMwZrN5dXXV47F5PAef/ezG9nbx6Mn6eEyPPELFIt11F79lHgu3tMIwzObm\nZi6X47ucacK1rAwGg0gk0ul0+C4HpptWq11aWqpUKnt7e1imuzymvD8XpoFMJjObzdlsFqeh\nH4dMRm94A73hDURE47Hyl79k1OoW0RQPvep0Ov1+/zjTNl7O295GBgP96Ef03e8+f8Vkoo98\nhJaWzqdCmBCRSGS32x94wPrgg/n/9t/2vd7s8vKcWGxKJJhGgz78YZqWebDc0gq386Rer2PW\nyvHJZLJgMLi3txeJRPx+/1leBwDUavXS0tLOzk40GvX5fCIRnrbPPgQVuAh2u319ff3w8BBZ\n5USO+umnejpvo9GQyWSnmEZ/hGHorrvoNa+hw0Oq18lopNMuzwAPpFLRAw/Yt7bMzzyTX1vb\nV6kOAgH7G99oUqv5ruyErFarTqfjzmJ2u92Y7XBMIpHI7/dnMpmdnR2Xy2W1WvmuCKaYSqUK\nBAI7OzuxWAxZ5TJAUIGLIJPJLBZLJpNBUDkpjUZTq9VOMc2dR+MxpVKUz9NgQFYrjUan3/d1\nPYYhg4Fefq4gCBfDUDAoCQYd/b4ll8sVi8lkMu90Oqcugcvl8kAgkM/nE4lEtVr1eDySaT84\n/KI4HA6ZTJZMJtvtNiZCwlkoFIpAILC9vb2zs7O4uHjSIcIwXfAKCxfEbrcXi8VKpXKLCdbw\nUjqdrlAojEajaXlulM3SV79K5TKZTCQWU6FA9Xr7/e83LyzwXRkIgFQqdbvddrs9m83u7u5q\ntVqn06lSqfiu62SsVqtWq93b2wuHw16vF9uZjslsNisUimg02uv1fD4f7i/h1LhTsHd2dra3\nt5eWlvC8YIZNx60PzACpVGo2mzOZDHrgTkSj0TAMU6/X+S7kWA4P6f/8H5qbo//8n+n3fo8+\n9Sn64z+mhYXeN74h29/nuzgQDKlU6vF4rly5IhaLw+FwLBabugO1lEplMBg0Go07OzupVAov\na8fEtdf3er2trS0MqIGzkEqly8vLRLS1tdW/flgyzBYEFbg4c3NzvV4PM1VORCQSabXaarXK\ndyHH8n//L9ls9N730tEjcrF4eOedw6tXZQ8/zGtlIDwKhcLn8wWDwX6/v7GxkUqlhsMh30Wd\ngEgkcjqdi4uLlUolHA63222+K5oOcrk8GAzKZLJwONxoNPguB6aYRCJZXl6WSCQ4PXyGIajA\nxZFIJFynykSfPhYK9PDD9LnP0T/+I33rW7S3N7m/6oKwLFsT5gTvl9jepjvuoOs3n3MPTV/7\nWlkqRbiRg5dSq9WBQGBhYaFara6vr+dyuelanWBZ9sqVK3K5PBKJ4PDiYxKLxX6/32g0bm9v\nl0olvsuBKSYWi5eWluRy+fb2NrLKTEJQgQtlt9sHg0G5XJ7Qn//00/S3W2WGcgAAIABJREFU\nf0uZDDkc5PdTs0mf/zx985s3H4w9LViW7Xa7wn8JHgyo3b5xMGWv1xOJRBaLhIjw8BRejsFg\nWFlZcTqdBwcH6+vr03XzKpFI/H6/x+PJZrM7OzvYhXIcDMO43W6Px5NIJFKpFN/lwBQTiUSL\ni4sqlWprawsLm7MH7UdwoY4WVYxG47mf+hKP03e/S+95D1279sLFdJo+/3kymejuu8/3b7s4\nCoVCLpdXq1WBH+spkZBEQq3Wiy72ej2ZTMZdVCh4qQumAzcj0mAwZLPZRCJRLBbdbvcU9dmb\nTCaNRsMdXjw/P48TDo/DbDbLZLJYLNbv971e77QcGQJCwzCMz+dLJBJbW1tLS0vqqTv7HF4e\nXhTgotnt9uFwOIknpk88QdeuvSilEJHTSfffT08+OfWLKlOx+8vrpY2NF10ZDocSiWR9nYxG\nwtlI8IrEYrHL5VpdXZVKpeFwOJFIDAYDvos6Lm4upMViicVi8Xh8NBrxXdEUYFk2EAi0Wi20\n18NZMAwzPz9vMBi2t7en5fgZOA4EFbhoYrHYarVms9lz34meSlEweJPrgQA1mzSx7WYXgWXZ\ner0u/Puee++l9XV66qkXrozH41iMHn+c7ruPv7Jg2shkMp/Pt7y83Gw2p6txhWEYh8MRCAQa\njcbm5iaaxY+DO0JNLBZHIpHWDWuyAMfGZRWLxbK7uzsVj/bgOKZv69d4PN7b24vFYlxi1ul0\nS0tLbreb77rgBGw2W6FQKBaLFovlvP7M8Zh6Pbrp9HNux5HgWzxuhWXZ8XjcaDQEPiDP7aZ3\nv5u++U165hlyu0kkokiEEgn64AdvXOkCeEVarTYUCpVKpXQ6XSqV3G63wL/+j6jV6lAolEwm\nt7e3nU6nzWbjuyKhk0gkS0tL3NadhYUFbJyDU3O5XBKJZHd3d2FhAXPbZsA0BZVKpfKZz3zm\nc5/7XD6fv+G3PB7PJz/5yU9/+tNKpZKX2uBEjhZVTCbTeW1KZhjS6ahUopcOFuR2mel05/L3\n8EMkErEsWy6XhX+jdu0aeb20tkYHBzQc0sIC3X03ve51fJcF04lrXNHr9dyASJZl3W63/KYP\nJARGLBYvLCywLJtMJuv1utfrxUy6W2MYxuv1qlSqWCxmt9sdDgffFcG0stvtRLS3tzcajUwm\nE9/lwJlMzetmNpu955579vb2lpaW3vGOd8zPz3PNUrVaLRqN/uhHP/rzP//zf/mXf3nssccQ\noKeCzWbL5/PFYvEcG8RDIXrqKbr9drrhfuDJJ8njoWlvrjOZTPF43OPxCL/flGXpnnue/3k2\nS1iBhzOSSCRut9tkMqVSqc3NTavVOjc3J/xvBCIymUxqtToWi4XD4YWFBY1Gw3dFQme1WqVS\naTwe73a78/PzU/GvDAJkt9vFYnEikRgOhwI/hwZubWqCyv9n787jIyvLfIH/Tu37vu9rlu6m\nbaABWUSkBRFUNlEYsVXUoUGcudzZ7mc+lz9mdBzHGedyRRnbkQsom4JLg4Ag0LJDAw1td5ba\ntyRVSSWVSiqVVKpSVfeP0/aSrqSz1jkneb9/QaWq8nRSqXqf877P89x1110DAwO//OUvb7jh\nhlO/Wq/X9+7de8cdd/zTP/3T3Xff3f7wiOXi8XhmszmXyxkMhrX6KLroIvT24uGHceWVoM+U\nTU1h/36EQvjyl9fkOzBJrVZTFFUsFnU6HdOxEAQDZDJZZ2cnfRKsUCg4nU5OHBCSSCRdXV2D\ng4PhcJhsFCyFVqsVi8XRaDQSifj9frITRayM0Wjk8/nJZLLZbJLjl9xFcaVC0Wq1Xnnllffd\nd98i97nxxhvfeOONdDq9tt967969e/bsKZVK5GLY2mo0GocPHzabzfQu7ZqYmMC+fUgkIJFA\nIMDUFAwGfOYz2BhFTKlUqlqtBoNBpgNZhlwuVywWu1p2OSCIFanX69lsdmRkRK1WO51OkUjE\ndERLUigUUqmUUqkkx8CWolarRaPRRqMRDAa58ismWGh8fDyRSFitVqvVynQs7FWtVsVi8euv\nv34B+yY5cOa9cmxszO/3L36f7u7u3/zmN+2Jh1g9Ho9ns9kGBgb0er1QKFyT51SrsXs3xscx\nPIy5ORiNMJmw1vNaGKPT6ehxcmv142oDoVBI5t8Ra4tuYazX61OpVE9Pj9VqNZvNaz6Xac3p\ndDq6AIMcA1sKoVDY2dkZi8X6+/vpcX5MR0Rwklar5fF4sVgMAMlVuIgzpz9tNtuhQ4cWv8/7\n779PdtW5xWg0SiSSwcHBtX1arRZdXdi2DWbzxslSACiVSpFIVOBUo2WSqBDrhO5p63K5hoeH\n+/r6yuUy0xGhXEYqhdFRLNRInD4GptFowuHw0NBQe6PjHnriuFKpDIVCpNsssWJqtdrv92ez\n2Ww2y3QsxLJxZkflmmuu+cEPfnDOOed885vfPLXlS7lc/t73vrdv375/+Id/YCQ8YsWcTmco\nFDIajWSU7FJotdpCocCh47ZCobDZbM7NzZGzLsR60Ov1KpVqcHCwv7/fYDA4HA4+n9/+MFIp\nPPsshodBUWg2IRLh/PNx8cU4tf6Ox+M5nU65XJ5Kpaanp8kxsMVRFOX1eoeGhqLRqMfjIRV6\nxMrQuQrZV+EiztSoFIvFXbt2HTx4UKlUnnvuuU6nU6FQ0JMlUqnUgQMHpqenP/KRjzzzzDNr\nvp9OalTWWzwer1arpIxhKSqVSk9Pz5YtW7jSibter3/wwQfd3d3k5AaxriYmJtLpdLPZdDqd\nbe79GIvhkUdw5pk47zzo9ZiZQTSKP/wBbjdaNX85qlKpxOPxer1OjoEtxcjIyMDAAOlGQKxG\nsViMx+M2m20NK2M3BlKjsgY0Gs2bb775ox/96Gc/+9kf//jHer1+7EtCofDss8++5ZZbbrnl\nFkaupRGr5HA4enp6CoUCuVp2WhKJRCaTFQoFu93OdCxLwufzeTzemp/+Gh7Gm29iaAilEvR6\n+Hy44IKjkz2JzUmtVm/dujWXyyUSibGxMZfL1Z4K7EYDTz2F887D5ZcfvUUux4c+BJsNP/kJ\nQiF0drZ+IOkGtiwmk0kkEiUSiXq9TkY8Eyuj0Wh8Pl88HsefZ60Q7MeZRAWASCS6884777zz\nzkqlkslk6Mn0KpWqbR9IxDoRiURms3lgYECj0ZCu+ael1+uHh4e5kqhgHcpUjhzBb38Lrxfn\nnguFAqOj+OAD/OlP+NKXQKYobWZ0fw6tVptKpXp7e+12u5HuU76eMhmUSrj44vm3G43YsgWH\nDy+YqOCUY2Ber5dca1uERqMJBAKxWKxarXq9XvJhQayARqPxer2JRAIkV+EILiUqx0gkEm51\naCVOy2KxjI2N5XI5clnxtHQ63cDAwMTEhFqtZjqWJRGLxZVKZa2erVjEvn3Yteukafcf/jAe\newy/+hW++lX2tk+o1ZDPo1KB0QilkuloNi66yJ4+KTQ+Pu52u9d1kn2hALW69W6exYIjR07/\nDCd2A/P7/Vw51ckIpVLZ2dkZjUaj0ajf7yd5HbEC9NFQkqtwBbkgQbACj8ez2+3Dw8PVapXp\nWNhOIBDodLrh4WGmA1kqmUw2PT29Vs928CCMRnz4wyfdKBDg05/G0BDY2UipWsUzz+Df/g3/\n/d949FH8539i716sda874iQmk2nr1q0Aent7c7nc+n0jgQBzc62/VKthiQtp+hiYTCbr7+8f\nHx9fw/A2HjoRnZubC4VC5POCWBmtVks3aRgZGWE6FuI0OLmj0lIsFrv11lsBvPDCC0t/1Pj4\n+F133bX4uZS+vr7VBkcsgU6ny+fzAwMDPp+P6VjYzmw29/b2zszMcOLiq0wmy+fza/Vs2Sx8\nvhbbJmo19Hpks2DbmbhGAw8/jFIJn/scPB4IhRgbw2uv4YEHsHv3BhlFyk4ikaijo2N0dDST\nyUxMTHg8nvXYWrHZUCphZAQm0/wvxWJY+g4xj8fz+Xyjo6OJRGJyctLlcrF/MgxT6BEr0Wi0\nv78/GAxy4m2QYJtj+yoURbXhjCixYhsnUSmVSi+++OJyH9VsNkul0szMzCL3WcOLwcTinE5n\nX19fqVRSkpMxi5JKpUqlcmRkxO12Mx3L6clksnq9Pjs7uybLxHodAgEaDbzzDvr6MDICkQhm\nM3buhECAE7pssMX77yOfx223HT/uZTDgmmvA4+F3v8NttzEa3CZgMBhUKlUymezt7bVarWt+\n0kOvRyCAp57CzTfjxBf4gQMYGMBnPrPsaMVicTwen52d9Xq9HBrt2mZ8Pr+joyORSIRCoUAg\nQNqmESug1WobjUYqlQJAchXW4kx74tOqVCrRaBTAtm3b1vaZSXvidkomkzMzM11dXeRq4uLo\nNotnnHEGJ5YyH3zwgdvtXpOmsb/7HSYnMTuL0VGcfTYsFtRqSKfxwQcAcOONYFv92oMPwmbD\nZZfNv31iAnffjdtvx4mfj7Ozs5VKZXZ2tvZn9Xq92Ww2Gg36vZqiKB6PR1EUn88XCAQCgUD4\nZ2KxWCQSrfkfzsQEEgmMjUGhgM3G4S2g0dHRgYEBqVS65lsrU1N48EFUq9ixA0YjymVEo4jH\ncfXV2L59JU9YrVbj8XitVvP5fGTA1OIGBgZGRka8Xm+be1ITG8bY2FgqlXI6nZs5VyHtidtB\nIpGseYpCtJ/dbu/p6RkbGzMYDEzHwmoajUYkEo2OjnJidhVdprImK4kzzsADD0Clwp49x/co\nPvQhzM3hT39CyyPrlQpEohaj99pjfBw7drS4Xa2GWIxCoSkWl0qlUrlcnp6ertfrPB5PJBKJ\nRCKhUCiTyfh8Pp2WHHvgsdSlVqtVq9VyuTw3N1er1RqNBkVRIpFILBbTbaxlMplEIllx6tJs\n4sUX8eabUCphMGBqCs8/D6cT11/PyWYA67e1olDgL/8Sb7+NWAwHD0Iuh9WKv/xLrHguK31o\nLZPJhMNhp9NJ3gwX4XA46LbFc3Nzm3mhSayYXq8HQPZVWGvjJCoAxsbGxsfHA4EA04EQKycU\nCi0Wy+DgoFarJR1dFmc0GnO5nMViYf/u0xrW09vt4PEwM4P+fgSDUCoxOop338WRIwgG8e67\n2Lr16D0nJ/HSS4hGUS6Dz4fFgvPPP/7VthEIcGoRXLPZLBTGR0bGI5HJcrmpUCjkcrnRaJTJ\nZCu+2F+tVmdnZ+k9mUqlMj4+XqvVKIqSSqVyuVwulysUimU9+R//iPfew+c/j46Oo7cUi/jV\nr/Dww/j615daJs4qdAJA18JNTk56PJ61am0vFOKii3DRRWvyZADA4/HcbrdcLk+n0+VymZSs\nLMJkMvH5/FQqValUyIgVYgX0en2z2Uyn0yC5CvtsqETl3//93//t3/5twxxm27TMZvPo6Gg2\nm3U4HEzHwmoGgyGbzRYKBfqCEJspFIp8Pt9sNle/2BodRaOBSy7BH/+IZ545eqPFgi9+EZUK\n9u07frf774dOh8sug8WC6WnEYvjNb5DN4uMfX2UIy2O3IxrFzp1H/7darY6MjIyNjWUyTYrS\n7tzpNRqVa5KT0/swJ9Z31Wq1mZmZ6enpcrk8MDAwNzcnFAqVSqVCoVAqlZJFB2ROT+P113H9\n9cezFAAaDf7iL/DDH+LQIZx11upDZobRaDy2tbJWJxLXicFgkEgk8Xg8HA77fD5OnPNkhF6v\nF4lEsVisXq+73W6S1BHLRe9bptNpHo/H/o/UTWVDJSrExkBRlMPhiMfj9Ic00+GwF5/P1+v1\nIyMj7H9XVSqVzWZzampq9W0S6HL588/HRRdhYgJTU9DrQXf9iUaPNoptNPDQQ5ibw9AQnnwS\nOh3OOAMf+xj8fvz85wgG0c4eBOedh5/+FIcOYevWuWw2m8/npVKpWm17+WXdxRfz17WJP127\nolKp6P+tVCpTU1NTU1O5XC6dTovFYtWfnTo7Lx6HSISurvnPKZWiuxvRKIcTFQBisbizs3Nk\nZCSRSNCzVli7f6tQKLq7u2OxGD1lhZSsLIQesRKJRCKRCBmxQqwAnavQZ8DY/6m6eZBEhWAj\njUajUCgGBgbIQb7FmUymfD4/NTXF8k4PfD5fLpdPTk6uPlHRakFRyOXgcECjgUZz/EvZLPR6\n1Ot48EFMTOCCCxAMgsfD4CDefBPRKL74RXR14eDBtiYqNhuuvBKPPprXaAZdLqHT6cvnNYcO\nwWDAJz/ZvjAASCQSiURCfxjPzs5OTExMTk4mEolms6lQKLRarUajOXbNvlyGStV6eqZajY0x\ne8BkMikUikQi0dvb6/V6WftHRHfjTafToVDI4XCYTm2ETAAApFIpnauEw+FgMCgQkBUOsTzH\nchWKonQ6HdPhEACHEpWdx05OLGyQTFDbQOhWxRyav84IsVisVquHh4dZu8Y6Rq1WFwoF+6qn\nnMhk8Puxfz9uvvmkZXS5jAMH8OEP4623MDICmex4oy2XC2ecgZ/+FC+/DJcLhw6tMoTlmZub\n02pTu3ZN5nL2Usl48CBlNOLSS3HWWYzV9wMQi8Umk8lkMjUajampqYmJCXqbRaFQaDQarVYr\nlYrKZTSbLXKVqSnIZEwEvQ5kMll3d/fg4GAoFDKZTA6Hg52nhiiKOlayQldisDNOxonF4q6u\nrmg0GgqFgsHgWtUgEZuHwWBoNBrJZBIAyVXYgDOJyvvvvw9g8RO6cwvNByY4SCqVmkymVCq1\ndetWsom/CLPZHAqF2D/8UaVSDQ4OVqvV1S8dPvlJ3Hcffv5zfPSjx9sTv/ACNBqcdx7uvRed\nnYjHT3qIQoFLLsEf/rCW5c5LUalUIpEIn8//yEe62XmOkcfj0ae/nE5nuVweHx+na80B+ciI\nLhrVBYMnfUzUaujrw4UXMhXv2uPxeE6nU61WJ5PJqakpr9fLzt8U/lyyEovFZmdnfT4feWNs\nSSAQdHR00LlKR0fHekz5JDY2etOS5CoswdwFvWX6u7/7O7lcfuTIkcrC/vZv/5bpMIm1ZLPZ\neDwe2ShbnEKhUKlUQ0NDTAdyGjKZTCgUTk5Orv6pdDp8/esQCvHgg/jud/H97+O3v0VHB3bv\nRrOJ8XEEApiaQrF40qNcLkxPI5FoMUF8nUxPT4dCIblc3tXVxdq174nkcrnD4di2bVt3d7fZ\nrHC5cv/1X396883Y+Ph4o9EAUKngiSfA53O7QKUllUq1ZcsWoVDY19c3wuKTbXTJytzcXF9f\nX6VSYTocluLxeMFgUCaT0RdxmA6H4B6TyWS325PJZKFQYDqWzY4zOyrf+ta3nn/++ZtuuumN\nN94gnU82CbpBZyQS0el07D/axCC73d7X11cul1leaKtSqSYnJ9dkKIRGg5tuwtwc8nmIRNBq\njx6joueo6PWw2fDcc/jc546fXKL/IxrF7t2r//6nNzMzEw6HNRoNF3sQ0TNYbr3V/otflB5/\nvKBUJrVaisfTTUwYdTrpzTdjQ74HCwSCQCAwMjIyODhYKpXcbjc7ixxEIlFnZ2c8Hg+FQj6f\nb/V1XxsSRVE+ny+RSITD4UAgwPL3RoKFzGYzyL4KC3BmR0UoFD788MM9PT3/+I//yHQsRPso\nlUqdTpdKpegLukRLMplMrVZns1mmAzkNtVo9OTm5hr9KgQBWK/T648UeIhHUagwO4pprkErh\n/vvR04N8HskknnsOAM47Dx7PWn3/BdXr9VgsplKpPB4P57KUYwQC6gtfUP3N33h27fqQXu9U\nKme6uno/9rF+YGwD/z2aTKaurq7Z2Vk6+Wc6nNZ4PJ7f7zcYDJFIJJ/PMx0OS1EU5fV61Wp1\nJBKZmppiOhyCe8xmM72vUpy3QU+0ERsvFy2ku7s7l8stUojyyU9+UnNiDyBiQ3A6nT09Pblc\nzmazMR0Le9lsNvZvqtB9EYrF4rpendqxA6+9hu5u3HorXnoJTz+NmRnweKAo+P34xCfW7zsf\nl0gk6OrndnyzdWa3w27nAXpAX6lU8vl8JpPJZDJ6vd5kMm3IAgCpVNrV1UVX2FssFna+81AU\nZbfbxWLxsfJ6piNiI4qiPB5PJpOhexYfa9VNEEtE76vE43Gfz0dWmIygyHjE09q7d++ePXtK\npRI5fcSU8fHxRCLR1dUl2zDNhtZBLBZrNBrBYJDpQBaTSqVqtdq6dp2u1fDzn2NyEh/5CBwO\n8HhIJPD22xAK8ZWvoA3ravrlumXLFk7UpaxAo9Gga+7L5bJGozGZTBv19NH4+HgqlVIoFB6P\nh53HwABMTU3FYjG5XO71ekl5/UKGhoZyuRxZaxIrk81ms9nsBn79VKtVsVj8+uuvX3DBBUzH\nMh9L33kJ4kRarbZQKKTT6c7OTu4epFlvNputt7eX5TNVdDpdJBKp1WrrV2kmFGL3brzyCl5+\nGaUSAMjlRwc+tqFVaaPRGBgYMJvNGzVLAUBPbtbr9dPT0yMjI5FIRCKRmEwmnU536uDIUzUa\nOHDg6JE8gQBmM84+G1u2tCHwZdNqtVKpNB6P9/X1sXbQikKhONaQNxAIkIa8LdGtWeLxuNvt\nJrP8iOWyWq3NZjMej/v9fjIyoc1IokJwg8vl6unpGRkZofdhiVNJpVKtVjs0NNTR0cF0LAtS\nKpVCoXB8fHxdh9YJBLj0Ulx6KSoVNBptHfqRz+ebzaZlXQfOs4ZMJvN4PDabbWRkZGBgYGho\nyGQyGY3GRa7r12p46CGMjWHnTlx0EebmkE7jN79BIoErr2w9X5JZEomEPgYWDodZewxMLBbT\n5fX9/f1kev1CLBYLn89PpVL1ep0MzSSWi/7bj8ViJFdpM5KoENwgFArtdvvAwIBGo9mQx+LX\nhNVq7e3tLZVKbD6Ko9PpxsbG2rNQaP+uRj6fX3ylvvGIRCKHw2Gz2fL5/PDwcC6Xo0dJtjwr\n9eKLmJzEnj04tjmxdSvOOAMPPnh0LicL0YNWFApFKpUql8sej4eFnScFAkEwGMxkMqFQyOPx\nkCZFLdF/m8lkstlskmtexHKRXIURnOn6RRBGo1Eul6dSKaYDYS+pVKrT6Vg+U4U+MrQhR0BM\nTk5Wq9U16b/MOTwez2w2n3HGGQ6Ho1AoHD58eGBgoFarnXifuTm8/z4+/nHMO0LlcOCcc/DO\nO20NeLm0Wm1XV1etVuvv72dnCymKolwul8PhSCaTZPzUQnQ6ndfrHRwcJD8iYgVsNpvZbI7H\n42syE4xYCpKoEFzidrvL5fLY2BjTgbCX1Wotl8tsfg+VSCQymWx0dJTpQNZeoVBQq9UsvNze\nNhRFGQyGrVu3ut3uycnJI0eOZDKZY60aCwVUq/B6WzzQ60Uud/x/JyZw6BD278c774A960n6\nGJhKpQqHw6wdCmkymfx+/8jISCKRIM1yWtJqtfSPKJPJMB0LwT12u91kMsVisRJdBEmsM5Ko\nEFwiFoutVmsmk5l3pZY4RiKR6PX6gYEBNq9RjEbj2NgGnMVRKpVI/1MAFEXpdLotW7b4fL6p\nqanDhw/Tf7P0L7zlsTg+H40Gmk00m3jhBfzgB3jpJWQyeOcd3HcffvYzsGSiCT2F1u12Dw4O\nJpNJdr6G1Wp1Z2dnqVSKRqP1ep3pcNhIrVYHAoGxsTGyRU+sAJ2rRKNRkqu0AUlUCI4xm81i\nsZhcCVuE3W6vVqts3rKgu+5ssJ2xarVarVbZXB3Ufmq1uru72+12T0xM9PT0zMwMAfWWg0mz\nWeh0oCjs34/33sPnP48778Tu3bj9dtxxB2Zn8fDDYE9SoNfrOzs7p6amQqHQ7Ows0+G0IJPJ\nurq6qtVqKBQil3VaUiqVHR0dxWKRbD0RK2C32w0GQzQaZe1Y2A2DJCoEx9ADvIrFIpkUuxCB\nQGC1WoeGhhaZjsosiqKMRiNrD8+szNTUlEAg2MBdiVdMp9Nt3brV4XBMTY1JpUf27Rup109a\nF5bLeOstbN+OchlvvIGrr8aJjet0OnzhCxgfx+HD7Y58EXQmIBAI+vv72XnSUiQSdXZ28vn8\n/v7+DVkStnoymayjo6NUKtFDqJgOh+AYp9Op0+mi0Sj5+1pXJFEhuEcqlZpMpnQ6TU41LITu\nuZRtee2aHYxG4+zs7MTEBNOBrJnZ2VnSj24hdO3Ktm3bPvtZezqd/c53jrz77tjMDCYmcOQI\nfvpTaDT48IcRj0MiQWfn/IfLZOjqQiTCROgLEwgEgUCAvqqaO7HChjUEAkFHR4dcLg+FQuxs\nAMA4qVTa0dExMzMTjUZJrkIsl8vlUiqV4XCYnTurGwNJVAhOoqd3kbYtC6EoyuFw5PP5mZkZ\npmNpTSgUarXajbSpUqvVyKy9xVEU5fMZ/vf/3mYy6f7f/0v//d/3f+97U089ha4u7N4NgQBT\nU1CpWk9T0WjAwpU2RVF2u93r9Waz2VgsxsJLJxRFeb1erVYbiUTGx8eZDoeNJBJJR0dHtVqN\nRCIs/A0SbEb/fUmlUnqQMdPhbExkjgrBSXRJazgc1mq1pCqgJbVarVQqM5lM++c/jo3hwAHk\ncpiehtGIQAA7duDUkeVms7mvr29mZkYqlbY5wvVQrVbJua+l0Gr5t95qr1SMPT2Dk5Mhl0vr\ndDqEQhEAqXTBovmpqbYO7lwWeoB9LBaj5y2y7WVAty0WiUSJRGJubs5oNDIdEevQEzPD4XAk\nEgkGg5tqDhKxShRF+f3+SCQSiUTow5ZMR7TRkB0VgquUSqXRaEwmk+Qa2EKcTufU1FSbj1cd\nOYIf/xjDw/D7ce65UCjwhz/ggQdw6sa4TCZTKBQbZlOl2WzyTs3GiAVIJKKzz/aee25XrVbt\n6enJZrONRsPrRamEU/sw1Wro72/d15gl6M7FYrG4v7+fnQcaLRaL2+3OZDJkI7oloVDY0dFR\nr9fJvgqxXDweLxAIAIhEIuQA4ZojH6sEhzkcDh6PR/pLLkQikRiNxkwm07aeNqOj+O1vceml\n+PKXcfHFOOccXHklvvENzMzgmWda3N9kMhUKhY2xY76CH3KlghdewN69+Pa38X/+Dx57rMUa\nfWOTy+VdXV0ulyufz/f09MzNjZ15Jn79awwPH79PpYLHH4dQiB0j3i5TAAAgAElEQVQ7mAt0\nCfh8fiAQoAcssDP91uv1gUAgn8/To9mZDod1hEJhZ2cnyVWIFeDz+cFgcG5uLhaLkT+utUUS\nFYLDeDye1+stFouFQoHpWFjKZrPV6/W2LZsOHIDDgfPPP+lGhQKf+hQOH25RY6DVasViMTsL\nkdfbxAT27kV/P7Zvx403YtcuiMV48EG8/TbTkbWdXq/funWrVqtNpVLBYMRimd27F/ffjyef\nxCOP4O67MT6OL3wBnBikabPZ6MHnqVSKhesVlUoVDAYnJibIiJWW6PYD9Xqd/HyI5RIKhcFg\ncGZmJplMMh3LhkISFYLbZDKZzWZLp9PVapXpWNiIz+fbbLZsNtueXYuBAbSsiHG5IBS2HjFu\ntVrz+fwG+PXxeLxlbfr/9rfQaLBnD84/H4EAtm/Htdfi2mvx3HPYhIkbn893OBxbtmzh8Zpd\nXb1XXZX1+ZpzczAa8elPY88e6PVMh7hkWq22o6NjYmIiHA6zsEU4vYs1OzsbiURYGB7j6DNg\nc3NzJFchlkssFtMXAtLpNNOxbBwkUSE4z2KxyGQyMrRrIQaDQSQSDQ0NteF71Wpo2fiKoiAS\noWWuRBcib4BNFaFQuPRscHQUySSuugqCkxuanHEGfD68++7ah8cJdP8lj8cjEIzo9T2XXVa6\n7DJs3dp6mD2byeXy7u7uRqPBzhkmdO14s9kMhUIb4BrBmqMvjddqNdKzmFguqVQaDAbHxsba\n85m7GZBEhdgIPB5PpVIZPvFgO/FnFEU5nc7R0dE2DFLQaJDPt7h9ehrlMjSa1o+yWq2jo6Nc\n70O/rEQll4NCAYOhxZe83s21o9Js4tAh/PKXuPde/PSn+N3vUK1qt23bplarI5FIMpnk6FV/\nuuBBKpX29/eXSiWmw5mP3jcQCoWhUIjrf3rrQSQSdXR01Go1Uh5NLJdcLvf7/blcjqxJ1gRJ\nVIiNQCQSuVyuoaGh8kLNTTc3pVJpMBhSqdR6f+Ju3YpDh3DqnO7XX4daDbu99aM0Go1MJuP6\npopIJFr6xel6fcFdAh4Pm2ddNDeHhx7Cs89CJsO556K7G8UifvITvP8+3+l0BoPBcrnc29tb\nLBaZjnQleDye3+83mUyRSCTfMoNnFF3+K5PJQqEQawcuMYjkKsSKqVQqj8czODg4OjrKdCy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sfD4/EAhUq1V2DmJmBElUiM2Ix+P5fL6p\nqSkyFPZURqNRqVSueXu0anXBSgmJBEtZNIrFYofDMTAwsIJWSLOzyGSwY0eLL515JuLx9eqL\nRVGU0+kcHR1tQ4nkOefgjjuwffvRLsZnnYVvfrP1P3kzo2eViMXiUCjEobpV1uYqGo3G6/UO\nDg6OjY0xHQu78Hg8v9/fbDYjkQhpNUksnVAoDAQCk5OTQ0NDTMfCCiRRITYpiUTidruHhoZI\nK8lTeb3eRqOxtu3R1GoUi2h5bXFsDGr1kp7EaDSqVKpkMrncbXF6RapStfiSSoV6HetX+KpU\nKjUaTea0e0ZrQaPBhRfi2mtx9dU4//zW/16CXkGq1epQKMSh2QUul0ur1bIwV9FqtW63O5VK\ncaivWnsIBIKOjo5arRaPx8lJHmLppFKpz+fL5XKcmyG2HkiiQmxeWq3WaDQmEglyjHgePp/v\n9/uLxeIq3yVrNQwO4vBhpNOw20FReO+9+fcpFtHbi+7upT6n2+2u1WrLPUxFV+q3bBlaKoHP\nX9++WA6Ho1wuk2Uce9CtwOhOsoVCgelwlsrtdms0mkgkwra9IDJCZCF0g+zp6Wly0phYFpVK\n5XK5MpkM+ZsiXQWITc3hcExPT8disc7OToo+7E8AAKRSqdPpTKfTUqlUoVAs9+HNJt5+Gy+/\njNlZKBSYmoJAAK8Xzz+PRgNnnw2hEM0mUik8+SSczmUkKgKBgG6NolarlScW5i9KLIbdjg8+\nwKn9tw4dgseDdf3li8Vis9k8MDCgUqn4fP46fidiOex2u1AoTCaT9XrdaDQyHc6SuN3uZrMZ\nDoc7OjpY1bfQYrHMzc3FYrFgMLiCd4wNTCwWB4PBUCiUTqddLhfT4RCcYTAYKpVKPB7v7OyU\nSqVMh8MYkqgQmxrdZKOvr29wcNDhcDAdDrsYDIapqalEItHd3b3cVomvvILXX8fll+NDH4JQ\niHodvb149lk4nXjlFTz/PNRqlMuYm8OOHbjiiuXlCSqVymAwJBKJLVu2LD2wSy/Fww9Dr8d5\n5x39do0GXnsNvb245ZZl/eNWwmq1jo+PDw4OkpUKq5hMJoFAkEwm5+bmONFml6Ioj8eTTCYj\nkUhHRwerli8Oh6Ner9PXfSSbeXbPKaRSaTAYDIfDQqGQEy8zgiUcDketVotEIpu51TVJVIjN\nTigUer3eSCQil8u1Wi3T4bCLy+UKhULxeDwYDC59x2liAq++iuuvP75PwufjjDOg0eD++/GV\nrwDA2BgUClgsWNm1V4fDUSqV0um0z+db4kN8Plx9NX73O7z5Jmw2NJsYHMTcHG64ocU2y5rj\n8XhutzsSieh0OnK9mVV0Oh2fz6e7R6zhxJv1Q+cqiUQiEonQjQGYjug4MkJkIXK5nJ48w+Px\nzGYz0+EQnEF/cND5PycGQK25zfhvJoh5lEql1WpNpVJklvA8dHu06enpZY1KCIWgUrU4zeV0\nwulEOAynEzt2IBBYYZZyLLCJiYll9UXdvh3/43/gox+FWg2dDrt24a//Gl1dK4xhuZRKpU6n\nS6VSpAUQ26jV6kAgMDIykk6nmY5lSehu3TKZjG2TOsgIkUWo1WqPxzM4OEjK1Yilo5t/1Ov1\nTduSgSQqBAEAVqtVoVDEYjHS834esVjs9XpzudzS+yNNTGChA/8GA9aqzZJUKnW73YODg1Mt\na+QXIJPhrLNwxRW4/HLs2LG+NfSncjqd9XqdDMhjIaVSGQwGC4XC2ja7Wz/0sVWRSBQOh1k1\nv5KMEFmETqez2+3JZHJZ71rEJicQCILBYLlcbk/3SLYhiQpBHOX1eimK2rQXLRahVqvNZnMi\nkVjijDyhcMG5KLOzWMPzIDqdzmAwxONxrly75fP5LpdreHiYLFNYSKFQBIPB8fFxruQqPB4v\nEAjweLxoNMqqlICMEFmE2WzW6/WxWIxs4BNLJxaL/X7/6OjoyMgI07G0G0lUCOIoeiLs9PT0\n5rxosTibzSaXyxOJxFKyOKcTAwMtegHXakgksLY9C5xOp0gkWmJgbKDRaPR6fSKRYNXKkqDJ\n5XJu5Sp8Pj8YDNIl7KxKCcgIkUU4nU6FQhGNRlm1FUawnEKh8Hq9AwMDxWKR6VjaiiQqBHGc\nSCSiL1qQKUvz0PW71Wp1KVmczwejEb/5DarV4zfW63jySQiF2LZtjQPz+XwzMzMcGuLrdDp5\nPB7Jh9mJc7kKfSxkdnaWbem6UCikz6tw5SfZNvTbKZ/Pj8VirPqVESyn1WqtVmsikWDb1Nd1\nRRIVgjiJQqFwu92ZTKZUKjEdC7sIhUKfzzc6Ojo2Nrb4PSkKn/88ikX88Id49lm8/Taeew4/\n+hFSKdx0E5bZ6Pj0RCKR1+sdHh7mynUmHo/n8XgKhQKHRg1uKnK5PBAIFAoFriSTIpGoo6Nj\namqKbSmBRCIJBoPFYnG5E1o3PHoDv1qtJhIJpmMhuMRqtWq12lgsVj3xQuCGRhIVgphPr9fT\nI6vJGeJ5FAqF0+lMpVKnzeI0GuzZgwsvRKmE99/H+DjOOgu33451asupUqksFksymVxiFQ3j\n5HK5zWZLp9PkNcZOdL3K6OgoV3bqxGJxIBAoFotsS65kMpnP5xseHibb1PMIhcJAIDA5OcmV\n1xjBEm63WyqVbp5mFSRRIYgWHA6HUqkkTcBOZTQa6fr106YEQiHOOw+f+xz27MGNN+Kii9a3\nxRZdRUNPw1jHb7N2LBaLQqHgUMCbjUKh8Pv9uVxuWS2wGSSXy/1+fz6fZ1vAKpXK5XJlMpnJ\nyUmmY2EXqVTq8/lyuRzJ4oilow88UxS1SY4OkkSFIFrzeDykCVhLTqdTJpOxrdEQAK/XOzc3\nl0wmmQ5kqbxeb6PRYNtxHeIYlUrl8/kGBwdHR0eZjmVJlEql1+tl4aQOg8FgNpvj8fjMzAzT\nsbALyeKIFaCPDlYqlc3w8UESFYJo7VgTsIGBAaZjYRf6cg4AthXv0lXFk5OTXBlUwufzfT5f\nsVgk11NZS6PROJ3OdDrNtqX/QrRarc1mY+GkDrvdrlarI5HI5jlbv0QGg8FkMpEsjlgWkUgU\nCATGx8e58nm3YiRRIYgF0U3A8vk8WUfOw+fz/X7/1NQU205XSyQSr9ebzWa5Uqcuk8kcDkcm\nk9lUXVy4xWg0Wq1WFi79F2KxWOhJHWwr2XK73WKxmG2dlNnA4XCQLI5YLroALJvNnrbDDaeR\nRIUgFkOagC1EIpHQNbJsOxWjVqvtdnsqleLK0t9oNNLLSrJGYS2r1crOpf9CnE6nXC6PRCKs\nmtRBD4Ks1+vkSO2pSBZHrMCxz7sNvEQhiQpBnAZpArYQlUrlcDjS6TTb3iLNZrNOp+PQ0t/l\nckkkErJGYTN6SB/blv4LoSjK6/XyeDy2ldvS5zPL5XI6nWY6FnYhWRyxMmaz2Wg0xuPxjbpE\nIYkKQZweaQK2EJPJtMQmYG3GraU/XfZTr9fJUAXWopf+9JA+Tryo6KH1LJzUIRaL/X7/2NjY\nyMgI07Gwy7Esjm09pgmWczgcCoUiGo1y4jLKcpFEhSCWhDQBW4jT6ZRKpWxrAnZs6c+VJmAC\ngcDv95dKJbaV/RDH8Hg8ekgfVzrtsHZSh0Kh8Hq9AwMDXBnS2jZ0Fjc6OkqyOGLp6MsoAoEg\nGo1y4jLKspBEhSCWhDQBWwhFUX6/H6xsAub3+znUBEwqlXq93lwut7ErI1uam8ORI3jhBTz9\nNA4cAGs7bNFL/2KxSF5Uq6TVaq1WayKR4EotWduQLI5YAfroYK1W48q1uaUjiQpBLBVpArYQ\n1jYBo1dpHGqKolarXS5XKpXaVGuUwUHccw+eeQa5HGZm8M47+OEP8fLLTIe1gGMvqomJCaZj\nWRK1Wu1wOFjYXsJqtWq1Wg7VkrUNyeKIFRAKhXSD/sHBQaZjWUskUSGIZSBNwBZyrAkY27I4\ntVrtdDpTqRRXlpUGg8FisSQSCa40w12lUgkPPQSfD3feiZtvxmc/i298AzfcgNdewzvvMB3c\nAjQaDf074kr1qslkoruW1Wo1pmM5idvt5lAtWTuRLI5YAYlE4vf7WfhBvBokUSGI5SFNwBai\nUqk8Hk8mk2HbaDyj0WixWOLxOFcuT9psNnpZuRleY6+/DqkUKhWeew5vvIHhYQDo6sJll2H/\nfrB2+Wqz2RQKBYcabLhcLrr7LavOZx6rJeNK2U870Vnchqw6INaPUql0uVyZTIYr1+ZOiyQq\nBLFsdrtdqVRGIhG2XZ5knE6nY+dUbJvNptPpotEoV5b+9ByMaDS6sV9j4+N47z1MTiKTQbWK\nw4fx4x/jySfRaGD7dszMgM2VIF6vFwBXVth0SlCtVtnWUUogEPh8vmKxSMrH56F/ZY1Ggyuv\nMYIlDAaD2WxOJBIzMzNMx7IGSKJCEMtGd9gQiUSRSIQr11PbxmKxGAyGaDTKtrdIl8tFN3Dk\nxNKfXqMIhcJwOLwhO04CmJvDQw+h2cSVV2L3blx3HW69FV/9KsJhPP88JBIIhZieZjrKhfH5\nfJ/PNzExwZVTFkKhkO4oxbYhrTKZzO12DwwMTE5OMh0Lu9AdQYrF4jC91UgQS2O321UqFVc+\n7xZHEhWCWAm6USkAcrr6VE6nU6VSRSIRVp2uptNLoVDIlaMU9GuMz+dv1Fzl/fdRrUKnw4kz\neBwOXHstDhxAPo9aDXI5c/EtgVQqdTqdmUxmms0Z1QnkcrnT6Uyn02zb89TpdEajMZFIsG0i\nE+Po5g2Dg4Mb5iQP0R4ej0ckErHttOcKkESFIFaInqc2Ozu78boBrp7X65VIJGzbcaIbODYa\njWg0yon3bvo1RlEU236SayIeR1cXgkEcOnRSLYrPB5kMr74KuRwWC3PxLY3BYNBqtfF4nCu/\nIKPRqNfr4/E42y61OhwOmUxGLv2cSqPRmEwmksURy8Lj8ZMdel8AACAASURBVOjTnul0mulY\nVoUkKgSxcsfmqXH9jWDN0cNVKIpi2/aFQCAIBAKVSoUr6SU9wIdOrlj1k1y96WkolbjgApRK\n+PWvcWL1kECAI0ewaxd4XPiMcrlcADj0JsDawnqv10tKMlqiR4+TLI5YFnqJUigUuHI8tSUu\nfAgQBItJpdJAIDA2NkbOEM9D7wZUq1W2DYIUi8WBQGBiYoIrszvp7vi1Wm2D5SpyOSYnIZdj\n925ks/jP/8T99+ORR3D33ZiYwLZtOPPMxR4+Po4//Ql//CMOHgSzn8J0scr4+Djb+t0t5Fhh\n/bE/gWYTiQTefBOvvIK+PjDVcoKUZCyCzuISiQTTgRBcIpPJ6CZg3J2pQBIVglgtepDw4OAg\nV6YKtg29wp6ammJboyGZTEbP7mTbhMqFiESijo6OarW6kc6ABQJH18RmM77xDXz2swgEYDSi\nuxs8Hi6/fMEHNhp45hnccw9efBGpFF57DffeiyeeAIMlUTKZzGq1ptNptp2nWohQKPR6vfl8\nvlgsDg/j3nvx8MM4fBixGJ58EnffjT/9iZnApFKp2+0eHBwkhfXz0JurpVIpl8sxHQvBJXq9\n3mAwJBIJVlWNLp2A6QAIYiPQaDT0VEGhUKhSqZgOh0UkEkkgEAiHwyKRyMKmggOlUun3+6PR\nKI/HY1VgCxGJRJ2dnZFIJBwOB4NBgYDz794f+hDeeguPPorrr4dKhY4OdHQgHscTT+D886FQ\nLPjAZ55BKIQvfhFe79Fbsln86ld4/HF84Qvtib0Fi8VSLBZTqRTdZoP9lEqlxWLp6Um++uqW\nQEB0yy2QSgGg0cDbb2PfPojF6OxkIDCdTjc9PZ1IJLq6usRiMQMRsJVEIvF4PPF4XCqVqtVq\npsMhOMPpdFYqlVgs1tnZyePEgdoTcCxcgmAto9FoNpvj8ThX+v+0jVwu9/l8Q0NDbNtxUqlU\ndGBcOWciFAo7OjqazWYkEtkAfcD4fNx8MxoN/OAH+O//xmOP4Z578NBD2L4du3Yt+KjRURw8\niBtuOJ6lALBa8Rd/gUQCsVgbAm+NLrEolUpse50vwmaz9fXJarX4ddc16SwFAI+H88/HBRfg\n+ecZC8xut5PC+pY0Gg09IoMU1hNLR787zc3NcaiU7hiSqBDEmrHb7RqNJhKJkI+QedRqNb3j\nxLYOmxqNhj62x5VaQ4FAsJFyFZUKt9yCm2/G1q3QanHBBfjGN3DFFaCoBR8SjcJggMs1/3ad\nDj4fIpF1jfc0JBKJ1WrNZDJcOQAGoFTyBgKz2ez8M5BnnYVCAYUCI0EdL6zn4rpqvdntdnok\n1IY5BUq0AT1GaXx8nHOTVbmdqFSr1XfeeWf//v2kvIxgCbfbLZPJyND6UxmNRovFEo/H2Xb0\nXKvVut3uTCZTYGpRtkx0rkJRVH9/P0fPHJ+IouDx4IIL8IlP4Oyzodef5v5TU9BoWn9JrcZC\n00GaTUxNoQ09Hcxms1gs5kqfBgAzM8LOTs/w8PC8P0z6h8zgtBWBQOD1eguFAod2qNrG6/U2\nm02utC4kWIIurB8YGOBWYT1nEpVvf/vb+/fvP/GWvXv3WiyWc88999JLL/X5fDt37vzggw+Y\nCo8gaHRbXoFAsMEaNK0Jm81mMplisRjbhs3p9XqHw5FMJrnStYnOVcRicX9//8zMDNPhtJVE\nsuDquVzGsfNLx6RSePBB/Ou/4vvfx3e/i4cfRja7juFRFOVyucbHx7myFJBKweOp6TEdJ15e\noX/Ip/4820kul9vt9nQ6XWGqDRlbkcJ6YmX0er3RaIzH4xw698GZROWuu+567rnnjv3v008/\nvWfPnunp6WuvvfbWW2+98MIL33vvvUsuuSTG4AllggDw54HijUYjHo+zqi0vG9jtdr1eH41G\ny+Uy07GcxGQy2e32RCLBtsNpC6FfZgqFIhQKsS3xW1deL3I5jI7Ov316GvE4PJ6Tbjx0CA8+\nCK0Wn//80cZiIhF++lOEw+sYoVwu1+v16XSaE3/+Xi8OH4bdbheLxSd2Ej9yBAoFDAZmo4PZ\nbFapVPF4nFz3mYcurB8aGuLKWxbBEg6HQyqVcuhvahmJSqlU6unpKRaL6xfN0t15551qtfr9\n99//9a9//eMf//i111771a9+NTk5+S//8i/r9B3JFR1i6eipgtPT02Rr/lQul0ur1UYiEbZ1\nHTCbzfThNK5cC6fP8et0ukgksnkWK3Y7AgH88pc48bNoehq//CW0WnR3H7+xVMLTT+OKK/CZ\nz8Dvh8GAYBA33ICLLsK+fVjX64l2u31ubo4TTRouugjpNF58kXK7vdPT03TMoRBeegmXXLJY\nsVDbeDyeer3OodN0bXOssJ6sT4ilo8co1et1rkxWXVKi8vLLL+/cuVOlUm3btu2tt96ib/zM\nZz7z4osvrmdsC8rn85FI5Bvf+Eb3CR9K11133dVXX/38urUpicfjG6B0lWgbeqpgsVjkyqSO\ndnK5XGq1OhKJsO3z1WazGY3GaDTKtkKahdAHjcxmcywWGz11l2GDuv56KJX44Q/x85/j6afx\nyCP4v/8X1SpuuumkSfaHD0OlwjnnzH/4xRcDQH//OkYoEAjsdnsul2P/p4bBgBtvxMGD+PGP\nxR984HrkkaF77pn5xS9w0UU4+2ymgwMA8Pl8r9c7OjrKlSqydqIL62OxGCmsJ5ZOIBD4fL5i\nsciJwvrTJyoHDhy4/PLLw+HwJz7xiWM35vP5d95558orr3zvvffWM7zW6MXNiVkKbdu2bev3\nQxcIBJFIhCs7ZQQbyGSyQCCQy+U48V7QThRFeTwepVIZDofZdlLW4XCYzeZoNMqS3eOlsNls\nbrc7nU6zbbDmOhGLcfPNuOkm2GyYmYHRiGuuwde+hnkTjPJ5OBwt9gT4fNhs6z7MXq/Xi0Si\n7LoWxKwRvx9/9Ve4+GIYjTq5XKPTJW6/vfnRjzId1gkUCgU9T5Ntbxds4PV6AZDde2JZZDKZ\n2+3mRGH96ROVf/7nf7ZYLL29vQ888MCxG41G46FDhywWy7e+9a11jG4BNptNrVafuhE8NDSk\nVCrX6Zv6fL5GoxGNRjlx7JhgCaVSSb8XcGjV2x70sSWZTBYOh9nWuspms9lstng8zqHfml6v\nDwQCY2NjHDp5vBoUBb8fu3bhs5/FZZcdHWbPKhRF2e32fD7PibW1RIKzz8ZVV+GrX3WdccZc\ntcq6/Mpqtcrl8hOraAgan8/3+XylUokTWTHBHjqdjhOF9ad/a3/rrbduu+02h8Mx73aTybRn\nz55XXnllfQJrIZ1Ov/vuu9FodHx8/Pbbb7/vvvtOPOPe39//i1/84sILL1yn705XHVQqFXLd\nglgWvV5vs9kSiQRXThO1DX1SViwWh8NhtnVztlgsdK7ClT5gAFQqVWdnZ7lcDofD7DxxlMvh\nvfewfz8OHUIbfq4mEzKZFi2J63UMDcFkWvcA1Gq1QqEYHBxc9++0dgQCgcvlyuVybGt3AcDj\n8VSrVW79PNtDKpW63e5sNsv+q+MEq9CF9SyfrHr6RGViYsLpdLb8ktVqbWe3mUcfffScc84J\nBoNGo/Ff//Vfo9Hos88+S3/pkUce2blz58zMzF133bV+AYjF4mAwODExQd4oiWWxWCx0W17y\nKTIP3bpKKBSycHyhxWKh+4Bx6GS8VCrt6upqNpv9/f2sqv+pVPDoo/jJT/Dmm8hksH8/7rkH\nv/891vXDcds2lEp4++35t//xjwDQ2Tn/9moVsRjefhsffIC1avpqt9vHx8fZ1jdicRqNRqvV\nJpNJtq1dhEKhx+MZHh7m0FZn22i1WoPBkEgk2PZGSrAZfbmQ5ZNVBae9h8Vi6evra/mlV155\nxWazrXVIrd1///3FE0xMTBSLRa1WS3+1WCxqNJrHHnvsnFMLJ9eUVCr1+XzRaFQoFJracEWO\n2Cjsdnu9Xo/FYsFgUC6XMx0Oi9C5SjgcjkQiHR0dfD6f6YiOM5vNPB4vmUw2m039aScRsoNQ\nKOzs7Ewmk319fV6vV7PQcMQ2ajbx2GOYmcFtt8FoPHpjPI5f/xoArrhivb6vUolPfQr79iGX\nw9atUKtRKODQIUQiuPFGiMUn3fnwYTz7LGo1GAyoVFAswu3GtddCrV5VDHK5XKVS5XI5n8+3\nqidqL5fL1dPTk81m7XY707GcRKVSWSyWVColl8uFQiHT4bCL0+ksl8vJZDIQCDAdC8EZdGH9\nkSNHmA5kQadPVK688sp77733uuuuOzEnGR8f/4//+I/777//9ttvX8/wjvvyl7+8yFd37969\nZ88eXlsOKatUKo/Hk0wmhULhsUyJIE7L5XI1m016OS6TyZgOh0X4fH4wGAyFQtFoNBgMtucP\neYmMRiNFUXQbR67kKjwez+fz5XK5eDxuNpsZX2uGQhgawh13nFTs7vPh+uvx85/jvPOwfu+j\n27dDo8HLL+OJJ1CtQiKBy4WvfQ0Wy0l36+3Fb3+LXbtw3nmgM+XxcezbhwcfxJ49EIlWFYPF\nYqEb3EkkklU9URvx+Xy32x2NRunTa0yHcxKbzVYqlRKJREdHB9OxsAt9dbyvr294eNhsNjMd\nDsEZ9MR6pqNYEHXaurRcLnfuuedms9nt27cfPHhwx44dAPr6+mZnZ10u14EDBzb838PevXv3\n7NlTKpVOfL/O5XLZbDYQCKxf+T6x8TSbzWQyOTk52dnZyaFVS3vUarVQKCQUCgOBAKv2VQCM\njo6m02mXy2VgfADeckxMTCQSCfraCoPp31NPYWYGn/tciy/94Ae44ALs3LnuMTSbmJnBidcH\nmk3EYsjlMDOD99/Hjh24/PKTHlKr4d57ceaZR9sZr0YoFJJIJG63e7VP1F7JZLJcLnd3d7Pq\n2gGA6v9n786jIyvLhIE/d6l93yu171VJmm5tpOFj00FERR0RZQSRo9M6oyKc+TjDHJ1zxDM4\n43fO55z5BpkBh3HGGZtBFgVFUGRVQEBapGmS1L4vSVWSSlVSVam96vvjYtOk01mrcu+tvL8/\nOHSlknqSVKre577v8zytlt/vHxsbG/nlxw6USqVEIuH1etHWPbJ1rVaLx+O99NJLF154Id2x\nrLX5q49er3/ttdf+4i/+grqm+MYbb7zxxhsSieQrX/nK73//+337MqHX6zUaTSwWq9frdMeC\nsAaT2/LSjjqz1O12GVgLrlarqf6/+UHVLuwJmUxGldeHQqFhP9+qVThb87ZaDc52AE0mg72p\nc8Swd2Qpi4vwve/Bgw9CKATZLNTrcPw4vPTSOz6Fw4F3vxtCoQE8uk6nKxaLTOsYsSmz2dzt\ndhn4nOdyuSaTKZfLofffMykUCqVSiSa/ISNj86NfAKDVau++++677rprfn6+UqlIJBIG5iex\nWOxLX/oSADzzzDNb/6x2u/3AAw9s/GL34osvrnu7yWTqdDqRSMTn83F3eTgA2TeotryxWCwc\nDnu9XvTMOR2Hw3G73ZFIJBKJuN1uktzSC9TeUKlUBEEkEol2u322/iIMJBAIxsfHE4kEVbIi\n22XJxRmqVXjmGQiFgCrdVyrhyBE4cuQd00sEgrNmI7UaCASDjWhz9TocOwYGA/z5n4NAAOEw\nFApvVbNwue8YEKlQwED6X8jlci6XWywW9WvOnDEbQRAmkymZTCqVSqbtAKvV6nK5nEwmfT4f\nduasnP3NYrEEAoF0Os2uyigEWdc21gH5fD6fz5fLZZVKheO45lRRJDNUKpVnn312u581Nzf3\n7W9/e+MLXVRX2XXPyFGneCORiNfrZdSiCmEy6iRxNBqlchVUEno6Dofj8Xio2nqm5Spyudzl\ncsVisU6nY7PZ2LI8IknS7Xbn8/lYLKbRaEwm06AiL5fhBz8AqRQ++lHQ66HZhGQSfvMbyGTg\nk598O1ex2+GJJ6DRgDVr3XweFhbAbh9ILNvw6qvA5cI117xVjsLjQasFPh+srsJzz8Hhw3Dq\n4OHq6tqYd0ytVi8uLrIrUQEApVK5uLiYyWTcbjfdsaxltVr9fn+hUGDdT3XYqCq1YDC4sLDA\ntKUagmzXlg6efv/737fb7QaD4fDhw5dddtmhQ4e0Wu34+PgDDzww7Pi2zufzTU1NTU1Nbeuz\nLBZLMBiMbegf/uEfAGDdt3ZqxYnjeDQaZVonR4TJmNyWl3YkSXq9XgzDQqEQ007LSCQSj8ez\nsrLC8MbzZ9Lr9U6nc2lpKRKJDOqn+otfgEoFR4/C5CSoVGAwwIUXwtGjEA7D6S1kJidBIoGH\nHoLTm/QWi/DjH8Pk5F7MM1kjGoWDB9/ORgwGIEkIBOBd74JmE05vPu/3w6DqSlQqVavVYuMw\nJYvFUqlUGDhQiMPhmM3m2dlZdADsTAKBwGQyZbNZdrXGRpAzbZ6ofO973/vLv/zLubm5yy+/\n/HOf+9yNN954/fXXHzlyJBQKXXfddceOHduDKLeCz+cfOHDgwIEDe/y4BEG4XK52ux2Px9HE\nXGTrqFwFw7BIJNLtdukOh1moPmAEQTBwFqRQKPT5fI1Gg3W/OJlMNj4+3u12A4HA7kf6VCoQ\njcIHPrB2JLxGA4cPw4kTb99CEHD99bC6Ct/9Ltx3Hzz2GPzwh3D33aBWw5/+6S6j2Ila7R39\nxzgcuPBCeOIJWFgAgQCoOYf9PjzzDMzNwaAqSzkcjlwuX1xcHMyX20N8Pl+n02UyGQY+25VK\npVwuR+Pq16XRaORyeTweZ+AvDkG2bvOuX16v1263P/jgg2sONycSiSuuuILL5c7MzAwzwrX6\n/X4ikYjH49QbrUwmc7vdQz0yvm7XrzWazWYwGJTL5azr64LQq9PphMNhHMc9Hg/TWuvQrtvt\nUsmAx+Nh2gG5drsdiUQAwO12My22jfX7/UwmQx1DGhsb2/ExsEQC/ud/4BvfgDO/wPQ0PPkk\n/PVfv+PGXg9CIcjlYGUFlEqwWmk49EX593+HiQm4+OK3b+n34fHH4cQJ6PdhYgJ4PEgmoV6H\nT30KnM6BPW65XE4kEocOHWLdX3qv1/P7/XK53GQy0R3LWp1OZ2ZmRqPR7NlUNxahrkqIxWKb\nzUZ3LAijsbvrVzKZvO22284swbTb7bfcckssFhtOYOsolUq33nordYDhAx/4wNVXX3311Ve/\n//3vt1gsVqv17//+72nc/+XxeC6Xa2lpaW5ujq4YEDai6ge63S46PXgmgiCoFCUUCrXO1lKK\nJlSPMoIg9qCh1mBhGGaxWBwOx8LCwm6C3yDB6ffX+SiOw/g4XH45XH01vO99tGUpAOB0wtQU\nnH6NDsPgYx+Diy4CgoBOB7pdOO88uPnmQWYpACCVSjEMW15eHuQX3RM4jpvN5vn5eQYesiJJ\n0mq15vP5GrUXhpyGIAi73b60tFQsFumOBUF2aPNCVZlMdraZBgRB7NlUgbm5uYsuuiiRSLjd\n7iuvvNJqtVI9wqnD4s8///w3v/nNhx9++Ne//jVdQxhFIpHD4YjFYhwOh13DFhB6Ua2uQqFQ\nLBajDoPRHRGDUAfkotFoKBTyeDy8NePEaUWdT4vFYqFQyO12C/a+fdUuyOVykUhEDbC3WCxK\npXK7X0GjgX4fMhk4c1BYKgVnawxZLkM2C0tLoFCAyTTEUY8buOACeP11+NnP4KMfhVObYdEo\nHD8Ol102sLNeZ8JxXCqVlstlNk4KlslkMpksnU57vV66Y1lLLpfL5fJkMsnAkS+0E4lERqMx\nnU6LRCKmtW5DkK3YPFH52Mc+9thjj11wwQVnfujxxx+/5pprhhDVOm677bZsNvvQQw+t+4jd\nbveee+656aabbr/99jvuuGNvQjqTTCazWCzpdJokSfnZBgcgyBm4XK7H4wmFQvF43OFwoFzl\ndFSuQjV0ZlquQsWWSCRCoZDD4ZCeXvrAeNRszXw+n0wmK5WK2Wze1iJPJAKvF556Cj73OTj9\n7FsuB2+8AZ/61Nr7d7vwq1/BH/4AYjHI5VAuQ7UK7343fPjDsMet3UQi+Oxn4aGH4P/9PzAa\nQSiEQgEWFuCii+B//a/hPrRCoUilUv1+n41/42azeWZmplQqMTDRslgsfr9/bm7OaDTSHQvj\n6HS6arUaj8d9Ph9K5BDW2bxGZW5u7qqrrnK5XNdee63b7RYKhbVaze/3/+AHP2i1Wt/73vdO\nz9GHd4B1bGzsyiuv/M///M8N7nPttde+/PLL6XR6sA+9lRqV083OzhYKBY/Hg+bCItvSaDTC\n4bBYLLbb7WxcxwxVv9+n5qsyLVehzM7O5vN5s9nMxmag1Wo1mUwCgM1m2+Kr3B8/EX7wAyAI\nOP/8t9sT/+53cOgQfPSja+/8s59BPA5XXw2nTsunUvDII2CxwCc/OYhvY5s6HQiFYG4OGg1Q\nq8HtBpVqDx60c/LkSZ/Px9J3h2w2Wy6XJycnGfgCtby8HI1GvV7vtp7D+0Sn0wkEAtS1VLpj\nQZiIyTUqm1/IogrUjh8//qMf/ejMj67prT68zhvFYtG52Xnh8fHxn/70p0MKYOsMBkO73aZe\nMdFOK7J1fD7f7XaHw+FUKoVqH9fAMMzpdDL2nJXBYOByuel0utFosGgcJEUsFk9MTORyuVAo\npFart761IhbDX/4lPP88vPwylMtAEKDVwsc+BgcPrr3n3By8+SZ88YtwesGz1QrXXQf//u9w\nwQWw99fBSRImJ2Fyco8flBQIBJVKhaWJytjYWLFYXFxcZGBCLpPJVCpVKpWamJhgYB5FL5Ik\n7XY7dSFsB+c8EYRGmycqV111FROuXxoMhpMnT258nxMnTjCk74fFYqG6OXm9Xib89BC2EAgE\nLpcrEolkMhnWrXeHjcpVEolEOBx2uVxMW+qp1WoulxuPx9vtts1mY9cRC6paWiaTJZPJarVq\nt9uFQuFWPpHPhw9+ED74Qeh0gCDW1tB3u3D8OPj9kM8DjsNzz8F73gM+39t30OvBZIJwmIZE\nhS5isbhare7Zw1UqcPIk5PPQaoFGAz4f7OZ1hSAInU43OzurVCrPVrxKl34fxGLT/PwMGgG5\nLrFYPDY2RhWroGUJwiKbJypM2KMAgKuuuurOO+8877zzbr755jP/xmq12ne+851HH330a1/7\nGi3hrUENgqRO1Xu9Xi6XS3dECGuIRCKn0xmNRnEcR+et18AwzG63ZzKZcDjscDjO7EZIL6lU\n6vV6o9EolUqRe1x7sWtSqXRiYiKdTgeDwe02Lz7ze2214H/+B5aW4D3vAT4fGg1QKOAnP4H3\nvAc+9KG376ZQwK5nurCJWCzOZDJ781jBIPz0pyCTgcUCMhnk8/DKK3DuuXDllRs1bduYVqtd\nWFgoFAoMuSwIAJUKPP00hELQapGrq8ZOJ/ORjyje9z4eq64V7AW9Xl+pVJLJpMfjQZtOCFts\n4310cXExEonUajWJROL1eve4WPzv/u7vXnzxxb/5m7/51re+deTIEbPZLBaL+/1+tVpNpVLH\njx9fXV295JJLvvGNb+xlVBugchVqyeL1etk1aQGhl0QioY45AQDKVdaguutyudxYLGaz2Zh2\njEEgEPh8vmg0GgwGXS4X6w5/kiTpcDhKpVImkymXy6f6K+7AM89ArQZf/jKIxfDss5DLwUc+\nAuecA8eOgcUCExNv3a1WO2uLsJEkEAg6nU673R72m8LCAvzkJ3DppXDJJW+nJdks3HcfSKVw\nySU7/LI4jhsMhnQ6rdFoaHxf6/chkYB8/q0tI6USPvEJ0Ouh1VK/+OLS009n83nnddftPB8b\nSRiG2Ww2v9+PNp0QFtlSovLb3/721ltvffXVV0/dgmHYZZdddscdd+zZJHi5XP7KK6/cdddd\nx44d+81vfnP6pFUOh3PuuecePXr06NGjjNqMpjoCRSKRSCTi8XhYd3kVoZFUKqXa8na7XVT+\neCa9Xo/jeDKZbLfbOoatc6kRK/F4PBQKOZ1ONpb2KhQKqVSazWaDwaBarTaZTNt9aW234Y03\n4BOfAOq7t9vhlVdgZQUsFjj3XPj9799KVCoVSKXg/POH8D0wFZ/PxzCs2WwOe5X/0ktgs8Gl\nl77jRpMJrrgCnnwSLrwQdvxuqVKp5ufn5+bmTr009XqwuAjtNmg0sAcHCAoF+MlPoFwGjQaW\nl6HZhIUFaDSAunx65ZVmlSrwm98snzghO3x46MGwC5fLNZvNqVRKJpMxrdIPQda1+dL5+PHj\nl19+eafTufjii71er0AgoLp+PffccxdddNHx48f3rKs6l8u95ZZbbrnllkajkclkqMn0UqmU\nury6NzFsF5WrhMNhKldhVB6FMJxEInG73dFoFABQrnImrVZLkmQymex0Okzbd8Jx3Ol0ptPp\nSCRis9kY2M51UwRBWK1Wqp2u3++3Wq3bar5cLEK7/fZUR7sdDAZ46CG49lqw24GqN6zV4Mc/\nBp0OXK4hfANMhWEYl8ttNBrDzmBTqfW3TSYm4Oc/h0IBdnN0y2AwxGIxrVaL4/ynn4YTJ+DU\nxUOXC668cogTcqpVOHYM7HY4ehR6Pfinf4LPfx7yeXjsMeDxYHycqvTTRqPpEycmDx9Gx7/W\nUqlU5XI5mUz6fD50AAxhvs0TlX/4h3/QaDRPP/207/QSSIATJ0586EMfuv3229ftBjZUVHOk\nPX7QHaOmwlG5itvtRrkKsnVisZjaV+n3+1arle5wGIeq6I3H4wzcd8IwzGq18ni8RCLRaDTG\nxsbojmgnpFLp5ORkLpeLRCIKhcJsNm9xH4Batp7aRcYw+PSn4f774c47QaeDdhseeAASCVCr\nYR+ez+Fyua1Wa9iP0mjAug0ReDzAcWg0dvXFZTKZSCTK5fLPPWdrNuFTnwKrFUgS5ubghRfg\nP/4DvvAFGNKpzN/+FmQy+OQnAcMgnYZ+H0wmsFigVoOnngKfDzAMxsbG1Oql117LAzClkIZR\nrFbrzMxMPp9n6esSsq9sfrHh5ZdfvvHGG9dkKQDw7ne/+8Ybb3zuueeGE9hIIUnS7XZ3u91o\nNNrr9egOB2ETsVjs8XjK5XIqlaI7FiaSyWQej6dUihMtjwAAIABJREFUKiUSieG1R98xvV7v\ndDoLhQJ1io/ucHaCagg2Pj7earWmp6dnZ2e38nNWKgHDYG7u7VtEIvjCF+ATnwAcBy4XFAr4\n+MfhC18AFp6M2y2CIPbgySCVwtLSOrcvL0OvB7ufTarX659/fqlcbh09Cj4fCATA4YDFAtdf\nD2Nj8MQTu/36ZxOJwLvf/VZyS5XLU8/Hw4ehXIZiEQCAIAi93lyt5hu7TMhGFEmSZrN5bm5u\ndXWV7lgQZBObJyrLy8tnG+Nos9mW1n0hRM7A4XDcbner1YrFYgxcTiFMJhQK3W53uVxm5lqc\ndiKRyOPxVCqVSCTCwGRAJpP5fL5msxkKhZrNJt3h7JBQKPT5fBaLZWFhIRAIbNpgVyAAtxt+\n/Ws4/coMhoHZDMUiXHopfPCDMDEB+7Mv094kKl4vvP46dDprb3/1VVCpQK3e7deXyWSplMDl\nKqzZt8EweO97IRaDIa2Bq1U41e1PrQYcB+oajlQKGAannpilksJolKLrO2ejVCrlcnkikUAX\nTxGG2/xdQqvVBgKBdT/k9/u1Wu2gQxpZXC7X4/HU6/V4PI6Wm8i2ULnKysoKylXWJRAIvF5v\nq9WKRCKdM5dmdOPz+VTrv2AwWGFzL16VSjU5OSkUCkOhENXJYIM7f+hDMD8Px45BPA71Oiwv\nw9QU/Od/gkoFR47sWchMhOP4HqwOL7wQul340Y+gXH7rlnYbnn8eXn31He2hd6Pb1ZPk4plP\nA70e+n0olQbzKGsIBG9nI3w+HDgATz0FzSasrkK/D1R9eC4Hr78OH/iAeXV1FV1OPRuLxdLt\ndvP5PN2BIMhGNk9Urrjiin/5l3959NFHT18e9fv9n/70p3fdddeHP/zhYYY3ang8nsfjqdVq\naLmJbJdQKPR6vdVqFT151sXj8bxeb7/fD4VCe1AAsF0kSbpcLrVaHYlEWL0yIEnSZrN5vd56\nvT49PZ3P58+25lYo4C/+AgQCuO8++M534I474PHHYXwcPvvZnfebGhlbKWLO5+H11+GllyAU\n2klJCZ8Pn/scdLvw3e/CHXfA3XfD//2/8PvfwzXXDKx7gUgkx3Hu/Pz8mtupawVD6nPpcMDU\n1Nv//NCHoN+Hf/s3ePxx4POhXIann4b//m84dAgOHeLpdLpsNsvAjVYmIEnSYrHk8/larUZ3\nLAhyVtimK55UKnXkyJH5+Xm9Xj8xMSESiaiuX1QZ1vHjx892MGxk3HPPPV/+8pcrlcqgmrTU\n6/VwOCyTyWw220C+ILJ/NBqNcDgsFAqdTidq2HImqhKs3W4zdobJ0tJSKpVSKpUWi4Xtv8Fi\nsZjL5TAMMxgMKpXqbHfrdqFYBA4H5PJ9Vze/rng8Tq0Rz3aHSgUeeQRSKZDLQSiExUXo9+ED\nH4D3vGcnD1covDWZXq0Gs3mQ+cOxY8DlLvp82XPOOef0PjEzM/Dzn8Pf/M1QcpWlJfi3f4P3\nvAcuv/yto4OtFvz85zAzAxgGHA7odHDeeXDOOQAAvV7P7/fLZDKz2Tz4UEZCIpFYXV0dHx/H\n9+dBTAQAAFqtFo/He+mlly688EK6Y1lr81cRq9X62muv3XbbbT/72c9Olc4rlcovfvGL3/rW\nt1DLiB0QCATUfJVMJoNePZFt4fP5Ho8nHA7HYjGHw4HeWtagmuwxeYaJUqnk8XixWCwcDjsc\nDlaPglWpVHK5PJ/Pp9PpxcVFk8m07nRIggB0Rvh0vV5vg7/cdhuOHQOBAG6++a0mv70enDgB\nTzwBBAHvfve2H06nG9ZIzSNH4Mc/VikUc3r9wqkBgisr8PTTcPjwsHZUlEq49lp4+GGYngaz\nGTgcyOdhfh7e9z64+OK1m3U4jptMpng8rtVqeTzeUAJiOYvF4vf7Z2dnR/6iM8JSm++onNLv\n96ktQrFYvK9mmg58R4VSrVYjkYhGo0GvDsh2tVqtUCjE5/OdTifKVc7U7/ez2ezCwgIDR9dT\nqL4anU7H6XQK120iyyqtViubzZZKJYVCYTAYmLmXxRx+v1+lUp1tUOkrr8Arr8BNN62dnPi7\n38ELL8Bf/zWzDs49/TQ880zBYChccsk5PB42OwsnToBOB9dfP6xEhdJswswMFArQaoFGA14v\nnH1LD8LhMEmSDodjiAGx2crKSjQa9Xg8DLyyg+wN9u2oZLPZs30Cn8/vdDqn3wGts3dGLBY7\nnc5YLEYQBNqYQraFy+V6vd5wOByNRl0uF8pV1sAwzGw283i8ZDLZaDQMu5lsNxzUbzCVSoVC\nIbPZrN59DyZacblch8NRq9VyudzMzIxCoTAajegC9rr6/X6j0dhgKHg4DAcPrjPf/fBhePpp\nyGSAUUeGP/ABsFjUP/vZ7FNPlTgcpUYDl10Ghw8PvZ8bjwdbnzpvNBqDwWCtVlt3xw+RSqVK\npTKZTE5MTKB3E4Rp1k9UtnUeCdX17phUKrXb7fF4HMOwfbVJhewe1USOGiTqcrnQINEzabVa\nLpebSCRarZbVamVaQQiO43a7fXFxMZ1OVyoVq9XK9iUC1Sd6ZWUll8v5/X6NRqPX68mhXldn\noUaj0e/3N9hGq1TWH+vO5YJIBExrGlcsQqdDjI8rxeLFSy5RMvMko0gkksvl2WzW6/XSHQtD\nmc1mv9+fy+XQcXSEadZ/C/n0pz+9x3HsW3K53G63JxIJgiA0Gg3d4SBssmZfBeUqZ5LL5R6P\nJxaLRaNRh8PBwB+RWq0WCoXxeDwQCDidzhE4NCWVSqVSaalUmp2dXVxc1Gg0Op0OpSunVKtV\nLpe7wQ+Ez19/AkmvB40GMOcJUqvBo49CJAJiMRCEJhwO/O53jY98hH/oEN2RrcdoNPr9/uXl\nZdmpISzIaQiCsNlsVJsf6e6ngSLI4Kz/WvnAAw/scRz7mUKh6PV6qVQKwzC2nwBB9hiHw/F4\nPJFIJBwOu91utBw8k0gk8nq90Wg0FAq5XC7umUdq6EbNUkwkEsFg0Gq1Kta9nM42CoVCoVBQ\n6cr8/Lxardbr9azuHDAo5XJZLpdvcAe7HWZm4OKL13ZIC4eh1wOGXO/udODee4Eg4CtfoTol\nCKenhbHY4s9/bsLxtzpuMQqfz1er1blcTiqVMm1zlSEkEolGo0mlUhMTEwy8poPsW1s9aXB6\nG/Jms/nqq6+eOHECHfoaFJVKZTab0+k0Gk2FbBeVq/T7fWbOOmQCHo/n8/lIkgwGg6tDGpe9\nOyRJut1uvV6fSCQymczIvLQqFIqJiQmr1bqysjI9PZ3NZjeeETnyOp1OpVLZOFE5/3xYXoZf\n/hJOH/4xNwePPw7nn8+UHZU//AGqVbjhhrf7uel0aput+L739Z98Epg5tsRgMLRaLfQmuwGT\nyYRh2AZVygiy9zZPVLrd7le/+tVrr72W+idVbnXBBRccPnz40ksvrZ6aEIvsDtX+K5lMLi8v\n0x0LwjIkSaJcZWNU22KJRBIKhRj7J6bX691ud6lUCofDI7OgxzBMqVROTk5ardbl5eWpqalU\nKtXYwfzCkVAsFkmS3Li3klgMn/kMBAJw553wyCPwq1/BsWPw/e+DywXvf/+eRbqJUAgOHXpH\n1qRSqfr9vstVqteBmQtdkiS1Wm0ulzvbiFIEx3Gr1VosFldWVuiOBUHesnmi8o//+I933333\nqdFUX/3qVxOJxFe+8pUbb7zx5Zdf/td//dchR7iPaLVavV4fi8UYu5BCGIvKVQBglNa4g4Vh\nmN1u1+l0sVhsYWGB7nDWJ5FIfD5fv9/3+/0jtlag0hWXy9Vut2dmZiKRyH57oev1eoVCQafT\nbXr0yGyGm2+Giy8GDgeWl8FohM9/Hq66auittLZuZQXW9P3GcVyhUFQqiyIRMPaZSzWtmZ+f\npzsQ5qIOgKXTaZTOIQyx+Yn2++677+qrr/6nf/onAMjlck888cTRo0fvvvtuAGg0Gg8++ODX\nv/71oYe5bxgMhn6/H4/HXS6XRCKhOxyETahcJRqNBoNBt9s9AmXZw2AwGHg8HnVRn5n9bage\nCZlMJhqNjo2NjVjvcqrUvlarFQqFaDQqEom0Wq1CodgPZQOLi4v9fn+LTVN4PDjvvGFHtHN8\nPtTra29Uq9WBQLBWa/H5jKsEo+A4PjY2lsvl1Go1qug7G4PBUCqV8vk8Axu7I/vQ5tdnksnk\nFVdcQf3/k08+2e/3r7vuOuqf5557bjKZHF5w+5PRaFSpVLFYrFar0R0LwjIEQXg8HqFQGAqF\nmFmMwQQqlcrlchWLxXg8zsyrhhiGWSwWu91eKBRGcotMJBI5HI4DBw4IhcJUKjU1NTU7Ozt6\n3+bpms1mLpcbGxtjexNqitUKfj+sqaUSiUSFAq9aLTF5uJpareZwOPl8nu5AmIsgCJPJlM/n\n9+0RTYRRNn/FPP1C1zPPPCMSiS655BLqn/1+f7TfWuhisVgUCkUkEkFrTWS7MAxzOBxyuTwU\nCo3Y2aEBkkqlXq+3VquFQqFWq0V3OOujKtGpY2AjeUqKx+NZLJaDBw/q9fpSqTQ1NRWPx0e1\n7jGVSlHbR3QHMhjnnw/FIjz99DtylYUFOH5c7naXzz7Nkn4Yho2NjS0sLKByvg0olUqxWJzJ\nZOgOBEG2kKhYrdYXXngBAAqFwmOPPXbFFVec6u958uRJNJZ+SCwWi0wmi0Qi6JIGsl0Yhlmt\nVo1GE41GS6US3eEwlEAgGB8fJwgiEAhUmDZF74+osZ4ajSYWiyWTSWbu/+wSQRBarZYqX+n3\n++FweGZmJp/Pj9JVsGw2u7q6arVa6Q5kYKRSuPZaeOMN+Nd/hccfh2efhfvvh3vuAbdbcehQ\nleG/O4VCweFwUKXKxqxWa6VSQe8gCO02T1Q+85nP/OhHP7rwwgsPHz5crVb/6q/+irr92LFj\nP/zhD//0T/90yBHuUxiG2Ww2iUQSDoebzSbd4SDsYzKZDAZDIpFYXFykOxaGopoCK5XKSCTC\n2J8ShmEGg8Htdq+srASDwfqZlQGjQiqVOp3Oc845R6VSLS4uvvnmm5FIpFQqsb1Zcz6fn5+f\ndzgcPB6P7lgGyW6Hm26Cc8+FZhPm5kChgOuug89+VsTnc8vlMt3RbQTDMJ1Ot7Cw0GVmH2Vm\n4PF4er0+k8mgnxJCr82LyW655ZZwOPzggw9yudw777zzve99L3X717/+da/X+7d/+7dDjnD/\nopoUxWKxcDjs9XoZOKgOYThqxF4qlep0OlS7G2QNDMPMZrNAIEin07VazWKxMLOqWyKRTE5O\nplKpYDBoNBpH5gTRmTgcjl6v1+v1lUqlWCwmk0kcx+VyOXUWhZm/nQ3Mzs7m83mHwzGS076F\nQrjwwrU3yuXyUqm0xZ4BdFGr1XNzc4uLizqdju5YmEuv1y8tLc3NzaGzMwiNNt9R4fP5//Vf\n/7W6uloul2+++eZTtz/yyCOvv/76aAxRZiyq3oDH441kQS2yB1QqlcPhmJubQ6eNN6BWqz0e\nz/LycjgcZuzJdYIgHA6HxWLJ5XKxWGzkL3NKJBKbzXbw4EGTydRqtSKRyNTUVCaTYUsRS6/X\ni8fj8/PzTqdz4wmPI0Yul1erVcb+HVGoTZVCoTCSxykHBcdxi8UyPz+PymURGu28/cgFF1yA\nuvvtARzHXS4Xh8NBs/yQnZHL5VSTq2QyyfZTNMMjFot9Pl+v12P48SqVSuXz+RqNht/vZ8uS\nfTcIglCpVG63++DBg2NjY/V6PRQKvfnmm6lUanl5mbGrzEql4vf7V1dXvV6vTCajO5w9JRaL\nCYJgfvsHjUbT7/fRoPqNSaVSmUyWTqfpDgTZv0ahT+LIo3IVDMMikcjIX0ZFhkEikVA7BrFY\njLFrO9pRA0yEQmEwGGTyIXuqDYBMJguHw9lsdp8knyRJajQaj8dDZSztdjsej588eTIWiy0u\nLjKndVur1Uomk+FwWCqVjo+PC5jcAGs4MAyTSCSMbVBxCo7jGo0mn8/vk7+gHTObzfV6nbFV\nfMjIQ4kKOxAE4Xa7e70eylWQnREKhV6vt16vR6NR9BQ6GxzHHQ7H2NhYPB7P5XJ0h3NW1JEM\nl8tVKpWoK/d0R7R3OByORqNxuVyHDh2y2+0kSc7Ozk5NTU1PT6dSqaWlJbpOyTYajWQyOT09\nXa/XvV6vxWIhCIKWSGgnFotZsd2n1Wrb7TZqbLUxLpdLTclEZzoQWqCzW6xBzR0Ph8ORSMTt\ndu/bt0Bkx/h8vs/ni0Qi4XDY7Xajo5tno9frBQJBIpFoNps2m42xE/qkUunExEQ2mw0Ggzqd\nzmAw7L7WvNmEcBioxq1aLXg8wNhWVVSRPVX+0Wg0VlZWKpVKOp3udrt8Pl/0RwKBYKgl+J1O\np1QqLS0tVatVsVjsdDr321mvM0kkkkwm02q1GN4DhiRJtVqdz+eVSiXdsTCaTqdbWlrK5XKj\n1GIbYQu0UmETDofj9XrD4TBaaCI7w+FwPB5PNBoNBoNut3vE+qUOkEwm83q9sVgsGAy6XC7G\nrrcIgrBarVKpNJ1OVyoVm83G5/N3/NWCQXj0USAIoFrEvf46PPEEfPzj4PUOLOAh4fP5fD5f\nq9X2+/16vV6tVmu1WqFQaDabOI4LBAKBQMDn86n/7v632e12q39Uq9VIklQoFGazWSgUDuTb\nYTuBQECSZLVaZX4CQPUpXl5eRunlBjAMs1gsoVBIpVKJxWK6w0H2F7TSZRmSJL1eL3VR3OPx\noFwF2S5qay4Wi4VCIbfbvQ/P0G+RQCDw+XzxeDwQCDgcDolEQndEZ6VQKMRicTqdDgQCY2Nj\nO2tFncnAj38M730vXHwxUHtI3S68+CI89BAcPQpG44BjHhIMw4RC4amEodPp1Gq1er1er9eL\nxWKj0ej3+ziOc0/D4XCI05y+/dLv9zudTrfb7XQ6nU6n2Ww2Go1ms9lqtXAcFwqFEonEaDSi\npduZRCIRKxIVLperUqny+TxKVDYmFotVKlU6nR4fH2ddl3CE1dAyl32oepVIJBIKhTweD4fD\noTsihGWo9gyJRCIUCrlcLrTMOhtqImQ2m41EIgaDgcmzaDgcjtPpLBaLmUxmZWXFZrNtd9/g\nuefgnHPg0kvfvoUg4H3vg6UleO45uOGGAQe8N0iSlMlkp9ag/X6/+UftdrvVaq2srLTb7W63\n2+12z1ZUjeM4SZIkSfJ4PJFIpFKp+Hy+UCjEMGx5GVIpWFoCmQxMJmD8snyrikX4/e+hUIDV\nVdBowOOBc86Bba1OxWIxWxpqabVav99fr9fRVZuNmUym6enp+fl5NHwG2UsoUWGlU7kKta+C\nchVku6hxoplMJhKJOBwOdDXxbKiJkCKRKJVKVatVu93O5PIw6mBGMpn0+/1ms1mlUm3xEzsd\nSKXgc59b50Pvehfcdx90u8Dg73urMAyjDomt+9Fer9ftdk9vi0elKOteP+714Mkn4fhxEIlA\noYDlZVhZgYMH4aMfBba/Hk9NwaOPgtEIDgfw+TA/D7/8JbzxBlx33Ta+NYlEksvlut0uk/9e\nKAKBQCQSLS4ums1mumNhNJIkjUZjLpdTKpVo1YHsGZSosBVBEFSxAbWvwtgz9AhjUceOSZKM\nxWI2m435hzRopFQqhUJhPB73+/0Oh0MkEtEd0VnxeDyv11soFNLp9NLSksVi2Uol0uoq9Puw\n7uk2qRR6PajXYeQ33nAc33rjhCeegEAArr8enM63bslm4ZFH4OGH4dprhxXhHlhYgJ/9DK64\nAs4//+0bL70UfvhD+NWv4GMf2+rXoXYn6vU6KzZsNRpNJpMxGo2M7ZzBEBqNhtq2dTgcdMeC\n7Bfob5LFqAM8XC43FAo1m026w0FYyWAwmEymZDI5T3V6Qs6C6pkmFovD4TDzRwrodLqJiQkA\n8Pv9W5kUIRAAhsG6oy8qFcAwQIdiTre4CH/4A/zZn72dpQCAyQSf+QxEIpBM0hbY7v3ud2Cz\nvSNLAQCZDD7yEXjjDdj6KFSqEIgtb0wKhQIAUJ/irbBYLKVSiRXtp5HRgBIVdqNyFT6fHw6H\n2fKWgDCNVqu12WzZbDaTyaDZZxvAcdxut5vN5nQ6nUwmGT46k8fjud1ui8VSKBSCweDGs1Y4\nHLBY4OTJdT508iTYbKNw7muAIhHQaMBiWXu7Wg02G4TDdMQ0INkseDzr3G63A46D3w9bH8LE\n5/MbjcYAYxseHMeVSiXzL0AwgVAoVCqV2WyW7kCQ/QIlKqxH5SoCgQDlKsiOKZVKr9e7tLSE\nxkFuSq1W+3y+SqXCip1MlUo1MTHB4/GCwWAul9sgEf2TP4GTJ+Gll+DUXXo9ePFFmJqCP/mT\nPYqWLSoVkMvX/5BCsf7GFFu0Wmsn53Q68Oyz8J3vQKcDjz8O/+f/wAMPQLm8+Zfi8XhsSVQA\nQKPRVKvVfTU7dceMRuPq6iragEL2BkpURgGGYU6nUygUhkKh+tb35hHkNCKRyOfztVqtUCjU\narXoDofRhELh+Pg4SZKBQID579YcDsfhcFA9wWZmZipnWUdbrXD11fDii/DP/wz33w/33w//\n/M/w0kvwqU8BqjFeg8+Hsy1oazV2H5OTy2Fh4e1/9npw333w5ptw2WUAAJ/7HFx/PbRa8P3v\nw6Y9vfh8PvMz+VOokvpisUh3ICzA5XK1Wu3s7CzagUf2AEpURgSGYVSNbyQSQbkKsjNUHTZB\nEJueFEKozsV6vT6RSLDiyJxMJpucnJRIJOFwOJVKrbtvNjkJf/VXcNlloFKBSgXvfz/87/8N\n4+N7HyzT2e2Qy8GZKerqKsTjYLPRENKgTE7CG29ArfbWP197DQoF+MIXYGkJlEqwWsHhgBtu\ngLEx+OUvN/lS1NEv5v9pnEJVijP8SCdDjI2NdToddFgO2QMoURkdVK5CLURQroLsDDUOknoW\nLS8v0x0O0+n1eqfTubS0FIlE2u023eFsghpj73a7V1ZW/H5/eb3jOwIBvOtdcMUVcMUV8K53\nwS7G3I8ysxnsdnjoIVhZefvGeh1+/GNQKMDnoy+yXTt8GJRK+O//hkQCej148004eBBefhl+\n/3v4yEfeGqWCYXDZZRCLwcYF1Twer9/vM//v4hRUUr91BEHodLrZ2Vl0VBgZNpSojBQMw2w2\nm0wmC4VCtVPXxBBkO6gRK1qtNhaLLZx+CgRZj0wmGx8f7/V6gUCAFZ1wpFLp5OSkQqGIx+PR\naJRFh3MY5VOfAi4X/uVf4P774Ve/ggcfhO9+F+p1uO46YHWHWxyHz34WTCa491749rdhdhZe\nfRUiEbj+eji9Ia1eDxi2yekvkiQBoNPpDDnkgcFxXKVSoRe9LdJqtTiOFwoFugNBRhyaozJq\nMAyzWq0AEIlE3G43kwc+IExmMBi4XG46nW40GmgO2sa4XK7H48lkMuFwmOED7Ck4jptMJrVa\nnclk/H6/TqfT6/VogsS2CATw+c9DOAzp9FuT6T/6UZiYYHeWQuHx4OMfhyuugEIBHnwQ3vte\nOP/8tWPpez3o9zf5ZqlnFLtOUqnV6vn5+WazuZXpQ/scjuMGgyGdTms0GjT/ERkelKiMIGpf\nJZVKoVwF2Q21Ws3lcuPxeLvdttlsaCG7ARzHrVarRCJJp9OVSsVmszH/nZvP57vd7mKxmMvl\nqNGQUqmU7qDYBMPA6wWvl+44hkMgAJsNjEZYXFybpQBAIgEEARrNRl8BwzAcx9l1NEggEPD5\n/FKpxPzLDUygUqnm5+fn5uYsZ/bqRpABQSuPkWW1WlUqVTgcPluTHwTZlFQq9Xq9tVotEomw\n6AgHXZRK5cTERK/X8/v9bKnwUalUk5OTMpksGo1Go1HU8A053XnnwRtvrB1huboKTz0FBw+u\nbWR8JhzH2bWjAgByuXzd8i1kXQaDYXFxkUV9qBHWQYnKKDObzWq1OhqNolwF2TGBQODz+Xq9\nXjAYRPUMm6KOgWk0mlgsxopuYABAEITZbPb5fJ1OZ2ZmBnUdRU7xeuHIEbj3XvjFL2B6GkIh\neP55+N73gMuFD35w808nCIJdOyoAoFAoarUayti3SCaTicXi2dlZugNBRhZKVEac2WzWaDTR\naHTl9PY0CLIdHA7H6/Xy+fxgMMiKenF6YRhmMBjcbnepVAoGg2y51igUCn0+n8lkmp+fZ0tj\nAGQPXHEFfPrTUC7Dk0/CI49AJAIXXABHj26+nQLsTFSEQiGPx0ObKltnNBpLpRJ6xUCGBNWo\njD6TyYTjeDQadTqdMpmM7nAQVsJx3Ol0ZjKZSCRis9moPp7IBiQSycTERDKZDAQCRqNRq9XS\nHdGWaDQahUKRzWZDoZBCoTAajaiqGPF4wOOhO4g9JJfLS6USW/5maScSiRQKRS6X845qwRZC\nK7Sjsi9QnYhisRi6SoTsGIZhFovFaDQmEgm00b8VJEm6XC6j0ZjNZuPxOFsuLZMkabPZxsfH\n2+32zMxMJpNhS+TIpvp92MtfZrfbJQhi7x5vQORyebVaZdEEGNoZjcZarcaWwjyEXdCOyn5h\nMBhwHI/H4w6HQy6X0x0OwlZarZbD4SSTyXa7bbFYsDP7ASHvpNVqJRJJIpHw+/12u10sFtMd\n0ZYIhUKv17u8vJzJZJaWlsbGxjQaDfp1s9fJk/DaazA/D50OqFQwPg4XXwzDbk3H0kRFLBZz\nOJxyuazZuK8Z8kc8Hk+j0WSzWalUil4lkMFCico+otfrMQyLx+M2m02pVNIdDsJWCoWCy+VS\nHaIcDgcbFyJ7jGpIkMvlwuGwXq83GAx0R7RVMplMKpUuLCzMzs4uLCyYzWbUwph1+n147DGY\nnoYjR+DSS4HDgXweXn0VgkH4/OdBIBjiQ7M0UYE/9v5CicrWjY2NFYvFYrGoVqvpjgUZKejo\n1/6i0+mMRmMymSwWi3THgrCYSCTyer3NZjMcDqMDEluB47jZbLbb7fPz8+z6oWEYptVqDxw4\nIJVKqRbGqPkbu0xPw/Q0/Pmfw+WXg9sNNhtccAF86UsAAE89NcTH7fV6/X6fpYmKQqGoVCqo\nJ/vWkSSp0+lmZ2dZ15AaYTiUqOw7Op3ObDZa1DVkAAAgAElEQVSnUimUqyC7wefzfT4fhmHB\nYHB1dZXucNhBoVCMj49Tg1bYVTBGkiTVwrjb7c7MzGSzWVS4whZ/+AOcey6Mjb3jRj4fLr8c\npqZgeFkn9QxhaaIiFosJgkDdMrdFp9P1+/3FxUW6A0FGCkpU9iONRmOxWFKp1MLCAt2xICxG\nkqTH4xGLxaFQqFQq0R0OO/B4PK/Xq1ar4/F4Mplk13KfKlyx2+3lcnl6erpQKKCrp8xXKIDV\nus7tNht0uzC8C1bUtiFJsvKEOYZhYrEYjSDbFhzHdTpdoVBAg5iQAUKJyj6lVqstFksmk5mf\nn6c7FoTFcBy32+1UK7BcLkd3OOyAYZjRaPR6vbVaze/3s24xpFAoJicnjUZjoVCYmZlZXFxE\n6xIm6/cBX++tnqp5Hl6mWa/XuVwuSxMVABCLxWg2yHZpNJput4vOayADhBKV/UutVttstmw2\ni3IVZJe0Wq3L5VpYWIhGo+zaIqCRSCQaHx9XKpWRSCSVSrFrawLDMLVafeDAAarVj9/vR1tq\njKVWw7rXEHI5wDBQqYb1uPV6XTDUUv0hk0gkjUYDlalsC0EQGo0mn8+jixfIoKBEZV9TKpV2\nuz2bzebzebpjQdhNKpWOj483m00WzWKnHY7jRqPR5XKtrKz4/X7WXb7FcVyv1x84cEAulyeT\nyWAwyLrdof3gXe+C48dhTUlUtwvPPgte7xC7frE9UREIBARBoKf0dul0una7za4aPITJUKKy\n3ykUCrvdPjs7i3IVZJd4PJ7P5+PxeKFQCBWhbp1UKp2YmJBIJOFwOJfLse5KJEmSRqNxcnJS\nIBBEIpFIJIKaKzDK4cNgMsF//Mdbc1TKZQgE4Ac/gOVl+PCHh/i4q6urrE5UMAwTiUSsu3xA\nO5IkVSrV3Nwc3YEgI4Kth0eRAVIoFNR8lW63azQa6Q4HYTGCIJxO5+zsbDQaNRgMer2e7ojY\ngSAIq9UqlUrT6fTy8rLdbmfdCo/L5VqtVp1Ol8vlAoGAQqEwGAx8Pp/uuBDAcbjuOvjtb+GF\nF4DaHuByYXwcPvMZEImG9aDtdrvT6bDuabyGWCxGOwM7oNfrp6enV1ZW0NglZPdQooIAAMjl\ncrfbHYvF2u221WpFk2WRHaMqxQUCQSqVqtfrVqsVX7eSFzmDQqGQSCSpVCoYDI6Njel0Otb9\nJfL5fKfTWavVcrnczMyMQqEYGxtj+2p1BOA4XHopXHop1OvQaoFMNvRHXFlZIUmS7ZmqRCKZ\nm5tj79hKunC5XKVSmc/nUaKC7B5aQCBvkUgkHo9neXk5Ho+zq64XYSClUun1eqvVKruGG9KO\nJEmn02mz2fL5fDgcZuloRZFI5PF4vF4vNTEmGo2iw2AMIRDsRZYCAOVyWS6Xsy7TXkMkEmEY\nVqvV6A6EffR6faVSQQfnkN1DiQryNmpIwurqKurdhOyeUCj0+XwAEAgE0Dv9tigUiomJCQzD\nAoEAe6enicVil8t16jmA0pX9o9frraysyOVyugPZLQzDhEIhqqffAT6fL5fLUe0rsnsoUUHe\ngRo33ul0wuEwasuI7BKHw/F6vVKpNBwOo87628Llcj0ez9jYWCaTiUajrVaL7oh2SCQSuVyu\n8fFxHMcDgUAkEkFZ68hbXl4GAIlEQncgAyAWi9Ezdmf0ev3y8jK6PIHsEkpUkLU4HI7H48Ew\nLBgMsvTkCcIcGIbZbDaz2ZxKpTKZDN3hsIxOpxsfH+92u36/f2Fhge5wdk4oFDocDp/PR72w\nRKNRtPgbYeVyWSaTjUZxGp/PR/3Wd0YkEkkkkkKhQHcgCLuNwusIMnAkSXo8HqrPbL1epzsc\nhPXUarXL5SoWi+hU4Xbx+Xyv12symXK5XCgUYvWa6dTuCpWuhMNh1MZ69HQ6nXK5rFAo6A5k\nMPh8frvdRq9aO6PX60ulErriiewGSlSQ9eE47nK5xGJxKBRC9XDI7p2aCBkIBFi92qaFWq2e\nnJwkSdLv97Nx1srphEKh0+mcmJjg8XixWMzv9y8uLqIGHiOjUChwOJwRKFChUI3L0FJ7Z6RS\nqVAoRJsqyG6gRAU5KwzD7Ha7QqGIRCLowieye9RESIFAEAwGqVPsyNZxOByn02m32xcXF0eg\nP4FAILBardRU+2w2Oz09PTs7i65bs123211YWNDr9Wzv93UKQRAkSaJrKzum1+sXFxdR70dk\nx1CigmwEwzCr1To2NhaNRpeWlugOB2E9aiKkVquNxWKoIcwOKBSKAwcOiESiUCiUyWTYvhHB\n4XAMBsM555yj1+uLxeLU1FQmk2Fv5wBkfn6eIAiVSkV3IIPE5/PRjsqOyeVyPp+PNlWQHUMD\nH5HN6fV6HMeTyWSn09FqtXSHg7AeNbM8lUo1Gg2LxTIaRbd7hhpjL5fLqTH2FouF7VPVCILQ\narUajWZpaSmfzy8sLKhUKq1WiyZFskuv15ufnzcYDCOznULh8XhoR2U3dDpdJpMZGxtDczOR\nHUDrA2RLtFqtzWbLZrO5XI7uWJBRQE2ErFQqoVAIXa3cAZlMNjExIZPJotEodRGB7oh2C8Mw\nlUo1OTnpdDqbzabf7w+Hw+VymdUFOfvK7OwsjuMjtp0CqPHXrimVShzH0aEMZGdQooJslVKp\ndDqd8/Pz6XSa7liQUSAUCsfHx0mSDAQCpVKJ7nDYhyAIs9ns8XhqtZrf7x+Zn6FMJvN4POPj\n4zweL5FITE1N5XI5dMad4arV6vz8vNVqHb0NUnT0a5eoaxCsbrCO0GjUXlCQoZLJZG63e2lp\nKZFIoMucyO6RJOl2u/V6fSKRyGQy6Em1A2KxeHx8XKVSJRKJeDw+Mgt6oVBotVoPHjxoMBjK\n5fLU1FQ8HkddPZip1+slk0m1Ws32U4jr4vP53W53ZP6yaKFWq+v1OttbgCC0QIkKsj1isZg6\nsROJRNheyIswhF6vdzqdS0tL4XAYrQZ2AMdxo9Ho8/mazebMzMz8/PzIpHwEQVCtmV0uFwBE\no9FAIIDaGTNNNpsFAKPRSHcgQ0GSJACMwOlKGvF4PKlUuri4SHcgCPugRAXZNoFA4PV6W61W\nOBxGr93IQMhksvHx8X6/7/f7K5UK3eGwEnWUzmw2z83NBQKBERt/JJVKHQ7H5OSkRCLJZrNT\nU1PZbBaNo2WCcrm8uLhotVpHtVSa+r5Q7+xdUqvVS0tL6MeIbBdKVJCd4PF4Xq+33++HQiHU\nSxQZCC6X6/V6lUplJBJBnYt3jKpHp/oXj0aR/el4PJ7JZDp48KDRaKxWq36/PxgMLiwsoNUP\nXarVaiKRGBsbk0gkdMcyLBiG4TiOnmO7JJfLCYJAJfXIdqFEBdkhDofj8XhIkkRdm5BBwTDM\nbDbbbLa5ublYLIZWBjtDkqTVavV6vaurq9PT06N0EoyC47harfb5fNQGy9zc3JtvvokqWPZe\nvV6PRqMqlWpsbIzuWIYLx3F02nCXUEk9sjMoUUF2jiAIt9stEAhCodDq6ird4SAjQqlUjo+P\nNxqNQCCAzvbsGFVkbzAYZmdng8HgSJax8vl8o9F4zjnnOJ1OAIhGo1SLMHTpZA80m81IJCKT\nySwWC92xDB1BEOi6ye6hknpkB1CiguwKjuNOp1MqlYZCIXQ5ExkUPp/v8/mEQmEwGET1lzuG\nYZhWq52cnBQIBMFgcPROglEwDKMqWM455xytVlsul6enpyORSLFYRIvLIaGyFIFAYLPZ6I5l\nL6AdlYGgSurRpgqyLeybTN/v96kunFTFLdUw12w20x3X/oVhmM1mI0kyGo3a7XaFQkF3RMgo\nIAjC4XAsLi6m0+lqtYoG2O8Yh8Ox2WwqlSqdTs/MzBiNRrVaTXdQQ8HhcHQ6nU6nq1arS0tL\n2Ww2lUrJZDKFQiGXy9HzZ1AqlUo8HheJRA6HY8SG0J8N2lEZFLVanUwmzWbzqLZeQAaOTYlK\nqVT69re/fe+9987Pz6/5kMVi+eIXv3jrrbcKBAJaYkNMJhNJkolEotvtjuoyCNl7arWaz+fH\n4/FQKORwOHg8Ht0RsZVEIpmYmFhYWMhkMsVi0WKxjPCrpVgsFovFZrO5VqsVi8V0Op1KpSQS\niUKhUCgUKGPZDeragUqlslgs+yRLAZSoDM6pknqNRkN3LAg7sCZRmZubu+iiixKJhNvtvvLK\nK61Wq0gkAoCVlZVYLPb8889/85vffPjhh3/961+jK/p00ev1BEGk0+lut6vT6egOBxkRYrF4\nYmIikUgEg0GbzSaTyeiOiK2ok2AymSyTyQQCAa1WOzY2NsLXNTEMO5WxrKysLC0tpdPpTCYj\nl8sVCoVUKt0/6+yB6Pf7mUyG6kSsUqnoDmdPoaNfg3KqpB4lKsgWsSZRue2227LZ7EMPPXTN\nNdec+dFut3vPPffcdNNNt99++x133LH34SEUjUbD4XASiUSr1ULn8ZBBIUnS5XJRrcB0Op3B\nYEBLzB3j8Xgul6tcLmcymaWlJYPBMPJboDiOy+VyuVze6/XK5XKpVIrFYjiOS6VSuVwuk8lG\nOFsblFqtlkql2u22x+MRi8V0h4OwmFqtzufztVqNutyMIBtjTaLyi1/84oYbblg3SwEAgiBu\nvPHGF1544ZFHHkGJCr3kcrnL5aJ6y1qtVrSgRAYCwzCDwSASiRKJRK1Ws9vtHA6H7qBYjFqg\nLywsZLPZQqFgNpulUindQQ0djuNKpVKpVHa73eXl5eXl5XQ63ev1xGKxTCaTy+XobOGZut1u\nLpdbWFhQKpVUS3q6I6JBt9tFz41BOVVSjxIVZCtYc1S3WCxSDSg3MD4+XigU9iYeZAMSicTt\ndi8vL8fjcbRdjgyQTCabmJjo9Xqj2m93L1EnwQ4cOCCVSqPRaDQa3T9dfQmCUCqVdrv90KFD\nHo9HJBItLi5OT09PT09nMpmVlZURmzyzY8vLy36/f2Vlxe122+32/ZmlAEC320XbbgOkVqtL\npRIq+0G2gjUvOgaD4eTJkxvf58SJEwaDYW/iQTYmEom8Xm8kEolGo06nE73EI4PC5XI9Hk8m\nkwmFQiaTSavV0h0Ru5EkaTabVSpVNpudmZnRaDQGg2H//MGeqmMxGo2NRqNcLi8vLy8sLOA4\nLpFIJBKJVCrl8/l0h0mDcrmcz+dXV1f1er1er9/nHQhQojJYqKQe2TrWJCpXXXXVnXfeed55\n5918881n7sDWarXvfOc7jz766Ne+9jVawkPOxOfzqVwlHA673e59eykOGTgcx6l2GplMplKp\nWK1W9OzaJaFQ6PF4lpeXqcKVsbExjUaz385t8vl8alHe6XRWVlYqlcr8/Hwmk+FwOKeSFi6X\nS3eYw9Xv95eWlvL5fKvVUqlUdrsdHXkClKgMGoZhSqUSJSrIVmBs2eAul8vvf//7X3/9dYlE\ncuTIEbPZLBaL+/1+tVpNpVLHjx9fXV295JJLfvnLXw68zu+ee+758pe/XKlUUAXhDnQ6nUgk\n0uv13G73yL/HI3us0WjE4/Fut2u329Gf50D0+/2FhYXZ2VkOh2MymVCPtVarRSUtlUql3W7z\neDwqaRGJRCO2gm+320tLS/Pz891uV6PRaLVaVAZ2yokTJxwOB/pzGKBqtRoKhQ4ePIieZkzQ\narV4PN5LL7104YUX0h3LWqy5DCmXy1955ZW77rrr2LFjv/nNb04/2sjhcM4999yjR48ePXoU\nXfNgGpIkPR5PLBYLBoMul0soFNIdETI6qAH2uVwuFApptVqTybTfNgEGjipcUSqVVI81iURi\nMplGeOLKprhcrlqtphqj1et1KmPJZDKdTockSdFpWPru0+l0SqXS0tJStVrlcrkajUaj0bD0\nexmSfr/f6/XQz2SwxGIxh8NZXl4e+a6DyC6xJlEBAC6Xe8stt9xyyy2NRoM68gEAUqnUYrGg\nS/VMRhCE2+1OpVLUzD50UQoZIBzHzWazRCJJpVJUN7ARu85NC6pwRaPRZLPZQCCgUqmMRiM6\nXycQCAQCAVUW1Ww2a7VarVZbXl6em5vr9/t8Pp/KWKi7MXxd22w2K5VKqVSqVCokSSoUCpPJ\nhLowrYtqCcPwXygbyeXyUqmEEhVkY6x84+Hz+W63m+4okG3AMMxms3G53FgshgqgkYGTy+VC\noTCZTAYCAYvFolQq6Y5oFPD5fGriClVnr9frNRrNPi+qPoXH4/F4POqZ1u/3V1dXqbylUChQ\nzdM4HA6VsfD5fOq/9K50+/1+vV6v/lG73eZwOHK5XK/XSyQSGgNjvk6nAyhRGQK5XB6NRqnN\nSbpjQZgLPTmQvWMwGHg8XiqVajabaBwkMlhUN7D5+flkMrmysmKxWNCSeiBOTVyZm5ubn583\nGAxKpRIdsTsdhmHUXgr1z16vV6/XG40G9d9SqdRqtQCAy+Xy+XwOh8Pj8bhcLofD4XK5XC53\nGE/Ufr/fbDYbjcap/66urna7XT6fT7U4E4vFaO9xi+r1OkEQ6ODGwEkkEoIglpeXVSoV3bEg\nzDU6iUosFvvSl74EAM8888y2PjGbzVLvImezuLi4q8iQ06hUKmpfpdVq2e12tJREBkur1VJD\nIQOBgMPh2M/FFQNEFa6o1WqqC1Y+nzcYDAqFgu64GArH8dPzFgDodrtU3tJsNqnq/Far1W63\nqWY2JElSeQtxGpIkT/3/2dLCXq/X6XS63W6n0zn9f1qtVqvV6vf7OI7z+XwejycWi6k/DVS4\nvAP1eh29kgwDhmEymaxcLqNEBdnA6CQqlUrl2Wef3e5nxWIxl8u1lXuypT0a80kkEp/PR7Ut\ndjqd6I0TGSyRSDQ+Pp5Op4PBoNFoROcMBwXHcb1er1arC4VCMpksFApGoxGdGtoKgiDWpC6U\ndrvdbDbb7TaVt1CZRrPZpLIOysZvPadnNSRJkiRJHUjj8XjU7s0wv639AiUqw6NQKKjOjehk\nHXI2o5Oo+Hy+qamp7X6W0+nMZrMbz2O+//77v/GNb6CjDgNENWuKxWKhUMjlcu3PeWrI8BAE\nYbfbi8ViOp1Gg1YGiyRJo9Go0Wjm5uYikYhEIjEajaib385wOJxNc4ler3e2XAXHcfTGtAdW\nV1d1Oh3dUYwmqVSKYdjKygraoUXOZnTevPl8/oEDB3bwiUajceM7oJYUw8DhcDweTyKRCAaD\nTqcTXZdFBk6lUolEong8HggE0KCVweJyuVarVafTzc7OBgIBhUJhNBpRzcMwoPOx9Or1es1m\nE+2oDAl1+qtUKqFEBTkb9iUq/X4/kUjE43GqPbFMJnO73agym41wHHc4HNlsNhKJ2Gw21KkJ\nGbhTg1bC4bBOpzMYDOgK9ADx+XyHw1Gr1XK53MzMjEqlMhgM6LgRMkrq9ToAoERleORyeTKZ\n7PV6KCdH1sWmRKVUKn3729++99575+fn13zIYrF88YtfvPXWW9GrCbtgGGY2m3k8XjKZbDQa\nBoOB7oiQUXP6oJVKpYIGrQycSCTyeDwrKyu5XG56elqr1er1enTiHBkN9Xqdx+Oh5/PwUKPV\nVlZW5HI53bEgTMSaRGVubu6iiy5KJBJut/vKK6+0Wq1UYeLKykosFnv++ee/+c1vPvzww7/+\n9a/RBiLraLVaLpebSCRarZbVakXXvJGBowatUN3A0KCVYZBKpVKpdGlpaXZ2dmFhQafTabVa\ntLxD2K5Wq6ELoEOF47hUKi2XyyhRQdbFmkTltttuy2azDz300DXXXHPmR7vd7j333HPTTTfd\nfvvtd9xxx96Hh+ySXC73eDyxWCwSiTidTrS+QQaOy+V6vV40aGWolEqlQqFYXFzM5/OFQgGl\nKwjbLS8vo63+YVMoFOl0ut/vo8uUyJlY8z79i1/84oYbblg3SwEAgiBuvPHGP/uzP3vkkUf2\nODBkUEQikc/na7fboVBo48k2CLJjWq3W6/VWq9VAIECdPkcGC8MwjUZz4MABs9lcLBanpqZy\nuRw12xtB2KVarXY6HXSlf9hkMlmv16MKjxFkDdYkKsVi0el0bnyf8fHxQqGwN/Egw8Dlcn0+\nH0mSwWBwdXWV7nCQ0UQNWuHz+cFg8MyCN2QgMAxTqVSTk5Nms7lU+v/t3XlwpHd95/Ff3/el\nPtXqQ/c5HoM941RwvBzGiSEkNtdiSAoSY4KBHJDAbpICTKiwyW68uSqEQGFCTBU2eCscC/aS\nQGwv59pc9ugc3d2j7la31JdaavW9fzwgxHg8npElPU+33q8/VNLTUus7o0eP+vP8jm/u3Llz\n8Xi8VqvJXRdwFfL5vNVqZXPzo6bRaGw2W6FQkLsQKFHbBJVgMPjUU09d/nN+9KMfMUTb7jQa\nzdDQkN1un5uby+fzcpeDzqTRaAYGBsLhsLQhGCN4R0SKK6dOnert7S0Wi5OTk8QVtBEWThwb\nm83GiAouqW2Cyu233/7QQw/de++9l2zOuL29fc8993zpS196wxvecPy14XCpVKre3l6/37+0\ntMQNbxwdj8czMTEhhJient7Y2JC7nE7mcrkmJiaIK2gjOzs7lUqFoHI8rFZruVxmjiieqW0G\nND/0oQ9985vffN/73vfhD3/4hhtuCIfDVqu11WqVSqXV1dUnnnhiZ2fnpptuev/73y93pTgc\nwWDQYDCsrq5WKhX65OCI6PX64eHhdDodi8Xy+Xw0GqUNyNFxuVwulyuXyyUSiY2NDY/HEwgE\n+A+HMuXzeYvFotfr5S7kRLBYLGq1ent7W9qtGNjTNkHF6XR+97vf/ehHP3r//fc/9thjjUZj\n7yGdTnf99dffeeedd955J9vLdBK3263X6xcXF6vVal9fH3s04Yj4fD6bzbaysjI9PR2NRrmH\neqSkuJLNZpPJpBRX/H4/LwehNLlczu12y13FSaFSqSwWS6lUIqjgIm0TVIQQer3+Pe95z3ve\n857d3d14PC5NZ7Tb7ZFIhD9yncpms42Ojs7Pz58/f35gYICbrzgiJpNpdHR0fX19aWnJ6XRG\no1Huehyprq6urq6uXC6XTCYzmUxXV5ff76dhBRSiWCxWKhUaLh0nq9VaLBblrgKK005BZY/R\naBwaGpK7ChwTo9E4Ojq6uLg4Nzc3ODhoNBrlrgidSaVSBQKBvaGV3t5em80md1EdThpdKZVK\nqVRqenraarUGAgFuqUJ2yWSyq6uLe6DHyWq1plKpZrPJ7Ansx9mANqDT6YaHh00m0+zsLBuD\n4EhJmxd3dXXNz8+vrq42m025K+p8Vqt1cHBwbGzMYDAsLi7OzMxsbm62Wi2568IJtbW1tb29\nHQgE5C7kZLFarUKI7e1tuQuBshBU0B7UanV/f7/b7Z6fn9/c3JS7HHQytVrd09MzODhYLBan\np6dLpZLcFZ0IZrO5t7f31KlTVqs1FotNTk6m02mCIo5fKpVyOp2M3h8ztVptNpu53uIiBBW0\nDZVKFQ6HQ6HQ6upqIpGQuxx0OLvdPj4+brPZzp8/v7a2xg3+46HX68Ph8OnTp/1+fyqVevrp\np9nLGMdpe3u7WCwynCILq9XKpAlcpC3XqOAk8/l8er1+eXm5Wq1Go1GVSiV3RehYGo1G2gRs\ndXW1UCj09vaazWa5izoRNBqNz+fzer3ZbDaVSkmr7QOBADe5cdSk4RR+02VhtVozmUyr1eIv\nO/YwooL243Q6h4eHi8Xi/Pz8/o2qgaPgcDjGx8cNBsPc3FwqlWJo5dhIje0nJib6+/t3d3en\npqaWlpaYGYKjs7Ozk8/nGU6Ri9VqbTabOzs7chcCBSGooC1JK57r9frc3Fy1WpW7HHQ4rVY7\nMDDQ29ubSqXm5uYqlYrcFZ0sTqdzdHR0ZGSk1WqdP39+enp6Y2OD5Ss4XK1Wa2VlxeVyWSwW\nuWs5obRarclk4mYE9iOooF3pdLqRkRGdTjc7O8sNGBwDl8s1Pj6uVqunp6fT6bTc5Zw4Vqt1\nYGDgmmuucTqda2trTz/99Orq6u7urtx1oUMkEolarRaJROQu5ERjmQouQlBBG9NoNIODg3a7\nfW5urlAoyF0OOp9erx8eHg6Hw2tra/Pz8yzyPn46nS4YDJ4+fToajUrzwebn53O5HFPy8Hzs\n7Oysr69HIhGtlrW7crJarYyoYD9+IdHeVCpVb2+vXq9fXFwMhUI+n0/uitD5PB6P1WqV+kKG\nw2HaVx8/lUolNYvc2dnJZDIrKysajcbj8fh8Pl5o4mpJk766urpcLpfctZx0Vqu10Wjs7u6y\ncwYkXNDRCYLBoNFoXF1dLZfLkUiEDUNw1IxG48jISCqVWllZyWazkUiEJtayMJvN0Wg0FApt\nbm6ur69LWzb5fD6peRxwJdbW1ur1ejgclrsQCL1er9FoCCrYw9QvdIiurq6RkZFisTg3N8eE\nHBwDlUrV3d09MTHRbDanpqZSqZTcFZ1c0nbGp06d6u/vbzQac3Nzs7Oz2WyWBfd4TqVSKZ1O\nR6NRjUYjdy0QQgiDwcDaM+whqKBzmM3m0dFRIcTMzMz29rbc5eBEMBgM0qoVaUMw/r7KSKVS\nOZ3OoaGhiYkJi8USi8WefvrpWCzGZht4Nru7u4uLix6Px+FwyF0LfsJoNLKzIvYQVNBRpK3A\n7Hb7+fPnNzc35S4HJ4XH45mYmNBqtTMzM4lEgoXd8jIajVJ7+2g0WqlUZmZmpCGver0ud2lQ\nkFqtNj8/b7FYmPSlKEajkTs+2MMaFXQaaXm91WpdXV3d2dnhLxCOh06nGxgYyOVysVgsn89H\no1G6MchLrVZLC+6r1Wo2m93Y2EgkEna73e12O51OVrKdcI1GY35+XqfT9ff3czIoClO/sB9B\nBZ3J4/Ho9fqlpaVKpdLX18fkYxwPl8tls9nW1tbm5ua8Xm9PT49azcC1zPR6fSAQCAQCxWIx\nm81KW4S5XC6Px2MymeSuDjJoNpsLCwtCiKGhIX5DlcZoNNbr9Xq9zg5+EEz9Qgez2+1jY2OV\nSmV2dpbbMzg2Wq02Go0ODAzk8/np6WmalymH3W7v7e09ffp0MBgslUrT09MzMzM0uT9pWq3W\n0tJSrVYbGhriHpYCSft9sUwFEoIKOihMMNEAACAASURBVJnBYBgdHTUajbOzs3SExHFyOBzj\n4+MOh2N+fn5lZYXVEcohdVwZGxsbGxuzWq1Sk/uVlZViscjioo7XbDaXl5d3dnaGhoZ0Op3c\n5eAS1Gq1Tqfj9iIkDKuhw2k0moGBgUQisbi4GAwGA4GA3BXhpNBoNOFw2OVyra6uSq0haSen\nKGaz2Ww2h0KhfD6/ubm5sLAgTQnr6uqiDUtHqtVqi4uL0liKwWCQuxw8Kzb+wh6CCk6EYDBo\nMplWVlbK5XI0GmVSMo6N1WodGxtLpVLLy8ubm5vRaJT7uIqy1+S+0Wjk8/lcLnf+/HmtVisd\nJLF0jJ2dncXFRZ1ONzo6yu+gwrHxF/YQVHBSuFwug8GwuLg4Nzc3MDBAH3EcG7VaHQwGpaGV\nqampUCjk8XjkLgoX02g0brfb7XbX6/VCoZDNZufm5vR6vdPpJLG0u1wut7Ky4nQ6uVHVFgwG\nQ6lUkrsKKAJBBSeI2WweGxtbWlqanZ0dGBhg91gcJ5PJNDIykslk4vF4NpuNRqNMPlEmrVYr\nJZZarZbL5XK5XDqdNhgMLpfL7XZLK33xfDQaYmND1GrC6xXH8EuQSqUSiQRTf9sIU7+wh6CC\nk0Wr1Q4NDcVisbm5uWg06na75a4IJ4hKpfL5fA6HQ1q10t3d7ff76eGgWDqdzufz+Xy+SqWS\ny+Wy2WwqlTKbzU6n0+FwmM1muQtsP9Wq+PrXxQ9/KBqNnxzp6xOvfKU4oiHGarUai8VKpdLA\nwAC959uI0WhsNpvVapW5DyCo4MRRqVRSMz6pI2QoFOKVIo6TwWAYHh7OZDJra2tSa0i6eSic\nwWCQOrHs7u5ms9lcLpdIJPR6vcPhcDqdNpuNa8iVqNfF/feLclm87nUiGhU6nUilxDe/Ke67\nT9x5p/B6D/N7tVqtTCaTSCSMRqO09+NhPjuOmF6vV6lUu7u7BBUQVHBCeTweo9G4uLi4u7vb\n39/Pbvo4Zl6v1+FwxGKxmZkZn88XDAaZOq98RqMxGAwGg8FqtVosFvP5/MLCgkqlstls0jAL\nq7Qv44knRKEg7r5b7M26DYXEHXeIBx8UDz8s3vKWQ/tG5XJ5dXV1d3c3GAx6vV5iZNtRqVRa\nrZZd3SEIKjjJrFbr6Ojo4uLizMzM4OAgt9xwzPR6/eDgYKFQiMVi2Wy2p6eHuYjtQq/Xezwe\nj8fTbDa3trby+XwikVhdXTWbzdIwCxPDnuncOXH2rLhobaBKJV7yEvGJT4hSSTz/DQuazWYy\nmVxfX7fb7ePj49yPb18ajaaxN0EQJxhBBSea1BFyeXl5dna2t7fX6XTKXRFOHIfDMTExkUql\nVldXNzc3I5EImbmNqNVqh8PhcDhardb29nahUMjlcslk0mAwOJ1Ou91utVoZK5PkcuKSq9n9\nfiGEyGafb1DJ5XIXLlwQQrAipQNoNJpmsyl3FZAfQQUnnVqtHhgYSKVSS0tLbAsDWUj7F7vd\n7lgsNj097fV6e3p6eHXbXlQqldVqtVqtPT09lUoln88XCoV0Oi2EsFqtNpvNZrNZLJaTPA1J\noxG12iWOSxN8tAd9PdJqtTY3N9fX16vVqtfrZRZlZ1Cr1YyoQBBUAEkgEDAYDHSEhIwMBsPQ\n0JA0E6xQKITDYe4KtymDweD3+/1+f7PZLJVKe3PD1Gq1FFrsdvsJnBsWDIrFRTExcfHxxUWh\n1R5kMX2z2dzY2FhfX280Gm63OxAIsEaoYzD1CxKCCvATLpfLaDQuLCzQERIykmaCJZPJxcVF\nu90eiUQ4FduXWq222+12u72np6fRaGxvb29tbeVyubW1Na1Wa7FYrFbryQktv/AL4oEHxPi4\nGBz82cFiUfzbv4nrrhNXFTHq9Xo6nc5kMkIIr9fr9/vZEKXDqNVqpn5BEFSA/UwmEx0hITu1\nWt3T09PV1RWLxaampvx+f3d390meMtQZNBrNXmip1WrFYnFra0vapVqv11utVovFYrFYzGZz\np/6sBwfFTTeJBx4Qp06JSETo9SKZFD/+sfD7xctffkXP0Gq1isWi1IVTp9NJ+0906n/XCafR\naNj1C4KgAlyEjpBQCKmT/ebm5oULF7LZbCQSsdvtcheFw6HT6dxut3R5qVQqxWJxe3s7k8nE\n43GVSmU2my0/ZTiGzu3H6CUvEdGo+P73xXe+85PO9C97mbjuOnH5ybatVqtUKmWz2Xw+32w2\n7XZ7X18fe590No1GQ3N6CIIK8Ez7O0KWSqVIJMIdO8jF7XY7nc5EIrGwsMBMsI5kMBi8Xq/X\n6xVCNBqNcrlcKpWk1+X1el2j0Vj20R54ybli9PWJvr4r/eRSqSSNn9TrdYvF0tPT43K5mOV1\nEjD1C5K2v+QBR2SvI2S1WqUjJGSk0WjC4bC0J9jU1FR3d7ff7yc8dySNRiNtHSZ9WKlUtre3\nt7e3i8ViKpVqtVpGo9FkMu29NRqNnXcm7EW1ra2ter1utVqDwaDT6eyAkIYrx2J6SPi1B54V\nHSGhHGazeXR0dP9MMOvzb48HZTMYDAaDoaurSwjRarV2dna2t7d3d3e3trbS6XSj0VCpVAaD\nYS+6mEwmg8HQdtFFakFT+qlGo2EwGKR84nA42MjrZCKoQEJQAS6HjpBQFLfbbbfb19bW5ubm\n3G53KBTiNvMJoVKppNlfe0dqtVq5XN7d3S2Xy/ujizTSotfr9Xq9wWDQ6XR6vV4550mr1apW\nq7u7u5VKRSp+Z2en2WyaTCabzeZ2u61WK+EETP2CRClXLkCxpI6QiUSCjpBQAp1O19vb6/F4\nYrHY5ORkMBj0er1tdxMdz59Op9PpdPu3WNgfXcrlcqFQqFar0qs9tVqtfwadTqfRaDQazVF0\njmq1WvWf2osllUqlUqm0Wi21Wi2NF9lstkAgYLVaj2F6bbMpMhmRzQqrVfh8orP2Keg0jKhA\nQlABrkgwGDSZTHSEhEJYrdaxsbF0Or22tpbNZsPhMLtp45nRRQjRaDSqP69YLFar1Vqt1mq1\npM9RqVSafbRa7d77V5KB6/V6o9G46O3e7XCVSqXX66VxHofDYTAYpAGfQ//n12riBz8QKysi\nmxU2mwiFxNmzYm+C5NSU+NrXxNaWMJtFuSzUanHDDeJlLxOKGWrCz1Gr1a1Wq9VqcRfmhOMX\nFLhSLpfLYDAsLS3NzMwMDAywZAXyUqlUfr/f5XJduHBhdnbW7Xb39PQwZwYX0Wg00vKVi45L\nIx6NZ1Gv12u1WqPReM7pNyqVSgo2er1+L+Rc9PYYXmsWi+L++0W1KiYmxMCAKBbF7Kx48knx\nxjeKcFg89ZT48pfFi18szpwRZrNoNMT8vHj4YZHLiTe84ahLw0FIKZqUAoIKcBXMZvPY2Njq\n6urMzEw0GpUWuQIy0uv1/f3929vb8Xh8cnLS5/N1d3cz4ofnpFKppBEYuQs5BK2WeOghYbOJ\nO+742YSul71MPPywePBB8fa3i//zf8TLXy5+8Rd/8pBGI0ZHhccj/umfxPnzYnhYrsLxrBqN\nBpttQgjBHzPg6mg0mv7+/p6enpWVldXV1b25E4CMLBbL6Ohob29vNpudnJzc2NiQuyLg+MTj\nYm1N3H77zy07UanErbcKnU489phoNsUNN1z8VR6PGB0V09PHWSmuFEEFEoIKcBA+n294eLhQ\nKMzOzlarVbnLAYQQwuVyTUxM+Hy+eDw+MzNTKpXkrgg4DhcuCL9fOBwXH9doxMCASKWEyyUu\n+aLX6xX5/DEUiKtGUIGEoAIckNVqHR8f12g0MzMzxWJR7nIAIYRQq9WBQGBiYsJkMs3NzS0t\nLRGk0fFqtWfdwstgEM2meLZfgkpFdMTctw5EUIGEoAIcnFarHRoa8ng88/Pza2trcpcD/IRe\nr+/t7R0dHa3ValNTU2tra2z0iQ7mdIqNDXHJebiZjPD5RC4nMpmLH2q1xMKCCIWOoUBcNYIK\nJAQV4HlRqVQ9PT0DAwOZTGZhYaFer8tdEfATFotlZGREWrgyNTXFwhV0qqEhUa2KH/3o4uOJ\nhFhcFGfOiMFB8cUvinL5Zw+1WuLrXxfForj++uOsFFeKoAIJu34Bh8DpdI6NjS0uLs7MzPT3\n99PRAsrhcrkcDkc6nb5w4UImkwmHw9a91hJARzCbxctfLh5+WOzuihe+UJhMolYTc3PikUfE\ntdeKSES8+tXiM58R//APYmJCeL1ia0ssLIhsVvzn/yz4bVCmRqOhpccNCCrAYTEYDKOjo/F4\nfG5uLhQK+Xw+uSsCfkJauOJ2uxOJxNzcnMPhCIfDBvpyo4PccIPQ68XXvy7+/d9/0tJRqxW/\n+IvixS8WQgizWdx1l/jhD8XyslhZETabGBgQd9whfr43JhSk0WhwjYIgqACHSK1WR6NRq9Ua\ni8W2t7dpYA9F0el00WjU6/XG4/GpqSmv1xsMBplcASHE7Kz4wQ/E+rqo14XPJ8bHxZkzou2u\nXi94gTh9WqTTIpcTdrvweoVe/7NHNRpx9qw4e1a++nA1mPoFCUEFOGRut9tkMtHAHspkNptH\nRkYKhUI8Hs9ms93d3V6vl/bPJ1arJR55RPzwh+KFLxSnTwutViST4rHHxMyM+I3fEG039Uat\nFoGACATkrgPPG0EFkna7CAHtwGw2j46OrqyszM7ORqNRl8sld0XAz3E4HHa7PZPJJBKJzc3N\nUChks9nkLgoymJwUP/qR+K3f+tnmV2Nj4swZ8alPiUcfFbfcImtxOMEIKpC028gu0Ca0Wu3g\n4GAgEFheXo7H4zSwh9KoVCqfzyd1XDl//vzS0tLu7q7cReG4PfGEOHv24i167XZx883iBz8Q\nbGoNuRBUICGoAEcoEAgMDQ3lcrnz58/XajW5ywEuptPpent7x8bG6vX69PR0LBbjRD1RUinR\n33+J4319olIRudyxFwQIUa1Wm80mi+khCCrAUbPZbKOjo61Wa3p6mgb2UCaz2Tw8PDw4OLi9\nvX3u3LnV1VU6Ap0ErZZoNsUlb1tLq1MYUYEsyuWyWq0mqEAQVIBjoNfrR0ZGPB7PwsJCIpGQ\nuxzg0ux2+9jYWF9f39bW1uTkJP3sO55KJbq6RCp1iYdSKaFWC6fz2GsChCiXyyaTiU0+IFhM\nDxwPqYG9yWRaXV3d2dnp6+tj9i2UyeVyOZ3Ozc3NRCKxsbHh9/v9fj+vGDrVNdeI731PXHut\nMJt/drDZFI8+KkZGBHe0IQspqMhdBRSBERXg+HR1dY2NjVWr1enp6e3tbbnLAS5NpVJ5PJ5T\np075/f5UKjU5ObmxsSF3UTgSv/iLwmoV990npqdFqSR2d8XSkrj/fpHNil/5FbmLw0m1s7ND\nUIGEERXgWBmNxtHR0dXV1fPnz4fDYY/HI3dFwKVJ/ew9Hs/6+no8Hk+n093d3ey13WF0OvGW\nt4hvfEN88YtC2kZBrRbDw+Jtb6NrO+TRarUqlQpBBRKCCnDc1Gp1X1/fxsZGLBYrlUqRSIQG\n9lAsrVbb09Pj8/kSicTy8nI6ne7p6bFarXLXhUOj14tXvELceqvIZkWtJrzeSy+vB45HuVxu\ntVoEFUh4eQTIw+PxjI6Obm1tzc3NVSoVucsBLken00Wj0fHxcZ1ONzc3Nz8/Xy6X5S4Kh0ml\nEm63CARIKZBZuVzW6/VaLXfSIQRBBZCR2WweGxvTarUzMzM5GhZA8YxGY39//+joqBBienp6\naWmJjA3gcLGSHvsRVAA5abXaoaEhGtijjVgslqGhoZGRkVqtNjU1tbq6So9IAIeFoIL9CCqA\n/AKBwMDAQDabnZ+f5zUf2oLVah0ZGZF6RNJ0BcBhYcsv7EdQARTB4XCMjY01m82ZmZlSqSR3\nOcAVkXpEhsPhzc3NqampdDrNqCCAA6vVavV6naCCPQQVQCmkBvYul+v8+fOpSzaLBpRnf9OV\nZDI5OTmZTqebzabcdQFoP8ViUavVGo1GuQuBUrCpAqAgKpUqHA6bzeZYLLazsxONRmlgj7ag\nVqv9fr/X693Y2EilUslk0u/3+3w+tt4GcOXy+bzT6VSpVHIXAqXgTwigOG63e3R0tFwuz8zM\n0MAebUStVvt8vlOnTnV3d6fT6XPnzqVSKUZXAFyJZrNZLBadTqfchUBBCCqAEplMprGxMYfD\nMTc3l0gkmPePNvLMuJJIJFhqD+DyCoWCEMJms8ldCBSEqV+AQqnV6nA4bLVaV1dXS6VSX1+f\nTqeTuyjgSklxxev1bm5uJhKJTCbj9Xr9fj+zGQFckjTvi/mi2I+zAVA0l8s1Pj7earWmp6el\nu01AG5GW2l9zzTU9PT0bGxuTk5OMruD5qNVEIiHOnxe5nGCkuZO0Wq1CocC8L1yEERVA6fR6\n/fDwcDKZXFxc9Hq9oVCIhYZoL1Jccbvdm5ubyWSS0RUcQL0uHn1UPPGEqNeFTidqNeFyiVe8\nQgwNyV0ZDkOxWGw2m3a7Xe5CoCwEFaANqFSqYDBos9mWl5e3trb6+vrYZh5tZy+uZLPZZDKZ\nTqe9Xm8gECCu4Dm1WuJ//S+RSIjXvEYMDAi9XhQK4oknxIMPite/XoyOyl0fnrd8Pu9wOLga\n4CLtHVSq1epTTz1VKpV6e3v7+vrkLgc4WjabbXx8fGVlZXZ2tqenx+fzyV0RcNVUKpXb7e7q\n6pLiijS6QlzB5c3OisVFcffdwu3+yRGHQ9xyi9DpxFe/KoaGBKdPW2u1Wvl8PhQKyV0IFKdt\n1qj8+Z//+aOPPrr/yMc//vFAIHDDDTe87GUv6+/vP3PmzI9//GO5ygOOh1arHRwcDIfDa2tr\nS0tLzPVHm5LiysTERDgczuVy586dW1tbq9frctcFhZqaEhMTP0spe170IlEui9VVOWrC4SmV\nSo1Gw+FwyF0IFKdtgsoHPvCBr33ta3sffvWrX7377rt3dnZe/epXv/3tb7/xxht/8IMfvOQl\nL1lcXJSxSOB4eDye0dHR3d3d6enpUqkkdznAAe2PK/l8/ty5c/F4vFaryV0XFCefF5ccQtbr\nhdMpcrljLwiHKp/P22w2rba9p/ngKLTrOfGe97zH4XB897vfHRsbk47867/+6+te97qPfOQj\nn/rUp+StDTgGJpNpdHR0bW3t/PnzgUCgu7ubFfZoUxdNBtvY2PB4PH6/X6/Xy10alEKrFdXq\npR+qVgU7t7e1ZrOZzWaDwaDchUCJ2mZEZb9MJjM/P/+ud71rL6UIIV7zmtfcdttt//Zv/yZj\nYcBxkhqt9PX1pdPp+fl57kOjre2NrkSj0VKpNDk5uby8vLOzI3ddUIRQSMzPX2I/4lRKbG0J\nlja0tUwmI/36y10IlKgtg8ru7q4QYn9KkZw6dSqdTstRESAbGq2gk6hUqq6urrGxseHh4Uaj\nMTMzMzc3x4mNM2dEOi2+9a2fO1guiy9/WQwPi64umcrC89ZqtdbX130+H30ecUltOfUrGAw6\nHI4LFy5cdDyRSNhsNllKAmREoxV0HqvVOjg4WC6X19fXFxcXjUaj3+/v6uri3D6ZnE7xmteI\nf/1XsbAgBgeFxSIyGXHunLDZxG23yV0cnoeNjY1Wq+X1euUuBArVTvk1Fot9//vfX1hYyOVy\n73znO++77779swJmZ2c/97nP3XjjjTJWCMhFarQyNDSUy+VmZmbK5bLcFQGHwGQy9fb2XnPN\nNU6nMx6Pnzt3jsb2J9bYmHjHO0R3t5ifF9/+tshmxU03ibe+VZjNcleGg9obTmF3cjybdhpR\neeCBBx544IH9Rx555JHXvva1QojPfvazv/M7v1Mulz/wgQ/IVB0gPxqtoCPpdLpgMOj3+zc3\nN9fX19PptNvtDgQCOtZQnzBdXeLWW+UuAocnm83W63X+VOEy2iao/PM//3N+n0KhkM/nXS6X\n9Gg+n3c6nQ8++ODZs2flrROQl9RoZWNjIx6Pl0qlaDTKnSp0Bo1G4/P5vF5vNptNpVKZTKar\nqysQCBiNRrlLA3DVWq1WKpXyer38kcJltE1Q+a3f+q3LPPrmN7/57rvvZiUWIPF4PBaLZXl5\neXp6uq+vz2q1yl0RcDik3YHcbnehUEin01NTUw6Hw+fz2e12uUsDcBVyuVy1WvX7/XIXAkVr\nm6ByebwOAy5CoxV0NofD4XA4dnZ20un0wsKCyWTy+XystgfaRSqV8ng8NHnE5TEEAXQsGq2g\n45nN5t7e3omJCavVGovFpqam0ul0s9mUuy4Al5PP53d3dwOBgNyFQOk6J6gsLi6+/OUvf/nL\nXy53IYCy0GgFHc9gMITD4WuuuaarqyuZTJ47dy6ZTJLMAWVqtVrJZNLj8bAfBp5T54y4bW1t\nfeMb35C7CkCJaLSCk0Cr1QaDwUAgsLGxkU6nk8mky+Xy+XwWi0Xu0gD8zPr6eqVSGRgYkLsQ\ntIHOCSqjo6Pnzp2TuwpAoaRGKzabbXl5eWtrq6+vz2QyyV0UcPjUarXP5/P5fMVicWNjY25u\nzmQyeb3erq4uNlwBZLe7u5tMJiORiF6vl7sWtIHOCSpGo/HUqVNyVwEoGo1WcHLY7Xa73V6p\nVDY2NtbW1i5cuOB2u30+n8FgkLs04IRqtVorKys2m83tdstdC9pD+wWVVqu1vLy8tLS0tbUl\nhHA4HENDQ+Fw+GDPFovFbrnllnq9fpnPkb4RU2XQGWi0ghPFYDD09PQEg8F8Pr++vj45OWm3\n2z0ej9Pp5KoOHLNkMsmkL1wVVavVkruGK5XL5T7ykY985jOfSafTFz0UiUTuuuuu9773vVc7\nm6VWq/3v//2/G43GZT5nZmbmnnvuqVQqDFOik5TL5eXl5UajQaMVnBw7OzuZTCabzep0Oo/H\nw+6owLHZ2dmZnZ3t6+vb69YNhahWqwaD4dvf/vaLXvQiuWu5WNsElWQyeeONNy4vLw8NDd14\n443RaFRaH1ksFhcXFx9//PFEInHttdc++uijh/4L8J3vfOfGG28kqKDzNJvNeDy+ubkpLUGW\nuxzgmNRqtc3NzUwmU6/XXS6X3+9nyRZwpFqt1szMjMFgYDhFgZQcVNrmTtIHPvCBCxcufP7z\nn3/961//zEcbjcbHP/7x3/3d3/2zP/uzv/3bvz3+8oB2pFaro9GozWaLxWLFYrG3t5c0jpNA\np9MFAoFAICC1t5+enjabzfSLBI5OIpGo1WrDw8NyF4I20zYjKt3d3a985Svvu+++y3zOHXfc\n8Z3vfCcWix3ut2ZEBR2vWq2urKzs7OyEQiGPxyN3OcCx2t3dzWQyGxsbGo3G7XZ7vV6u9sAh\n2t7enpub6+/vdzqdcteCS1DyiErb7NW4ubn5nMOFY2Nj6+vrx1MP0EmkRiuhUCgej9PDHieN\n0WgMh8OnT58OBoOFQmFycnJpaalYLMpdF9AJms3myspKV1cXKQUH0DZTv4LB4FNPPXX5z/nR\nj34UDAaPpx6g83g8HqvVurKyMjU1FYlEurq65K4IOD4ajUZaXl8sFtPp9Pz8vMlk8ng8XV1d\nLLgHDmx1dbXZbB54d1accG0zonL77bc/9NBD9957b6VSeeaj29vb99xzz5e+9KU3vOENx18b\n0DGMRuPIyEggEFhZWVlaWrr8zt1AR7Lb7YODg9dcc43T6VxfX3/66acXFxcLhUK7zJQGlCMe\njxcKhcHBQfbBx8G0zRqVfD5/8803//CHP7TZbDfccEM4HLZara1Wq1Qqra6uPvHEEzs7Ozfd\ndNPDDz986ButskYFJ5C0eXG9Xo9Gow6HQ+5yANmUSqXNzc1sNqvRaFwul8fjYYsw4Eokk8lU\nKjU0NMQO+Aqn5DUqbTOc7XQ6v/vd7370ox+9//77H3vssf2dT3Q63fXXX3/nnXfeeeedRHbg\nUJhMptHR0WQyubi46Ha7w+GwWt02A7DAIbJarVarNRQK5XK5zc1NaYswr9frcrn4iwM8m0wm\nk0wm+/v7SSl4PtpmRGW/3d3deDwuNYy32+2RSORIxzoYUcFJViqVVlZWhBC9vb38vQF2d3c3\nNzc3NjaazabD4fB4PHa7Xe6iAGXJ5/NLS0uRSIRtJNsCIyqHzGg0Dg0NyV0FcCJYrdaxsbEL\nFy7Mzc35fL5QKESjCZxkRqOxp6cnGAwWi8XNzc2FhQWDwSBNCeNmFiCE2NraWl5e7unpIaXg\n+WvLoLLn3nvv/eIXv/itb31L7kKATqbRaKLRqMvlWllZ2dra6u3tNZvNchcFyEmlUjkcDofD\nITW539jYSCaTdru9q6vL5XIxTxInVrlcXlxc9Hg8fr9f7lrQCdo7qCwsLHz729+WuwrgRLDb\n7RMTE7FYbHZ2NhAIdHd3M7QC7DW539nZyWQysVgsHo+7XC6v10uex0lTqVTm5+cdDgebEeOw\ntHdQAXCcNBpNX1+f0+mMxWLFYrG3t9doNMpdFKAIZrM5Go3urbmfmZkxm80ej8flctGGBSdB\ntVqdn583m829vb1y14LOwdUTwNVxuVxWq3V1dXVmZqa7uzsQCMhdEaAUe10jpTX3yWQyHo/b\nbDapLTe7hKFTlUqlxcVFs9nc39/PYDsOEUEFwFXT6XSDg4MbGxvS/nvRaJRlxMB+0pr7np6e\nUqmUy+XW1tZWV1ftdrvL5SKxoMNsbGzEYjG32x2JREgpOFxtuT3xnnw+XyqVQqHQkX4XticG\nnk2lUllZWSmXy6FQiA1egGfTarW2t7dzuVw2m202mzabzeVysewe7a7VaiUSifX19VAo5PP5\n5C4HB8T2xEfF6XQ6nU65qwBOLoPBMDIykk6npVUrkUiE6fjAM6lUqr3GkcViMZfLxePxWCzm\ncDjcbrfdbuc+NNpOo9FYXl7e3t4eGhqy2Wxyl4POxEsKAM+Xz+ez2WwrKytTU1PRaJTbB8Cz\n2dvXuNlsbm1t5XK5paUllUrldDpdLheJBe2iUqksLCwIIUZGRthVBUeHoALgEJhMptHR0WQy\nubS05HQ6o9Eos/CBy1Cr1VJiCYfD+Xw+l8stLi5qNBqHw9HV1UW3eyhZsVhcWlqyWCz9/f1c\n6nGkCCoADodKpQoGgw6HY2VlhDvUrAAAGt1JREFUZXp6ure3l8kAwHPSaDRut9vtdjcaDSmx\nLCws6HQ6aYzFarXKXSDwc6Sl816vNxQKMQCIo0ZQAXCYLBbL2NhYMpmcn593u93hcJjlwsCV\n2EsstVpNWnafTqcNBoO0GtNisfCiEPKq1WrxeLxQKESjUbfbLXc5OBEIKgAOmVqt7unpsdls\nUq+Vvr4+WnQDV06n0/l8Pp/PV61Wc7lcPp9Pp9PSrDCHw2G325lsg+OXyWTW1takDVS4pOPY\nEFQAHAm73T4+Pn7hwoXZ2Vm/3x8MBrkfDFwVvV7v9/v9fn+9Xt/a2ioUCqurq81m02KxOBwO\np9PJImYcg3K5vLq6Wi6Xu7u7/X4/V3IcJ4IKgKOi0Wii0ajdbo/FYoVCoa+vz2QyyV0U0H60\nWq3Ud0Xqx1IoFDY3N6Xb2w6Hg6UsOCLNZjOVSqVSKbvdPjExQTc5HD+CCoCj5XK5pGlgs7Oz\n3d3dgUBA7oqAdrXXj6Wnp6dcLhcKhUKhkE6ntVotE8NwuLa2tmKxWKPRYEUKZERQAXDktFrt\nwMBALpdbXV0tFAq9vb0Gg0HuooD2ZjKZTCZTIBCo1+tSYlldXW21WlarVZoYxv1vHEytVltb\nW9vc3PR4PKFQiOgLGRFUABwTl8tlsVhWVlZmZmZCoZDH45G7IqATaLVaabswqYlkPp9PpVLx\neFxayuJwOFj6jCvUarU2NjakWYWjo6MWi0XuinDSEVQAHB+9Xj88PJxOp+PxeDabjUajDK0A\nh2WviaQQQlrKks/nE4mEVqu1/RTr73FJzWZzY2NjfX290Wh0d3f7fD4WzUMJCCoAjpvP53M6\nnaurq9PT036/v7u7m7+IwOGyWCwWiyUYDNZqtWKxuLW1lUqlYrGYXq+XEovdbtfpdHKXCfnV\n6/VMJpNOp1Uqlc/n83q9zPWCchBUAMhAr9cPDQ3lcrlYLJbP53t7e5mdAhwFnU4nTQwTQlQq\nla2trVKptLa2trKyYjAYpMRis9m0Wl4PnDi1Wk2KKBqNpru72+Px0J8XSsOFCYBspG1V19bW\npF4r3d3d/JkEjo7BYDAYDNLyMCm0FIvF1dXVRqOxF1rYN+wkqFQq6XR6Y2PDYDCEw+Guri6G\ntaFMBBUActLpdL29vS6XKxaL5XK5aDRqs9nkLgrofHuhpdVqlctlaXrYyspKq9UymUzSMIvV\nauXeQYfZ2dlJp9PZbNZisfT390srmgDFIqgAkJ/D4RgfH08kEvPz8263mw0xgWOjUqnMZrPZ\nbA4EAs1ms1QqbW1tbW1tra+vS21bLD/F9LD2Va/Xc7lcNpstlUpOp3N4eJgmoWgLXHQAKIJG\nowmHwy6Xa3V1dWpqKhKJOJ1OuYsCTha1Wi3N/hJCNBoNKbEUi8X19fVms2kwGPZCi9lsZrKQ\n8jUajVwul8vltra2tFqty+WKRCImk0nuutpbqyVyOdFsiq4uwYjjUSOoAFAQq9U6NjaWTCaX\nlpacTmckEuEmLiALjUbjdDql+wWtVmt3d3dnZ6dUKmUymXg8rlKpDAaD1Wq1Wq1ms5nXvooi\nddTZ3NzM5/MajcbhcAwMDNjtdrLl81SpiH//d/H006JWE0IIjUacOiV++ZcFe8EcHV4BAFAW\ntVrd09MjDa1MTk7SGhKQnUqlMplMJpNJ2j2s0WiUy+VSqVQqlS5cuFCv1zUajWUf7i/IQson\n0hCKSqVyOp3kk0NUqYhPfUq0WuLVrxahkFCrxdqaeOwx8clPire+VdAb84hwKQGgRGazeXR0\ndH19PR6P5/P5SCSi1+vlLgqAEEJoNBppLEX6sFKpbG9vb29vF4vFVCrVarWMRuPeDDGTycSK\n/CNVr9e3trby+Xw+n1epVA6Ho7+/n3xy6P7v/xX1unjb28Re09ThYdHXJ+67T3zjG+LXf13W\n4joXQQWAQqlUqkAgsLdqpbu7OxAIyF0UgItJG4h1dXUJIVqt1s7OjpRb1tfXK5WKEEKv10sD\nMkajUXpLdHmeKpVK6ad2d3fVarXD4ejt7XU4HPzfHpGnnxYvfenPUopEpxMvfrH44hfFq17F\nepUjQVABoGgGg2F4eHhjY+PChQuFQiEajRov+kMBQDFUKpU0liJ92Gg0KpVKuVze3d0tl8u5\nXE6KLjqdbn9uMZvNvLy+PGmZ0Pb2trQtW7Va1Wq1FovF7XZLO7MxfnKkqlVRKonu7ks81N0t\nqlWxtSXY6vkoEFQAtAGPx+NwOGKx2PT0tN/vDwaD/FUGlE+j0Uh7H+8duSi6FAoFosuzkVrc\nSMMmW1tb9Xpdp9NZrVa/3y/tYSB3gSeIdDI2Gpd4SDp44s/Wo0JQAdAedDrdwMBALpeLxWLS\n0IqF1YtAu3lmdKnX61Jokd5ms9l6va5SqXQ6nV6vNxgM0jt7OrXJUrVarVQqu7u7e2+lCGcy\nmaxWayQSsVqtOp1O7jJPKK1WeDxieVmEQhc/tLwsrFZBW5ojQlAB0E5cLpfdbr9w4cLc3JzX\n6+3p6eG2K9DWtFrt/qX5Qoh6vV4ulyuVSrVarVar29vb+Xy+Wq02m00hhEaj2Z9bdDqdwWCQ\n3mmXgVYpm10US5rNpkql0uv1RqPRaDQ6HA5pZKlTg1nbOXtWPPqoGBkRPt/PDuZy4vHHxZkz\nok1OvfZDUAHQZjQaTTQadTqd0tBKJBKR+tMB6AxardZms9lstouO1+v16s/b2dmpVqs1qauF\nEFJo0Wq1Wq1W8yykh46u+EajUa/X6/W69M5Fb2u12u7ubqPREEJI40VGo9HtdhuNRmlPgnbJ\nWifQ2bMiHhf33Seuv16EQkKlEomE+P73RTgsfumX5C6ucxFUALQlh8MxPj6eSCQWFha6urpC\noRCtG4DOJiWQZ67NaLVa+9OLlBNqtVrj5+3/kmcGmIONzTabzYvSyN5DKpVKCkV7b/V6vcVi\nkcKJwWBgNLi9qFTiNa8RTz8tfvxj8dRTotkUPp+4+WZx/fUMpxwh/q4DaFcajSYcDkv7F09P\nT0vvy10UgOOmUqmk4YjLf9peYpFCxTMd4FtLS272p5G9t0zZ6jwqlbj2WnHttXLXcZIQVAC0\nN6vVOjY2lkqllpeXNzc3o9Eo600BPBPhAWg7DDsCaHtqtToYDI6NjdXr9ampqY2NDbkrAgAA\nzxdBBUCHMJlMIyMjwWAwHo+fP39e2tkTAAC0KYIKgM6hUql8Pt/4+LgQYnp6OpVKtVotuYsC\nAAAHQVAB0GkMBsPw8HAkEllfX5+dnd3Z2ZG7IgAAcNUIKgA6k9vtHh8f1+v1s7OzyWSSoRUA\nANoLu34B6Fg6nW5gYCCXy8Xj8Ww2Gw6HaQ0JAEC7IKgA6HAul8tut0utIe12eyQS0ev1chcF\nAACeA1O/AHQ+qTXk6OiotH9xIpFgJhgAAApHUAFwUpjN5tHR0Ugkkslkpqeni8Wi3BUBAIBn\nxdQvACeL2+12OBzJZHJhYaGrq6unp4dO9gAAKBAjKgBOHK1WK80EK5fLU1NT6XSamWAAACgN\nQQXACSXNBAsGg4lEYnZ2dnt7W+6KAADAzxBUAJxcUif7iYkJk8k0Ozu7srJSr9flLgoAAAhB\nUAEAnU7X29s7PDy8vb0tzQSTuyIAAEBQAQAhhBA2m218fLy7u3ttbW1ubq5cLstdEQAAJxpB\nBQB+Ym8mmMFgmJmZicfjjUZD7qIAADih2J4YAH6OXq/v7e11uVzxeDyXy/X09LjdbrmLAgDg\nxCGoAMAlOBwOm82WSqVWV1c3NzcjkYjRaJS7KAAAThCmfgHApanV6mAwODExoVKppqen4/F4\ns9mUuygAAE4KRlQA4HIMBsPQ0FChUIjFYvl8PhQKuVwuuYsCAKDzMaICAM/N4XBMTEy43e7l\n5eWFhYVKpSJ3RQAAdDiCCgBcEWkm2Pj4eLPZnJ6eTiQSrVZL7qIAAOhYBBUAuApGo3F4eDgS\niWQymampqWKxKHdFAAB0JtaoAMBVc7vdTqczkUgsLCzY7fZIJKLX6+UuCgCAjsKICgAchEaj\nCYfDo6Oj9Xp9amqKmWAAABwuggoAHJzZbB4dHZVmgk1PT29tbcldEQAAHYKpXwDwfLndbofD\nkUwm5+fnu7q6QqGQVsvVFQCA54URFQA4BFqtNhwODw8P7+zsTE5OZjIZuSsCAKC9EVQA4NBY\nrdaxsbHu7u61tbWZmZlSqSR3RQAAtCuCCgAcJpVK5ff7JyYmTCbT3Nzc0tIS3SEBADgAggoA\nHD6dTtfb2zs2Nlar1aampuLxeKPRkLsoAADaCcs9AeComM3mkZGRQqEQj8ez2Wx3d7fX61Wp\nVHLXBQBAGyCoAMDRcjgcdrs9k8kkEolMJhMKhRwOh9xFAQCgdASV5yY1nDYYDHIXAgAAABw+\n6eWu0qhopXwlnnrqqXq9LncVOEIPP/zw3/zN3/z93/+93IVAEe688853v/vdp0+flrsQyO/T\nn/709vb2u971LrkLgfyWl5c/+MEPfvKTn+TeJYQQf/qnf/r617/+TW96k9yFHAKtVnvttdfK\nXcUlEFQAIYT47Gc/+773vW9tbU3uQqAIJpPpC1/4wq233ip3IZDfO9/5zmw2++CDD8pdCOT3\n5JNP3nDDDaVSyWKxyF0L5Hf69Om3ve1tv/d7vyd3IZ2MXb8AAAAAKA5BBQAAAIDiEFQAAAAA\nKA5BBQAAAIDiEFQAAAAAKA5BBQAAAIDiEFQAAAAAKA5BBQAAAIDiEFQAAAAAKA5BBRBCCL1e\nr9fr5a4CSsH5gD2cDNij1+vVarVWq5W7ECgCF4djoGq1WnLXAMivXq8nEolIJCJ3IVCE5eXl\naDSqVnMrB6JQKNTrdbfbLXchUISlpaX+/n65q4AirK2teTweg8EgdyGdj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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_25_0.png" } }, "output_type": "display_data" } ], "source": [ "iplot(function() {\n", " post <- extract.samples(m_bc_vis)\n", " a2 <- apply(post$a_district, 2, mean)\n", " b2 <- apply(post$b_district, 2, mean)\n", "\n", " plot(a2, b2,\n", " xlab = \"intercept\", ylab = \"slope\",\n", " pch = 1, col = rangi2, ylim = c(min(b2) - 0.1, max(b2) + 0.1),\n", " xlim = c(min(a2) - 0.1, max(a2) + 0.1)\n", " )\n", "\n", " Mu_est <- c(mean(post$a), mean(post$b))\n", " rho_est <- mean(post$Rho[, 1, 2])\n", " sa_est <- mean(post$sigma_intercepts_slopes[, 1])\n", " sb_est <- mean(post$sigma_intercepts_slopes[, 2])\n", " cov_ab <- sa_est * sb_est * rho_est\n", " Sigma_est <- matrix(c(sa_est^2, cov_ab, cov_ab, sb_est^2), ncol = 2)\n", " library(ellipse)\n", " for (l in c(0.1, 0.3, 0.5, 0.8, 0.99)) {\n", " lines(ellipse(Sigma_est, centre = Mu_est, level = l),\n", " col = col.alpha(\"black\", 0.2)\n", " )\n", " }\n", "})" ] }, { "cell_type": "markdown", "id": "e6f46832", "metadata": {}, "source": [ "This is a similar relationship to what we saw in the cafe example at the start of the chapter; more\n", "extreme intercepts (cafes, districts) are associated with more extreme slopes. In this case the\n", "districts with especially low contraceptive use are associated with a greater increase in use when a\n", "woman 'moves' to an urban area within the district.\n", "\n", "**14H2.** Now consider the predictor variables age.centered and living.children, also contained\n", "in data(bangladesh). Suppose that age influences contraceptive use (changing attitudes) and number\n", "of children (older people have had more time to have kids). Number of children may also directly\n", "influence contraceptive use. Draw a DAG that reflects these hypothetical relationships. Then build\n", "models needed to evaluate the DAG. You will need at least two models. Retain district and urban,\n", "as in 14H1. What do you conclude about the causal influence of age and children?\n", "\n", "**Answer.**\n", "[cc]: https://en.wikipedia.org/wiki/Counterfactual_conditional\n", "\n", "Consider the following causal diagram. Is this diagram reasonable? The author asked us to only\n", "consider this one DAG, but it's worth thinking whether it's reasonable so we know what to expect\n", "from our inferences.\n", "\n", "The Age variable only has arrows pointing out of it. As discussed elsewhere (see question 12H7),\n", "this is the only way we should put time-based variables on DAGs. We can think about Age as\n", "describing the timing of someone's birth. In terms of a [counterfactual conditional][cc], we would\n", "say that if a woman had been born e.g. 10 years earlier she would not have used contraception. A\n", "counterfactual conditional like this describes a causal theory, but expressed regarding the past.\n", "Casual theories should still be tested, when possible, by actively controlling a variable in the\n", "future. In this case we won't be able to test the theory in the future (as well as the past) because\n", "we can't control the date of anyone's birth, unless we ran an experiment with identical twins where\n", "we somehow froze the zygote of one twin in time for years. We'll include a description of all\n", "existing and potential arrows in this DAG as counterfactual conditionals below.\n", "\n", "It's reasonable to think that Age could affect Urban. More people are moving to cities every\n", "year across the world, for jobs, and so in general we'd expect younger women to be living in cities.\n", "That is, if a woman was born later she would be more likely to be urban.\n", "\n", "It's possible that Age could affect District if there was a people migration happening across\n", "the country at one point in the past and slightly older women were less likely to move. That is, if\n", "a woman was born later she could be living in a different district.\n", "\n", "Some districts could be more urbanized and therefore District could predict Urban, and vice\n", "versa. That is, if a woman was living in a different district she could be more likely to be urban.\n", "If a woman was not in an urban area she would be more likely to be in a different district.\n", "\n", "Some districts might have governmental programs or tax incentives to encourage or discourage\n", "children, implying a relationship between District and Children mediated by the program. This\n", "would confound our causal inference about the effect of Children on UseContraception if we\n", "didn't include District in our model. Similarly, for urban programs encouraging or discouraging\n", "children. If a woman was living in a different district, she may have had more or fewer children.\n", "\n", "It's also likely that women move to more rural areas for e.g. cheaper housing when they have more\n", "children, or to districts with cheaper housing and costs of living. That is, a woman had fewer\n", "children, she may be living in a less urban area or in general somewhere else.\n", "\n", "Like the controversy over global warming in the United States, there are often many possible\n", "confounds we can suggest to make a DAG more complicated. It can be hard to decide which need to be\n", "included in every model without getting into a lot of details.\n", "\n", "In this question we are predicting UseContraception from Children but we'd typically think of\n", "the opposite causal path: contraception clearly influences the number of children a woman will have.\n", "In this case, we are essentially assuming that the number of children a woman has in the present\n", "influences her present decision to use contraception. In general, though, these variables interact,\n", "so we have to look at the casual paths similar as a causal time series similar to how the author\n", "treated the causal influence of group size on brain size at the beginning of section **14.5.2**. Our\n", "causal inferences here will only apply to the point in time when these surveys were taken.\n", "\n", "We'll ignore all of this. The DAG expected by the question:" ] }, { "cell_type": "code", "execution_count": 14, "id": "550c5dd9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\n", "Attaching package: ‘dagitty’\n", "\n", "\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "The following object is masked from ‘package:ape’:\n", "\n", " edges\n", "\n", "\n" ] }, { "data": { "image/png": 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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_27_2.png" } }, "output_type": "display_data" } ], "source": [ "library(dagitty)\n", "\n", "expected_dag <- dagitty('\n", "dag {\n", " bb=\"0,0,1,1\"\n", " Age [pos=\"0.3,0.1\"]\n", " Children [exposure,pos=\"0.5,0.1\"]\n", " District [pos=\"0.65,0.2\"]\n", " Urban [pos=\"0.65,0.1\"]\n", " UseContraception [outcome,pos=\"0.4,0.2\"]\n", " Age -> Children\n", " Age -> UseContraception\n", " Children -> UseContraception\n", " District -> UseContraception\n", " Urban -> UseContraception\n", "}')\n", "iplot(function() plot(expected_dag), scale=10)" ] }, { "cell_type": "markdown", "id": "061c5b5e", "metadata": {}, "source": [ "Implied conditional independencies:" ] }, { "cell_type": "code", "execution_count": 15, "id": "041c9734", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Age _||_ Dstr\n", "Age _||_ Urbn\n", "Chld _||_ Dstr\n", "Chld _||_ Urbn\n", "Dstr _||_ Urbn" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(impliedConditionalIndependencies(expected_dag))" ] }, { "cell_type": "markdown", "id": "30ee7a4d", "metadata": {}, "source": [ "We will build two models, as the question suggests. The first will include both predictors, so we\n", "can infer the direct/total causal effect of children on UseContraception:" ] }, { "cell_type": "code", "execution_count": 16, "id": "d3005d83", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{ Age }" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "{ Age }" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(adjustmentSets(expected_dag, exposure=\"Children\", outcome=\"UseContraception\", effect=\"direct\"))\n", "display(adjustmentSets(expected_dag, exposure=\"Children\", outcome=\"UseContraception\", effect=\"total\"))" ] }, { "cell_type": "markdown", "id": "9185f134", "metadata": {}, "source": [ "The first model will also predict the direct effect of Age on UseContraception:" ] }, { "cell_type": "code", "execution_count": 17, "id": "979d1acc", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{ Children }" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(adjustmentSets(expected_dag, exposure=\"Age\", outcome=\"UseContraception\", effect=\"direct\"))" ] }, { "cell_type": "markdown", "id": "5bbe057b", "metadata": {}, "source": [ "The second will include only Age so we can infer the total causal effect of Age on\n", "UseContraception:" ] }, { "cell_type": "code", "execution_count": 18, "id": "6228bea5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " {}" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(adjustmentSets(expected_dag, exposure=\"Age\", outcome=\"UseContraception\", effect=\"total\"))" ] }, { "cell_type": "markdown", "id": "1e928129", "metadata": {}, "source": [ "Fitting the first model:" ] }, { "cell_type": "code", "execution_count": 19, "id": "9e171a82", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“The largest R-hat is NA, indicating chains have not mixed.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#r-hat”\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#bulk-ess”\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#tail-ess”\n" ] }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% \n", "b_district[1] 1.0999167 0.3908649 0.49159563 1.7417916 \n", "b_district[2] 0.7624000 0.6713341 -0.29147820 1.8229521 \n", "b_district[3] 1.0043785 0.8060123 -0.20528392 2.3405111 \n", "b_district[4] 1.6438375 0.6611769 0.66845155 2.7468812 \n", "b_district[5] 0.7022189 0.5919901 -0.23480486 1.6426724 \n", "b_district[6] 1.4202445 0.5546021 0.60059064 2.3576044 \n", "b_district[7] 0.9034358 0.7198666 -0.18233987 2.0596096 \n", "b_district[8] 1.0075832 0.6370145 0.03735138 2.0919893 \n", "b_district[9] 1.1294339 0.6425540 0.14775703 2.1998940 \n", "b_district[10] 1.1811700 0.7393612 0.05655746 2.3937003 \n", "b_district[11] 1.5655565 0.8298174 0.33789497 2.9904372 \n", "b_district[12] 0.4899962 0.5848951 -0.46789684 1.3872553 \n", "b_district[13] 0.3906549 0.5638410 -0.54148595 1.2365869 \n", "b_district[14] 1.4123033 0.4611426 0.69587260 2.1682716 \n", "b_district[15] 0.4825745 0.6121071 -0.52356196 1.4521823 \n", "b_district[16] 0.5243952 0.6783461 -0.53337786 1.6515876 \n", "b_district[17] 0.8794557 0.7167730 -0.23753859 2.0253755 \n", "b_district[18] 1.0268427 0.5122685 0.21549225 1.8279752 \n", "b_district[19] 1.0270314 0.6237950 0.06036288 2.0466071 \n", "b_district[20] 0.5158529 0.7126419 -0.66672066 1.6332599 \n", "b_district[21] -0.3279448 0.7220129 -1.58727814 0.7005328 \n", "b_district[22] 1.1335031 0.7273222 -0.00905651 2.3106420 \n", "b_district[23] 0.9190812 0.7432049 -0.20580069 2.0794233 \n", "b_district[24] 1.2563269 0.7596747 0.09519452 2.4983379 \n", "b_district[25] 0.4333071 0.4399538 -0.26694340 1.1220195 \n", "b_district[26] 0.7074407 0.7235723 -0.42221307 1.8767707 \n", "b_district[27] 1.1893079 0.5969365 0.25626517 2.1375584 \n", "b_district[28] 0.7021765 0.6034404 -0.30269080 1.6450539 \n", "b_district[29] 1.2046125 0.5733478 0.32493704 2.1606517 \n", "b_district[30] 0.9428385 0.4741211 0.22253355 1.7132574 \n", "⋮ ⋮ ⋮ ⋮ ⋮ \n", "a_district[44] -1.00757529 6.136324e-01 -1.9911938 -0.02934434\n", "a_district[45] -0.97830892 5.980057e-01 -1.9538494 -0.02719440\n", "a_district[46] -0.03314476 5.566992e-01 -0.9117773 0.86163084\n", "a_district[47] -0.38205712 6.907393e-01 -1.4876866 0.73290678\n", "a_district[48] -0.10582759 6.133921e-01 -1.0728309 0.85300833\n", "a_district[49] -0.94369673 7.508873e-01 -2.1100061 0.23350557\n", "a_district[50] -0.51192605 6.692862e-01 -1.5518202 0.56943445\n", "a_district[51] -0.67770025 6.343153e-01 -1.6873408 0.33168960\n", "a_district[52] -0.06297412 5.825162e-01 -0.9578809 0.84667572\n", "a_district[53] -0.66126462 8.167981e-01 -1.9708303 0.71126875\n", "a_district[54] -0.70715221 8.193827e-01 -2.0321862 0.58303659\n", "a_district[55] 0.04195840 6.380596e-01 -0.9442829 1.07382583\n", "a_district[56] -1.11721014 6.541691e-01 -2.1445767 -0.07994060\n", "a_district[57] -0.01447033 6.520955e-01 -1.0314944 1.03048964\n", "a_district[58] -1.21266444 6.882528e-01 -2.2795963 -0.09667581\n", "a_district[59] -1.08185653 6.427204e-01 -2.0945485 -0.07955301\n", "a_district[60] -1.21806642 6.201448e-01 -2.2460559 -0.27990187\n", "a_children[1] -1.02952192 5.207069e-01 -1.8500820 -0.19564254\n", "a_children[2] 0.08108856 5.209392e-01 -0.7603851 0.89890579\n", "a_children[3] 0.31428682 5.225278e-01 -0.5115419 1.14501164\n", "a_children[4] 0.29755674 5.199256e-01 -0.5168079 1.12623139\n", "a -0.63573454 5.211178e-01 -1.4590586 0.18399513\n", "b 0.71397519 1.589268e-01 0.4585300 0.96581740\n", "bAge -0.22737831 6.922955e-02 -0.3359584 -0.11826217\n", "sigma_intercepts_slopes[1] 0.60466470 1.017295e-01 0.4521114 0.77621481\n", "sigma_intercepts_slopes[2] 0.77828611 2.040382e-01 0.4604246 1.12411203\n", "Rho[1,1] 1.00000000 0.000000e+00 1.0000000 1.00000000\n", "Rho[1,2] -0.64507055 1.684769e-01 -0.8600055 -0.32967889\n", "Rho[2,1] -0.64507055 1.684769e-01 -0.8600055 -0.32967889\n", "Rho[2,2] 1.00000000 6.153016e-17 1.0000000 1.00000000\n", " n_eff Rhat4 \n", "b_district[1] 1839.5571 0.9984079\n", "b_district[2] 3409.2984 0.9999534\n", "b_district[3] 1706.9000 0.9987609\n", "b_district[4] 669.9120 1.0055624\n", "b_district[5] 3190.8290 1.0003951\n", "b_district[6] 1044.2280 1.0018416\n", "b_district[7] 2599.6768 1.0010587\n", "b_district[8] 1737.1760 0.9997373\n", "b_district[9] 2613.2646 0.9985529\n", "b_district[10] 1507.0233 1.0003189\n", "b_district[11] 1326.2529 1.0000899\n", "b_district[12] 1944.0288 0.9995990\n", "b_district[13] 2282.0064 0.9993529\n", "b_district[14] 1403.3040 1.0000731\n", "b_district[15] 2218.0897 1.0004139\n", "b_district[16] 2212.6778 1.0010683\n", "b_district[17] 2962.5253 0.9990428\n", "b_district[18] 2344.2862 0.9990850\n", "b_district[19] 2133.9400 0.9998191\n", "b_district[20] 2473.1233 0.9997963\n", "b_district[21] 656.1066 1.0051644\n", "b_district[22] 1823.7037 0.9991960\n", "b_district[23] 2581.8564 0.9991919\n", "b_district[24] 1221.3117 1.0003195\n", "b_district[25] 2773.4273 1.0004201\n", "b_district[26] 2760.2540 0.9990907\n", "b_district[27] 1834.5880 0.9995749\n", "b_district[28] 1917.9901 0.9994573\n", "b_district[29] 1352.9754 0.9996811\n", "b_district[30] 2076.7044 1.0010753\n", "⋮ ⋮ ⋮ \n", "a_district[44] 63.01853 1.0496414\n", "a_district[45] 58.62364 1.0528270\n", "a_district[46] 53.68775 1.0638962\n", "a_district[47] 78.95846 1.0383481\n", "a_district[48] 62.06339 1.0590729\n", "a_district[49] 99.78424 1.0320701\n", "a_district[50] 72.83560 1.0464830\n", "a_district[51] 73.44679 1.0488270\n", "a_district[52] 55.62306 1.0669655\n", "a_district[53] 101.89727 1.0326683\n", "a_district[54] 109.91239 1.0319721\n", "a_district[55] 61.94630 1.0530400\n", "a_district[56] 59.75073 1.0507623\n", "a_district[57] 61.80999 1.0585249\n", "a_district[58] 75.79770 1.0377480\n", "a_district[59] 73.98629 1.0443772\n", "a_district[60] 67.82203 1.0530765\n", "a_children[1] 44.84983 1.0711356\n", "a_children[2] 43.03068 1.0756245\n", "a_children[3] 44.55434 1.0768130\n", "a_children[4] 42.62129 1.0777767\n", "a 42.14154 1.0779772\n", "b 1048.78662 1.0006900\n", "bAge 2819.64745 0.9999493\n", "sigma_intercepts_slopes[1] 695.84499 1.0051581\n", "sigma_intercepts_slopes[2] 210.86961 1.0173553\n", "Rho[1,1] NaN NaN\n", "Rho[1,2] 489.22550 1.0078223\n", "Rho[2,1] 489.22550 1.0078223\n", "Rho[2,2] 1753.63666 0.9979980" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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CrzkQWd6MBfgyKSprZkz4itIA5QCjri4Pzo8tnLjsiehHQIRQdu6BwVEDdfHQri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WtrBiK6W+aOBJNj4v2Ls7KqckrgY49hUv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\nQMc7cXTv8/qLF4tgFDXEQQK+q8INb8TRW2RPaOC8eL5PBsQ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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_37_4.png" } }, "output_type": "display_data" } ], "source": [ "data(bangladesh)\n", "bc_df <- bangladesh\n", "bc_df$district_id <- as.integer(as.factor(bc_df$district))\n", "\n", "bc_dat <- list(\n", " UseContraception = bc_df$use.contraception,\n", " DistrictId = bc_df$district_id,\n", " Urban = bc_df$urban,\n", " Age = standardize(bc_df$age.centered),\n", " Children = bc_df$living.children\n", ")\n", "m_bc_age_children <- ulam(\n", " alist(\n", " UseContraception ~ dbinom(1, p),\n", " logit(p) <- a_district[DistrictId] + b_district[DistrictId] * Urban + bAge * Age +\n", "a_children[Children],\n", " c(a_district, b_district)[DistrictId] ~ multi_normal(c(a, b), Rho, sigma_intercepts_slopes),\n", " a_children[Children] ~ normal(0, 1),\n", " a ~ normal(0, 2),\n", " b ~ normal(0, 0.5),\n", " bAge ~ normal(0, 0.5),\n", " sigma_intercepts_slopes ~ exponential(1),\n", " Rho ~ lkj_corr(2)\n", " ),\n", " data = bc_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "display(precis(m_bc_age_children, depth=3), mimetypes=\"text/plain\")\n", "iplot(function() {\n", " plot(precis(m_bc_age_children, depth=3), main=\"m_bc_age_children\")\n", "}, ar=0.4)" ] }, { "cell_type": "markdown", "id": "a8b93075", "metadata": {}, "source": [ "Fitting the second model:" ] }, { "cell_type": "code", "execution_count": 20, "id": "13d81d9c", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#bulk-ess”\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#tail-ess”\n" ] }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% \n", "b_district[1] 1.0702136 0.4067277 0.43379121 1.7248416 \n", "b_district[2] 0.6305582 0.6912087 -0.47099620 1.6988042 \n", "b_district[3] 0.9705495 0.7902006 -0.25163575 2.2485909 \n", "b_district[4] 1.6429103 0.6505227 0.66302723 2.7696751 \n", "b_district[5] 0.6356402 0.6139752 -0.33570188 1.6054755 \n", "b_district[6] 1.2899324 0.5596966 0.46314778 2.2128706 \n", "b_district[7] 0.7735038 0.7020769 -0.33740407 1.8648556 \n", "b_district[8] 0.9321451 0.6491707 -0.06116912 1.9916973 \n", "b_district[9] 0.9917004 0.6714883 -0.03799627 2.0999914 \n", "b_district[10] 1.2438967 0.7840562 0.07436494 2.5460826 \n", "b_district[11] 1.6047628 0.8444329 0.31912278 2.9721018 \n", "b_district[12] 0.4267246 0.5973661 -0.52816545 1.3816863 \n", "b_district[13] 0.2860661 0.5781811 -0.67536741 1.1610802 \n", "b_district[14] 1.2535781 0.4232179 0.61710183 1.9822707 \n", "b_district[15] 0.4207730 0.5816601 -0.51392978 1.3405875 \n", "b_district[16] 0.5996888 0.6929692 -0.45002673 1.7215217 \n", "b_district[17] 0.7783539 0.7053412 -0.30324018 1.9164783 \n", "b_district[18] 0.8717355 0.4831137 0.12611949 1.6636872 \n", "b_district[19] 0.9747263 0.6338828 0.04406323 2.0289520 \n", "b_district[20] 0.5074256 0.7368209 -0.67157506 1.6615544 \n", "b_district[21] -0.3972980 0.6662763 -1.51749499 0.6102074 \n", "b_district[22] 0.9984948 0.7441407 -0.10027794 2.1627915 \n", "b_district[23] 0.8053357 0.7483680 -0.35752667 1.9867326 \n", "b_district[24] 1.2397900 0.7926735 0.07207726 2.6201476 \n", "b_district[25] 0.1991053 0.4276917 -0.49510261 0.8834087 \n", "b_district[26] 0.5621284 0.7225624 -0.58839125 1.6748054 \n", "b_district[27] 1.1391534 0.5962353 0.18383570 2.0653965 \n", "b_district[28] 0.7071302 0.5805124 -0.21788665 1.6359116 \n", "b_district[29] 1.1159222 0.5861940 0.20646296 2.0684271 \n", "b_district[30] 1.0274215 0.5023722 0.28346471 1.8659726 \n", "⋮ ⋮ ⋮ ⋮ ⋮ \n", "a_district[40] -0.56713225 3.942035e-01 -1.196080694 0.05692364\n", "a_district[41] -0.09445060 3.518192e-01 -0.646965536 0.47154724\n", "a_district[42] -0.07645624 4.785484e-01 -0.819215319 0.67868498\n", "a_district[43] -0.20928463 3.245208e-01 -0.706348092 0.30756017\n", "a_district[44] -1.05076852 3.564967e-01 -1.631410062 -0.51042323\n", "a_district[45] -0.90137965 3.195985e-01 -1.430802543 -0.39026654\n", "a_district[46] -0.09572654 2.242291e-01 -0.458310570 0.26297881\n", "a_district[47] -0.52708188 4.322266e-01 -1.204760880 0.15630742\n", "a_district[48] -0.23006057 3.313788e-01 -0.745034819 0.29127181\n", "a_district[49] -1.03023255 5.507298e-01 -1.939590161 -0.17612258\n", "a_district[50] -0.68555663 3.984149e-01 -1.333323326 -0.04795596\n", "a_district[51] -0.63496193 3.707027e-01 -1.231812436 -0.04323402\n", "a_district[52] -0.11045522 2.763375e-01 -0.548731329 0.32194903\n", "a_district[53] -0.71767053 5.517730e-01 -1.635052142 0.15193477\n", "a_district[54] -0.73863665 5.836698e-01 -1.661464909 0.14930034\n", "a_district[55] -0.12110828 3.453037e-01 -0.655014058 0.43152436\n", "a_district[56] -1.18951735 3.893304e-01 -1.803571667 -0.59085226\n", "a_district[57] -0.17772950 3.702615e-01 -0.786031845 0.39128593\n", "a_district[58] -1.15459443 4.728163e-01 -1.948179197 -0.45065063\n", "a_district[59] -1.15298373 3.783223e-01 -1.753136917 -0.57052335\n", "a_district[60] -1.18366333 3.435825e-01 -1.755721227 -0.66582234\n", "a -0.69088692 9.915224e-02 -0.847275102 -0.53470701\n", "b 0.64328244 1.582692e-01 0.390786598 0.89773685\n", "bAge 0.08306864 4.881746e-02 0.006175679 0.16085576\n", "sigma_intercepts_slopes[1] 0.57408849 9.799291e-02 0.424628883 0.73759442\n", "sigma_intercepts_slopes[2] 0.78539789 1.963405e-01 0.483581293 1.10263891\n", "Rho[1,1] 1.00000000 0.000000e+00 1.000000000 1.00000000\n", "Rho[1,2] -0.64207947 1.638724e-01 -0.854575139 -0.34237655\n", "Rho[2,1] -0.64207947 1.638724e-01 -0.854575139 -0.34237655\n", "Rho[2,2] 1.00000000 6.192971e-17 1.000000000 1.00000000\n", " n_eff Rhat4 \n", "b_district[1] 1829.9801 1.0010016\n", "b_district[2] 2009.4880 1.0004020\n", "b_district[3] 1741.9526 0.9989266\n", "b_district[4] 743.9184 0.9995581\n", "b_district[5] 2805.5472 0.9998584\n", "b_district[6] 1618.8969 0.9998220\n", "b_district[7] 1825.5960 1.0007015\n", "b_district[8] 1679.4763 0.9997061\n", "b_district[9] 2363.5877 0.9992498\n", "b_district[10] 1563.5257 1.0045377\n", "b_district[11] 1167.8123 1.0002489\n", "b_district[12] 2498.4809 0.9991042\n", "b_district[13] 1756.7462 1.0007052\n", "b_district[14] 1228.6417 1.0001107\n", "b_district[15] 1901.5656 0.9994154\n", "b_district[16] 2039.6668 0.9990231\n", "b_district[17] 2409.0061 0.9997818\n", "b_district[18] 2201.4167 0.9996737\n", "b_district[19] 1558.7646 1.0014130\n", "b_district[20] 1943.8058 1.0000445\n", "b_district[21] 822.0622 1.0015318\n", "b_district[22] 1979.9077 0.9994562\n", "b_district[23] 2290.9894 1.0005602\n", "b_district[24] 1513.2038 0.9984700\n", "b_district[25] 1832.4354 0.9993031\n", "b_district[26] 2059.9716 0.9999822\n", "b_district[27] 1594.2774 1.0006990\n", "b_district[28] 2185.1060 0.9984959\n", "b_district[29] 1720.6701 1.0000656\n", "b_district[30] 1947.2835 0.9995516\n", "⋮ ⋮ ⋮ \n", "a_district[40] 1670.8647 0.9995937\n", "a_district[41] 1792.6930 1.0000349\n", "a_district[42] 1172.3509 0.9993053\n", "a_district[43] 2325.3694 0.9993269\n", "a_district[44] 3272.7154 0.9992261\n", "a_district[45] 2406.2164 0.9993421\n", "a_district[46] 2844.9845 0.9996790\n", "a_district[47] 2090.3225 0.9991635\n", "a_district[48] 2392.3548 1.0011711\n", "a_district[49] 2326.2755 1.0012745\n", "a_district[50] 2666.9974 1.0002669\n", "a_district[51] 2380.2410 0.9985290\n", "a_district[52] 1783.3829 0.9995301\n", "a_district[53] 2138.6105 1.0030239\n", "a_district[54] 1778.1201 0.9996700\n", "a_district[55] 1840.4563 0.9994024\n", "a_district[56] 2513.9127 0.9999035\n", "a_district[57] 1381.4852 1.0009826\n", "a_district[58] 1886.2134 1.0009924\n", "a_district[59] 2061.4345 0.9985233\n", "a_district[60] 1931.9196 1.0007637\n", "a 1396.8717 1.0008768\n", "b 1163.2596 1.0003428\n", "bAge 3897.3416 0.9989784\n", "sigma_intercepts_slopes[1] 645.1497 1.0061509\n", "sigma_intercepts_slopes[2] 240.2612 1.0026197\n", "Rho[1,1] NaN NaN\n", "Rho[1,2] 442.8782 1.0064511\n", "Rho[2,1] 442.8782 1.0064511\n", "Rho[2,2] 1692.5187 0.9979980" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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c0oHDUVHu7pc9xo++pZRyc6kBeJYxsbYtyawn4kJw584xD/jeOL6+X/n31uiapf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\n0Q7MOLgbFsMhDnURKo5jLRu/u+mPNxpcdVLgi1ZmSGaODjGSgg7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cwoA4KONVHkdpmaOIDgT2AHFQhmR0IOffdgkN77acIzpQYSAOypCM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\nZCnFAclPde/Ql5E7f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HNcxNFVEi6eky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\n9/z3bHKp9V3i+EadrNbaLQB9SuloLdO0sHbjQqVJW/2X/rk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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_39_3.png" } }, "output_type": "display_data" } ], "source": [ "bc_dat <- list(\n", " UseContraception = bc_df$use.contraception,\n", " DistrictId = bc_df$district_id,\n", " Urban = bc_df$urban,\n", " Age = standardize(bc_df$age.centered)\n", ")\n", "m_bc_age <- ulam(\n", " alist(\n", " UseContraception ~ dbinom(1, p),\n", " logit(p) <- a_district[DistrictId] + b_district[DistrictId] * Urban + bAge * Age,\n", " c(a_district, b_district)[DistrictId] ~ multi_normal(c(a, b), Rho, sigma_intercepts_slopes),\n", " a ~ normal(0, 2),\n", " b ~ normal(0, 0.5),\n", " bAge ~ normal(0, 0.5),\n", " sigma_intercepts_slopes ~ exponential(1),\n", " Rho ~ lkj_corr(2)\n", " ),\n", " data = bc_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "display(precis(m_bc_age, depth=3), mimetypes=\"text/plain\")\n", "iplot(function() {\n", " plot(precis(m_bc_age, depth=3), main=\"m_bc_age\")\n", "}, ar=0.4)" ] }, { "cell_type": "markdown", "id": "81f7da91", "metadata": {}, "source": [ "In the first model, we see that with more children the likelihood of using birth control goes up, as\n", "expected. The likelihood of using birth control also goes down with age, as expected if you assume\n", "that younger women are more open to newer ideas like birth control.\n", "\n", "In the second model we see the total causal effect of age on whether a woman uses birth control is\n", "positive. That is, the older a woman is the more likely she is to use birth control. That is, the\n", "tendency for a woman to use birth control as she gets older because she has more children is\n", "stronger than the influence of changing acceptance of birth control.\n", "\n", "**14H3.** Modify any models from 14H2 that contained that children variable and model the variable now\n", "as a monotonic ordered category, like education from the week we did ordered categories. Education\n", "in that example had 8 categories. Children here will have fewer (no one in the sample had 8\n", "children). So modify the code appropriately. What do you conclude about the causal influence of each\n", "additional child on use of contraception?\n", "\n", "**ERROR:** The author uses the term *week* above as if he has a syllabus for the book.\n", "\n", "**Answer.** Fitting the model:" ] }, { "cell_type": "code", "execution_count": 21, "id": "f4c67dc9", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#bulk-ess”\n" ] }, { "name": "stderr", "output_type": "stream", "text": [ "Warning message:\n", "“Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.\n", "Running the chains for more iterations may help. See\n", "https://mc-stan.org/misc/warnings.html#tail-ess”\n" ] }, { "data": { "text/plain": [ " mean sd 5.5% 94.5% \n", "b_district[1] 1.1172469 0.3947964 0.48297366 1.7406465 \n", "b_district[2] 0.7614204 0.7128541 -0.32013969 1.8925728 \n", "b_district[3] 0.9775367 0.8165073 -0.28479200 2.3091791 \n", "b_district[4] 1.6304651 0.6217377 0.70311733 2.6565408 \n", "b_district[5] 0.6884590 0.6266713 -0.30505475 1.6964227 \n", "b_district[6] 1.3976158 0.5506682 0.58861327 2.3132589 \n", "b_district[7] 0.8752725 0.6839709 -0.19915593 1.9709745 \n", "b_district[8] 0.9775638 0.6223842 0.02468108 2.0054431 \n", "b_district[9] 1.1287229 0.6457095 0.15336211 2.2037115 \n", "b_district[10] 1.1993028 0.7611886 0.10176672 2.4951891 \n", "b_district[11] 1.5533671 0.8312594 0.32903001 2.9187281 \n", "b_district[12] 0.5132767 0.6062558 -0.46498870 1.4522622 \n", "b_district[13] 0.3750357 0.5881354 -0.59452498 1.2741826 \n", "b_district[14] 1.3850316 0.4405043 0.67993847 2.0776020 \n", "b_district[15] 0.4313439 0.6274121 -0.61220327 1.4028669 \n", "b_district[16] 0.5163426 0.6432999 -0.46993826 1.5422191 \n", "b_district[17] 0.8800332 0.7051507 -0.19434518 1.9770823 \n", "b_district[18] 1.0208456 0.4937756 0.23166464 1.8259519 \n", "b_district[19] 1.0040505 0.6176643 0.07376052 2.0267407 \n", "b_district[20] 0.4920475 0.7194264 -0.65689430 1.6608345 \n", "b_district[21] -0.3435313 0.7086118 -1.55182460 0.6896701 \n", "b_district[22] 1.0893223 0.7290794 -0.05315765 2.2403613 \n", "b_district[23] 0.8678881 0.7129492 -0.25082946 2.0184497 \n", "b_district[24] 1.2810500 0.7522196 0.11836281 2.5333473 \n", "b_district[25] 0.4349194 0.4393901 -0.24534788 1.1284563 \n", "b_district[26] 0.6664842 0.7000972 -0.46075819 1.7295660 \n", "b_district[27] 1.1723796 0.6142847 0.21989934 2.1488261 \n", "b_district[28] 0.6975674 0.6067147 -0.28778595 1.6661818 \n", "b_district[29] 1.1837080 0.6063302 0.27756238 2.1866475 \n", "b_district[30] 0.9411080 0.4801367 0.20010201 1.7490492 \n", "⋮ ⋮ ⋮ ⋮ ⋮ \n", "a_district[44] -2.01565316 3.889580e-01 -2.65596603 -1.4197053\n", "a_district[45] -1.97231042 3.553071e-01 -2.54360962 -1.4135556\n", "a_district[46] -1.05993405 2.479984e-01 -1.47103244 -0.6728968\n", "a_district[47] -1.40711734 4.719714e-01 -2.15791705 -0.6477676\n", "a_district[48] -1.09022149 3.433844e-01 -1.62885343 -0.5490830\n", "a_district[49] -1.97443974 5.736895e-01 -2.92491602 -1.0750045\n", "a_district[50] -1.52572109 4.364849e-01 -2.21756447 -0.8397019\n", "a_district[51] -1.69507483 3.930730e-01 -2.33437232 -1.0770527\n", "a_district[52] -1.09322637 3.058946e-01 -1.58148714 -0.5976245\n", "a_district[53] -1.69162223 6.504140e-01 -2.71149771 -0.6315280\n", "a_district[54] -1.72704061 6.375521e-01 -2.75649355 -0.7129678\n", "a_district[55] -0.96697391 3.694604e-01 -1.54392148 -0.3801536\n", "a_district[56] -2.13901583 4.255826e-01 -2.83738719 -1.4699294\n", "a_district[57] -1.00697529 3.769271e-01 -1.59853190 -0.4072379\n", "a_district[58] -2.24133056 5.284252e-01 -3.12622964 -1.4170601\n", "a_district[59] -2.12211217 4.168315e-01 -2.81841840 -1.4745107\n", "a_district[60] -2.23019533 3.914657e-01 -2.89008046 -1.6357820\n", "bC 1.38506932 1.591415e-01 1.13804534 1.6396411\n", "a -1.65171232 1.529888e-01 -1.90285604 -1.4009028\n", "b 0.70576856 1.594368e-01 0.45896996 0.9545962\n", "bAge -0.25808498 6.446993e-02 -0.36040392 -0.1548705\n", "sigma_intercepts_slopes[1] 0.60851857 1.033183e-01 0.45612360 0.7832236\n", "sigma_intercepts_slopes[2] 0.77719933 1.977456e-01 0.48570605 1.1170490\n", "Rho[1,1] 1.00000000 0.000000e+00 1.00000000 1.0000000\n", "Rho[1,2] -0.63287420 1.694468e-01 -0.85518047 -0.3378406\n", "Rho[2,1] -0.63287420 1.694468e-01 -0.85518047 -0.3378406\n", "Rho[2,2] 1.00000000 6.513255e-17 1.00000000 1.0000000\n", "delta[1] 0.73575546 7.864344e-02 0.60302275 0.8571040\n", "delta[2] 0.16514339 7.786641e-02 0.05346976 0.3011820\n", "delta[3] 0.09910115 5.303689e-02 0.02646703 0.1976305\n", " n_eff Rhat4 \n", "b_district[1] 1858.6535 1.0021939\n", "b_district[2] 2422.5678 0.9998569\n", "b_district[3] 2364.3998 1.0004502\n", "b_district[4] 799.8742 1.0005938\n", "b_district[5] 2641.5894 0.9984578\n", "b_district[6] 1016.8648 1.0012057\n", "b_district[7] 2286.4364 0.9990444\n", "b_district[8] 1947.3531 1.0010813\n", "b_district[9] 1700.2795 1.0002677\n", "b_district[10] 1220.2683 1.0032249\n", "b_district[11] 908.4975 1.0035830\n", "b_district[12] 1876.7732 0.9991535\n", "b_district[13] 2190.9224 1.0006425\n", "b_district[14] 1216.8354 1.0014568\n", "b_district[15] 1807.2520 0.9985229\n", "b_district[16] 1998.1333 1.0005741\n", "b_district[17] 2069.1264 1.0008744\n", "b_district[18] 2138.1279 0.9998421\n", "b_district[19] 2460.2234 0.9988916\n", "b_district[20] 2318.7812 0.9983729\n", "b_district[21] 726.9583 1.0003159\n", "b_district[22] 1815.5166 0.9988166\n", "b_district[23] 2638.9181 1.0000360\n", "b_district[24] 1296.3829 1.0019795\n", "b_district[25] 2110.8114 1.0005550\n", "b_district[26] 2391.6174 0.9994238\n", "b_district[27] 1657.3948 1.0023487\n", "b_district[28] 1419.3083 1.0008453\n", "b_district[29] 1603.2549 0.9994156\n", "b_district[30] 2471.6563 0.9992102\n", "⋮ ⋮ ⋮ \n", "a_district[44] 1409.2554 1.0008529\n", "a_district[45] 1064.7414 1.0004311\n", "a_district[46] 1543.1175 0.9996723\n", "a_district[47] 1993.7202 1.0010994\n", "a_district[48] 1475.3781 0.9997769\n", "a_district[49] 1532.6337 0.9992893\n", "a_district[50] 1927.3143 1.0005260\n", "a_district[51] 1398.2887 1.0005994\n", "a_district[52] 1627.6985 0.9995263\n", "a_district[53] 1621.6553 1.0004567\n", "a_district[54] 1710.0057 0.9999061\n", "a_district[55] 2001.8494 1.0008422\n", "a_district[56] 1499.8706 1.0055149\n", "a_district[57] 1729.1973 1.0018148\n", "a_district[58] 1560.1178 1.0038867\n", "a_district[59] 1365.4777 1.0006630\n", "a_district[60] 1717.9668 1.0004389\n", "bC 555.2256 1.0100292\n", "a 566.5249 1.0060587\n", "b 965.3262 1.0032480\n", "bAge 1144.8212 1.0040346\n", "sigma_intercepts_slopes[1] 587.3616 1.0079381\n", "sigma_intercepts_slopes[2] 248.2555 1.0146701\n", "Rho[1,1] NaN NaN\n", "Rho[1,2] 463.0337 1.0047042\n", "Rho[2,1] 463.0337 1.0047042\n", "Rho[2,2] 2144.0760 0.9979980\n", "delta[1] 3036.3896 1.0011396\n", "delta[2] 2264.5731 1.0002415\n", "delta[3] 2666.5015 0.9993974" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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hIWaZuCOIAhcK+KbJAAJgbE4QggDtlAHGJAHI4A4pANogPFgDgcAcQhG0QHigFx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\nNQfEoQQQBzXEmaN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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_41_3.png" } }, "output_type": "display_data" } ], "source": [ "data(bangladesh)\n", "bc_df <- bangladesh\n", "bc_df$district_id <- as.integer(as.factor(bc_df$district))\n", "\n", "bc_dat <- list(\n", " UseContraception = bc_df$use.contraception,\n", " DistrictId = bc_df$district_id,\n", " Urban = bc_df$urban,\n", " Age = standardize(bc_df$age.centered),\n", " Children = as.integer(bc_df$living.children),\n", " alpha = rep(2, 3)\n", ")\n", "m_bc_ordered_children <- ulam(\n", " alist(\n", " UseContraception ~ dbinom(1, p),\n", " logit(p) <- bC*sum(delta_j[1:Children]) + a_district[DistrictId] + b_district[DistrictId] *\n", "Urban + bAge * Age,\n", " c(a_district, b_district)[DistrictId] ~ multi_normal(c(a, b), Rho, sigma_intercepts_slopes),\n", " bC ~ normal(0, 1),\n", " a ~ normal(0, 2),\n", " b ~ normal(0, 0.5),\n", " bAge ~ normal(0, 0.5),\n", " sigma_intercepts_slopes ~ exponential(1),\n", " Rho ~ lkj_corr(2),\n", " vector[4]: delta_j <<- append_row( 0 , delta ),\n", " simplex[3]: delta ~ dirichlet( alpha )\n", " ),\n", " data = bc_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "display(precis(m_bc_ordered_children, depth=3), mimetypes=\"text/plain\")\n", "iplot(function() {\n", " plot(precis(m_bc_ordered_children, depth=3), main=\"m_bc_ordered_children\")\n", "}, ar=0.4)" ] }, { "cell_type": "markdown", "id": "f56a4136", "metadata": {}, "source": [ "Notice in the summary of this data frame, above, that the women surveyed had a minimum of one and\n", "a maximum of four children. It appears the maximum jump in likelihood of a woman using contraception\n", "occurs after having the second child.\n", "\n", "**14H4.** Varying effects models are useful for modeling time series, as well as spatial clustering.\n", "In a time series, the observations cluster by entities that have continuity through time, such as\n", "individuals. Since observations within individuals are likely highly correlated, the multilevel\n", "structure can help quite a lot. You’ll use the data in data(Oxboys), which is 234 height\n", "measurements on 26 boys from an Oxford Boys Club (I think these were like youth athletic leagues?),\n", "at 9 different ages (centered and standardized) per boy. You’ll be interested in predicting\n", "height, using age, clustered by Subject (individual boy). Fit a model with varying intercepts\n", "and slopes (on age), clustered by Subject. Present and interpret the parameter estimates. Which\n", "varying effect contributes more variation to the heights, the intercept or the slope?" ] }, { "cell_type": "code", "execution_count": 22, "id": "2e981e0d", "metadata": {}, "outputs": [], "source": [ "data(Oxboys)\n", "ox <- Oxboys" ] }, { "cell_type": "markdown", "id": "2aa3aeaa", "metadata": {}, "source": [ "**Answer.** A head and summary of the Oxboys data.frame (no help exists):" ] }, { "cell_type": "code", "execution_count": 23, "id": "213d6523", "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\t\n", "\t\n", "\n", "\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\t\n", "\n", "
A data.frame: 6 × 4
SubjectageheightOccasion
<int><dbl><dbl><int>
11-1.0000140.51
21-0.7479143.42
31-0.4630144.83
41-0.1643147.14
51-0.0027147.75
61 0.2466150.26
\n" ], "text/latex": [ "A data.frame: 6 × 4\n", "\\begin{tabular}{r|llll}\n", " & Subject & age & height & Occasion\\\\\n", " & & & & \\\\\n", "\\hline\n", "\t1 & 1 & -1.0000 & 140.5 & 1\\\\\n", "\t2 & 1 & -0.7479 & 143.4 & 2\\\\\n", "\t3 & 1 & -0.4630 & 144.8 & 3\\\\\n", "\t4 & 1 & -0.1643 & 147.1 & 4\\\\\n", "\t5 & 1 & -0.0027 & 147.7 & 5\\\\\n", "\t6 & 1 & 0.2466 & 150.2 & 6\\\\\n", "\\end{tabular}\n" ], "text/markdown": [ "\n", "A data.frame: 6 × 4\n", "\n", "| | Subject <int> | age <dbl> | height <dbl> | Occasion <int> |\n", "|---|---|---|---|---|\n", "| 1 | 1 | -1.0000 | 140.5 | 1 |\n", "| 2 | 1 | -0.7479 | 143.4 | 2 |\n", "| 3 | 1 | -0.4630 | 144.8 | 3 |\n", "| 4 | 1 | -0.1643 | 147.1 | 4 |\n", "| 5 | 1 | -0.0027 | 147.7 | 5 |\n", "| 6 | 1 | 0.2466 | 150.2 | 6 |\n", "\n" ], "text/plain": [ " Subject age height Occasion\n", "1 1 -1.0000 140.5 1 \n", "2 1 -0.7479 143.4 2 \n", "3 1 -0.4630 144.8 3 \n", "4 1 -0.1643 147.1 4 \n", "5 1 -0.0027 147.7 5 \n", "6 1 0.2466 150.2 6 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ " Subject age height Occasion\n", " Min. : 1.0 Min. :-1.00000 Min. :126.2 Min. :1 \n", " 1st Qu.: 7.0 1st Qu.:-0.46300 1st Qu.:143.8 1st Qu.:3 \n", " Median :13.5 Median :-0.00270 Median :149.5 Median :5 \n", " Mean :13.5 Mean : 0.02263 Mean :149.5 Mean :5 \n", " 3rd Qu.:20.0 3rd Qu.: 0.55620 3rd Qu.:155.5 3rd Qu.:7 \n", " Max. :26.0 Max. : 1.00550 Max. :174.8 Max. :9 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "display(head(ox))\n", "display(summary(ox))" ] }, { "cell_type": "markdown", "id": "b0984089", "metadata": {}, "source": [ "Fitting the model:" ] }, { "cell_type": "code", "execution_count": 24, "id": "3cc9e197", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " mean sd 5.5% 94.5% \n", "b_boy[1] 7.137421 0.3470028 6.593290 7.685841 \n", "b_boy[2] 5.481388 0.3354717 4.953505 6.018759 \n", "b_boy[3] 4.871198 0.3242252 4.349729 5.384686 \n", "b_boy[4] 9.248308 0.3286225 8.723941 9.775897 \n", "b_boy[5] 6.262325 0.3430345 5.720164 6.794605 \n", "b_boy[6] 4.065094 0.3414588 3.507843 4.625468 \n", "b_boy[7] 5.057129 0.3254772 4.550538 5.600158 \n", "b_boy[8] 6.472143 0.3409617 5.918703 7.011299 \n", "b_boy[9] 6.008275 0.3482750 5.451821 6.546127 \n", "b_boy[10] 3.822563 0.3308904 3.288179 4.352849 \n", "b_boy[11] 8.414984 0.3420993 7.896069 8.966929 \n", "b_boy[12] 7.003539 0.3169374 6.496528 7.504444 \n", "b_boy[13] 8.411397 0.3244596 7.903736 8.921488 \n", "b_boy[14] 8.584270 0.3479208 8.024445 9.140723 \n", "b_boy[15] 7.084154 0.3311591 6.576340 7.612390 \n", "b_boy[16] 4.632670 0.3351358 4.111953 5.170819 \n", "b_boy[17] 8.503973 0.3483309 7.942851 9.053097 \n", "b_boy[18] 5.993513 0.3326001 5.483076 6.526629 \n", "b_boy[19] 8.976750 0.3399502 8.432994 9.514783 \n", "b_boy[20] 4.472405 0.3421088 3.928483 5.025561 \n", "b_boy[21] 7.459345 0.3350197 6.935254 7.996470 \n", "b_boy[22] 8.026042 0.3425854 7.475904 8.563561 \n", "b_boy[23] 7.155082 0.3293630 6.633925 7.688765 \n", "b_boy[24] 6.758130 0.3489079 6.217386 7.324170 \n", "b_boy[25] 4.119345 0.3261452 3.618808 4.628240 \n", "b_boy[26] 5.611484 0.3198873 5.097121 6.124518 \n", "a_boy[1] 148.113666 0.2214899 147.760040 148.470348 \n", "a_boy[2] 142.852459 0.2277650 142.483513 143.220769 \n", "a_boy[3] 155.647841 0.2273460 155.290838 156.013241 \n", "a_boy[4] 165.077054 0.2245467 164.719447 165.438460 \n", "⋮ ⋮ ⋮ ⋮ ⋮ \n", "a_boy[6] 146.7816740 0.21651718 146.4285482 147.1306175\n", "a_boy[7] 146.1256625 0.22946990 145.7590553 146.4807607\n", "a_boy[8] 148.2952714 0.22680539 147.9407225 148.6682984\n", "a_boy[9] 138.1430095 0.21399152 137.8103545 138.4762010\n", "a_boy[10] 130.2641576 0.22281089 129.9045046 130.6156562\n", "a_boy[11] 150.0505071 0.22596823 149.6941118 150.4049100\n", "a_boy[12] 156.8038612 0.21954019 156.4661561 157.1615807\n", "a_boy[13] 156.0790796 0.22703441 155.7234655 156.4528918\n", "a_boy[14] 159.4761872 0.22282774 159.1283867 159.8305711\n", "a_boy[15] 144.2824583 0.22543143 143.9169227 144.6406060\n", "a_boy[16] 147.5473591 0.22410248 147.1885303 147.8914143\n", "a_boy[17] 142.9797313 0.22542690 142.6231427 143.3483465\n", "a_boy[18] 151.1778984 0.21780214 150.8322288 151.5216472\n", "a_boy[19] 164.5871053 0.23456883 164.2127483 164.9628855\n", "a_boy[20] 151.4691104 0.21856394 151.1150465 151.8145878\n", "a_boy[21] 150.5169563 0.21928624 150.1524631 150.8591893\n", "a_boy[22] 154.5666657 0.22340787 154.2099223 154.9231753\n", "a_boy[23] 151.0604161 0.23528629 150.6893835 151.4446547\n", "a_boy[24] 153.1466540 0.23028317 152.7808444 153.4993456\n", "a_boy[25] 139.2048731 0.21329264 138.8642392 139.5451884\n", "a_boy[26] 137.9953264 0.21980365 137.6500644 138.3334579\n", "a 0.6537408 1.01336819 -0.9283681 2.2715824\n", "b 0.1333895 0.48955902 -0.6369618 0.9309867\n", "sigma_intercepts_slopes[1] 74.6934922 4.68032793 67.4601565 82.1614231\n", "sigma_intercepts_slopes[2] 3.5748334 0.32779123 3.0554130 4.1134228\n", "Rho[1,1] 1.0000000 0.00000000 1.0000000 1.0000000\n", "Rho[1,2] 0.8880278 0.03607893 0.8246749 0.9352457\n", "Rho[2,1] 0.8880278 0.03607893 0.8246749 0.9352457\n", "Rho[2,2] 1.0000000 0.00000000 1.0000000 1.0000000\n", "sigma 0.6647896 0.03639783 0.6084315 0.7252927\n", " n_eff Rhat4 \n", "b_boy[1] 3528.749 0.9999860\n", "b_boy[2] 4168.444 0.9996024\n", "b_boy[3] 2986.183 0.9986559\n", "b_boy[4] 3184.555 0.9988569\n", "b_boy[5] 4628.295 0.9986748\n", "b_boy[6] 3157.599 0.9986585\n", "b_boy[7] 3067.210 1.0018310\n", "b_boy[8] 3605.736 0.9991257\n", "b_boy[9] 3235.929 0.9989471\n", "b_boy[10] 3524.432 0.9991593\n", "b_boy[11] 3555.813 0.9985748\n", "b_boy[12] 3295.006 0.9983287\n", "b_boy[13] 3261.745 0.9985648\n", "b_boy[14] 3638.736 1.0001942\n", "b_boy[15] 3922.221 0.9984418\n", "b_boy[16] 3387.989 0.9991188\n", "b_boy[17] 3695.833 0.9999522\n", "b_boy[18] 4232.337 0.9991695\n", "b_boy[19] 3671.879 0.9997550\n", "b_boy[20] 2721.981 0.9992497\n", "b_boy[21] 3176.938 0.9983887\n", "b_boy[22] 3561.369 0.9994862\n", "b_boy[23] 3902.230 0.9987558\n", "b_boy[24] 3227.228 1.0002230\n", "b_boy[25] 3818.300 0.9996149\n", "b_boy[26] 3410.292 1.0004828\n", "a_boy[1] 4561.809 0.9987926\n", "a_boy[2] 3535.504 0.9998455\n", "a_boy[3] 3005.947 0.9996865\n", "a_boy[4] 3959.527 0.9986625\n", "⋮ ⋮ ⋮ \n", "a_boy[6] 3586.519 0.9993449\n", "a_boy[7] 3621.095 0.9999323\n", "a_boy[8] 2529.734 0.9983566\n", "a_boy[9] 2600.322 0.9996230\n", "a_boy[10] 3124.062 0.9989691\n", "a_boy[11] 3161.117 0.9988722\n", "a_boy[12] 3231.492 0.9985778\n", "a_boy[13] 3953.531 0.9989110\n", "a_boy[14] 2868.897 0.9992057\n", "a_boy[15] 3993.774 1.0000635\n", "a_boy[16] 3126.013 0.9988499\n", "a_boy[17] 3317.890 0.9990095\n", "a_boy[18] 3539.491 0.9989600\n", "a_boy[19] 2805.662 0.9986506\n", "a_boy[20] 3454.852 0.9985530\n", "a_boy[21] 3114.616 0.9984869\n", "a_boy[22] 3719.990 1.0003180\n", "a_boy[23] 3721.650 0.9988570\n", "a_boy[24] 3812.427 0.9991344\n", "a_boy[25] 3265.778 0.9990980\n", "a_boy[26] 3590.703 0.9994189\n", "a 4519.370 0.9981847\n", "b 2040.379 0.9995646\n", "sigma_intercepts_slopes[1] 2474.403 0.9992004\n", "sigma_intercepts_slopes[2] 2001.709 0.9986325\n", "Rho[1,1] NaN NaN\n", "Rho[1,2] 2216.757 0.9990147\n", "Rho[2,1] 2216.757 0.9990147\n", "Rho[2,2] NaN NaN\n", "sigma 2050.545 1.0026862" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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AcQLNQj6CE4AKEeQRfBAQj1CLoIDkCoR9BFcABCPYIuggMQNivWRXAAQnDoIjgA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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_47_1.png" } }, "output_type": "display_data" } ], "source": [ "ox_dat <- list(\n", " Subject = ox$Subject,\n", " Age = ox$age,\n", " Height = ox$height\n", ")\n", "m_ox <- ulam(\n", " alist(\n", " Height ~ dnorm(mu, sigma),\n", " mu <- a_boy[Subject] + b_boy[Subject] * Age,\n", " c(a_boy, b_boy)[Subject] ~ multi_normal(c(a, b), Rho, sigma_intercepts_slopes),\n", " a ~ normal(0, 1),\n", " b ~ normal(0, 0.5),\n", " sigma_intercepts_slopes ~ exponential(1),\n", " Rho ~ lkj_corr(2),\n", " sigma ~ normal(0, 2)\n", " ),\n", " data = ox_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "display(precis(m_ox, depth=3), mimetypes=\"text/plain\")\n", "iplot(function() {\n", " plot(precis(m_ox, depth=3), main=\"m_ox\")\n", "}, ar=0.7)" ] }, { "cell_type": "markdown", "id": "679e7469", "metadata": {}, "source": [ "The intercepts term contributes much more to the heights than the slopes. Notice the b_boy terms\n", "are the maximum that the slopes can contribute to mu since Age is at most equal one.\n", "\n", "---\n", "\n", "**14H5.** Now consider the correlation between the varying intercepts and slopes. Can you explain\n", "its value? How would this estimated correlation influence your predictions about a new sample of\n", "boys?\n", "\n", "**Answer.** The correlation is positive, because more positive intercepts are associated with more\n", "positive slopes. That is, boys who are on average taller also grow faster.\n", "\n", "---\n", "\n", "**14H6.** Use mvrnorm (in library(MASS)) or rmvnorm (in library(mvtnorm)) to simulate a new\n", "sample of boys, based upon the posterior mean values of the parameters. That is, try to simulate\n", "varying intercepts and slopes, using the relevant parameter estimates, and then plot the predicted\n", "trends of height on age, one trend for each simulated boy you produce. A sample of 10 simulated boys\n", "is plenty, to illustrate the lesson. You can ignore uncertainty in the posterior, just to make the\n", "problem a little easier. But if you want to include the uncertainty about the parameters, go for it.\n", "Note that you can construct an arbitrary variance-covariance matrix to pass to either mvrnorm or\n", "rmvnorm with something like:\n", "\n", "R code 14.54\n", "\n", "R\n", "S <- matrix( c( sa^2 , sa*sb*rho , sa*sb*rho , sb^2 ) , nrow=2 )\n", "\n", "\n", "where sa is the standard deviation of the first variable, sb is the standard deviation of the\n", "second variable, and rho is the correlation between them.\n", "\n", "**Answer.** The expected plot:" ] }, { "cell_type": "code", "execution_count": 25, "id": "f645d077", "metadata": {}, "outputs": [ { "data": { "image/png": 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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_49_0.png" } }, "output_type": "display_data" } ], "source": [ "post <- extract.samples(m_ox)\n", "Mu_est <- c(mean(post$a), mean(post$b))\n", "rho_est <- mean(post$Rho[,1,2])\n", "sa_est <- mean(post$sigma_intercepts_slopes[,1])\n", "sb_est <- mean(post$sigma_intercepts_slopes[,2])\n", "cov_ab <- sa_est*sb_est*rho_est\n", "Sigma_est <- matrix(c(sa_est^2, cov_ab, cov_ab, sb_est^2), nrow=2)\n", "\n", "library(MASS)\n", "set.seed(5)\n", "N_boys <- 10\n", "vary_effects <- mvrnorm(N_boys, Mu_est, Sigma_est)\n", "\n", "iplot(function() {\n", " plot(NULL, main=\"Posterior predictive plot, 10 simulated boys\",\n", " xlab=\"age\", ylab=\"height\",\n", " xlim=c(-1.1, 1.1),\n", " ylim=c(min(vary_effects[,1] - vary_effects[,2]) - 10, max(vary_effects[,1] + vary_effects[,2]) + 10)\n", " )\n", " for (idx in 1:N_boys)\n", " abline(a=vary_effects[idx, 1], b=vary_effects[idx, 2])\n", "})" ] }, { "cell_type": "markdown", "id": "6f6463c0", "metadata": {}, "source": [ "The lesson here is that vague priors can kill predictive power, and that in situations like this one\n", "the priors have a strong influence on the results. In the previous plot the priors on a and b\n", "were copied and pasted from another model:\n", "\n", "\n", "\\begin{align}\n", "a & \\sim Normal(0, 1) \\\\\n", "b & \\sim Normal(0, 0.5)\n", "\\end{align}\n", "\n", "\n", "These are clearly unreasonable. If we fix these priors we get a much better result:\n", "\n", "\n", "\\begin{align}\n", "a & \\sim Normal(150, 40) \\\\\n", "b & \\sim Normal(40, 40)\n", "\\end{align}\n", "" ] }, { "cell_type": "code", "execution_count": 26, "id": "5d65d43f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ " mean sd 5.5% 94.5% \n", "b_boy[1] 7.122827 0.3322087 6.583848 7.655954 \n", "b_boy[2] 5.460675 0.3309538 4.937802 6.000382 \n", "b_boy[3] 4.934086 0.3372113 4.401751 5.461362 \n", "b_boy[4] 9.290755 0.3408733 8.753078 9.830426 \n", "b_boy[5] 6.279010 0.3414299 5.738504 6.831309 \n", "b_boy[6] 4.107758 0.3332389 3.586919 4.640147 \n", "b_boy[7] 5.064438 0.3433725 4.520589 5.604039 \n", "b_boy[8] 6.463974 0.3402083 5.927326 6.991294 \n", "b_boy[9] 5.958746 0.3234855 5.461362 6.483401 \n", "b_boy[10] 3.754424 0.3422636 3.209548 4.298276 \n", "b_boy[11] 8.376141 0.3459315 7.827744 8.901756 \n", "b_boy[12] 7.037235 0.3251566 6.529788 7.552236 \n", "b_boy[13] 8.421781 0.3320623 7.887876 8.969216 \n", "b_boy[14] 8.606473 0.3324009 8.088091 9.125618 \n", "b_boy[15] 7.052871 0.3329311 6.496938 7.582998 \n", "b_boy[16] 4.648309 0.3358858 4.131960 5.187072 \n", "b_boy[17] 8.427887 0.3242495 7.909494 8.945488 \n", "b_boy[18] 6.003476 0.3500593 5.438516 6.563315 \n", "b_boy[19] 9.016830 0.3303680 8.477545 9.540540 \n", "b_boy[20] 4.527208 0.3365359 3.984102 5.066829 \n", "b_boy[21] 7.447827 0.3292831 6.908307 7.986375 \n", "b_boy[22] 8.023659 0.3309146 7.499065 8.543218 \n", "b_boy[23] 7.152485 0.3387705 6.633455 7.682342 \n", "b_boy[24] 6.784337 0.3493435 6.229581 7.355831 \n", "b_boy[25] 4.106523 0.3317459 3.575951 4.634723 \n", "b_boy[26] 5.557906 0.3539407 4.985938 6.127773 \n", "a_boy[1] 148.125102 0.2240055 147.756752 148.485698 \n", "a_boy[2] 142.868576 0.2203292 142.518234 143.210920 \n", "a_boy[3] 155.632299 0.2254481 155.266723 155.978131 \n", "a_boy[4] 165.064997 0.2285159 164.709111 165.443212 \n", "⋮ ⋮ ⋮ ⋮ ⋮ \n", "a_boy[6] 146.7861098 2.194073e-01 146.4384452 147.1318658\n", "a_boy[7] 146.1210404 2.337751e-01 145.7343224 146.4824160\n", "a_boy[8] 148.2930374 2.243746e-01 147.9392885 148.6591341\n", "a_boy[9] 138.1513979 2.313018e-01 137.7888748 138.5179245\n", "a_boy[10] 130.2768959 2.161344e-01 129.9233319 130.6063412\n", "a_boy[11] 150.0537839 2.192917e-01 149.7113235 150.4125345\n", "a_boy[12] 156.7994271 2.247133e-01 156.4529092 157.1583169\n", "a_boy[13] 156.0717378 2.231343e-01 155.6971782 156.4154992\n", "a_boy[14] 159.4622504 2.268403e-01 159.1051252 159.8277467\n", "a_boy[15] 144.2840014 2.288367e-01 143.9157850 144.6475227\n", "a_boy[16] 147.5418819 2.208381e-01 147.1855594 147.8994849\n", "a_boy[17] 142.9979601 2.268262e-01 142.6356783 143.3596771\n", "a_boy[18] 151.1794610 2.169724e-01 150.8242030 151.5177369\n", "a_boy[19] 164.5677562 2.193259e-01 164.2165483 164.9211439\n", "a_boy[20] 151.4573911 2.289793e-01 151.1095460 151.8243764\n", "a_boy[21] 150.5201332 2.205926e-01 150.1666056 150.8674592\n", "a_boy[22] 154.5665399 2.197841e-01 154.2112713 154.9120035\n", "a_boy[23] 151.0684985 2.245058e-01 150.7159832 151.4270030\n", "a_boy[24] 153.1327253 2.242584e-01 152.7759679 153.4905381\n", "a_boy[25] 139.2209405 2.212194e-01 138.8686246 139.5646712\n", "a_boy[26] 138.0036029 2.302090e-01 137.6423519 138.3753935\n", "a 149.3923945 1.455555e+00 147.0672831 151.7613879\n", "b 6.5311084 3.284126e-01 6.0277505 7.0514299\n", "sigma_intercepts_slopes[1] 7.3280618 8.909815e-01 6.0736747 8.8576264\n", "sigma_intercepts_slopes[2] 1.6304761 2.332820e-01 1.2976833 2.0271578\n", "Rho[1,1] 1.0000000 0.000000e+00 1.0000000 1.0000000\n", "Rho[1,2] 0.5257282 1.299665e-01 0.2859021 0.7119550\n", "Rho[2,1] 0.5257282 1.299665e-01 0.2859021 0.7119550\n", "Rho[2,2] 1.0000000 7.984801e-17 1.0000000 1.0000000\n", "sigma 0.6652505 3.387909e-02 0.6144083 0.7236621\n", " n_eff Rhat4 \n", "b_boy[1] 3397.241 0.9993882\n", "b_boy[2] 3824.896 0.9991548\n", "b_boy[3] 4551.947 0.9986551\n", "b_boy[4] 4846.730 0.9984812\n", "b_boy[5] 3796.926 0.9981290\n", "b_boy[6] 3969.628 0.9994277\n", "b_boy[7] 3717.169 0.9995144\n", "b_boy[8] 3885.725 0.9988696\n", "b_boy[9] 3130.566 0.9982011\n", "b_boy[10] 3829.525 0.9996160\n", "b_boy[11] 4275.056 0.9990806\n", "b_boy[12] 3486.493 0.9986922\n", "b_boy[13] 3565.861 0.9988748\n", "b_boy[14] 5191.336 0.9989458\n", "b_boy[15] 3540.452 0.9982362\n", "b_boy[16] 3274.932 0.9995209\n", "b_boy[17] 3718.099 0.9982985\n", "b_boy[18] 3729.188 0.9992369\n", "b_boy[19] 4254.105 0.9986004\n", "b_boy[20] 3826.369 0.9985832\n", "b_boy[21] 3864.268 0.9989389\n", "b_boy[22] 3111.481 0.9993075\n", "b_boy[23] 3595.851 0.9989247\n", "b_boy[24] 3738.130 0.9983798\n", "b_boy[25] 3236.979 0.9988405\n", "b_boy[26] 4879.405 0.9984281\n", "a_boy[1] 3237.550 0.9987787\n", "a_boy[2] 4049.226 0.9986528\n", "a_boy[3] 3117.776 0.9985072\n", "a_boy[4] 5100.197 0.9987063\n", "⋮ ⋮ ⋮ \n", "a_boy[6] 3308.713 1.0001489\n", "a_boy[7] 3880.149 0.9990667\n", "a_boy[8] 3317.791 0.9991302\n", "a_boy[9] 5297.428 0.9994021\n", "a_boy[10] 4105.215 1.0000839\n", "a_boy[11] 3896.860 0.9988511\n", "a_boy[12] 3777.433 0.9989543\n", "a_boy[13] 4259.095 0.9990450\n", "a_boy[14] 4502.372 0.9996217\n", "a_boy[15] 4221.052 0.9987526\n", "a_boy[16] 4264.674 0.9988805\n", "a_boy[17] 3706.006 0.9986395\n", "a_boy[18] 3493.254 0.9986243\n", "a_boy[19] 3833.874 0.9992270\n", "a_boy[20] 3961.773 0.9986611\n", "a_boy[21] 4278.342 0.9984816\n", "a_boy[22] 4313.655 0.9987957\n", "a_boy[23] 5199.071 0.9988071\n", "a_boy[24] 4171.203 0.9989638\n", "a_boy[25] 4217.568 0.9995400\n", "a_boy[26] 4517.137 0.9988017\n", "a 2719.812 0.9993785\n", "b 2536.216 1.0007571\n", "sigma_intercepts_slopes[1] 2971.258 0.9986441\n", "sigma_intercepts_slopes[2] 2646.944 0.9995006\n", "Rho[1,1] NaN NaN\n", "Rho[1,2] 2607.412 0.9985915\n", "Rho[2,1] 2607.412 0.9985915\n", "Rho[2,2] 1956.060 0.9979980\n", "sigma 2380.168 0.9985868" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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xGksdZuPcL0tA557jE4wXGLs978zZHGtlA48ok8qfd0bTc3Ep5WS8q7C4MRpLHN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aoC1FjEiq0SxzBo6uyz9C92QydXZ2/qCKfhOjupIx05Emw59tsVpKxxHonFSMF/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\nQW2GGFiZtUIps2Z5qfXkAgSsIUOo5oa9A8pVSO2unqM02cfsaq8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MqnWKp7tquNbFlabJCyBJefvhuoZ+NDtHfe3konb3d11wVBUpLC0i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}, "metadata": { "filenames": { "image/png": "/tmp/_build/jupyter_execute/notes/practice-14_51_2.png" } }, "output_type": "display_data" } ], "source": [ "m_ox2 <- ulam(\n", " alist(\n", " Height ~ dnorm(mu, sigma),\n", " mu <- a_boy[Subject] + b_boy[Subject] * Age,\n", " c(a_boy, b_boy)[Subject] ~ multi_normal(c(a, b), Rho, sigma_intercepts_slopes),\n", " a ~ normal(150, 40),\n", " b ~ normal(40, 40),\n", " sigma_intercepts_slopes ~ exponential(1),\n", " Rho ~ lkj_corr(2),\n", " sigma ~ normal(0, 2)\n", " ),\n", " data = ox_dat, chains = 4, cores = 4, log_lik = TRUE\n", ")\n", "display(precis(m_ox2, depth=3), mimetypes=\"text/plain\")\n", "iplot(function() {\n", " plot(precis(m_ox2, depth=3), main=\"m_ox2\")\n", "}, ar=0.7)\n", "\n", "post <- extract.samples(m_ox2)\n", "Mu_est <- c(mean(post$a), mean(post$b))\n", "rho_est <- mean(post$Rho[,1,2])\n", "sa_est <- mean(post$sigma_intercepts_slopes[,1])\n", "sb_est <- mean(post\$sigma_intercepts_slopes[,2])\n", "cov_ab <- sa_est*sb_est*rho_est\n", "Sigma_est <- matrix(c(sa_est^2, cov_ab, cov_ab, sb_est^2), nrow=2)\n", "\n", "library(MASS)\n", "set.seed(5)\n", "N_boys <- 10\n", "vary_effects <- mvrnorm(N_boys, Mu_est, Sigma_est)\n", "\n", "iplot(function() {\n", " plot(NULL, main=\"Posterior predictive plot, 10 simulated boys\",\n", " xlab=\"age\", ylab=\"height\",\n", " xlim=c(-1.1, 1.1),\n", " ylim=c(min(vary_effects[,1] - vary_effects[,2]) - 10, max(vary_effects[,1] + vary_effects[,2]) + 10)\n", " )\n", " for (idx in 1:N_boys)\n", " abline(a=vary_effects[idx, 1], b=vary_effects[idx, 2])\n", "})" ] } ], "metadata": { "jupytext": { "cell_metadata_filter": "-all", "formats": "md:myst", "text_representation": { "extension": ".md", "format_name": "myst", "format_version": 0.13, "jupytext_version": "1.11.5" } }, "kernelspec": { "display_name": "R", "language": "R", "name": "ir" }, "language_info": { "codemirror_mode": "r", "file_extension": ".r", "mimetype": "text/x-r-source", "name": "R", "pygments_lexer": "r", "version": "4.1.2" }, "source_map": [ 14, 18, 21, 100, 143, 147, 171, 191, 250, 254, 260, 281, 352, 356, 362, 379, 448, 452, 507, 527, 533, 538, 541, 545, 592, 603, 628, 696, 714, 718, 720, 725, 728, 732, 734, 739, 741, 745, 776, 780, 804, 825, 859, 875, 878, 882, 885, 889, 912, 948, 971, 993 ] }, "nbformat": 4, "nbformat_minor": 5 }