{
 "cells": [
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   "cell_type": "markdown",
   "id": "35b3177d-c3fc-4c9f-a6a4-e4824c0f16f4",
   "metadata": {},
   "source": [
    "# 2. Small Worlds and Large Worlds"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dbd8a8ba-296a-4092-90db-dff6f28c96b7",
   "metadata": {},
   "source": [
    "## 2.1 The garden of forking data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fcc2b1c1-c716-4e0c-ba04-42d1aea49252",
   "metadata": {},
   "source": [
    "### 2.1.1 Counting possibilities"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f27a37ae-d826-4273-9602-48c65f257beb",
   "metadata": {},
   "source": [
    "The author's footnote refers to [Cox's theorem](https://en.wikipedia.org/wiki/Cox%27s_theorem); other justifications are given in [Bayesian probability § Justification](https://en.wikipedia.org/wiki/Bayesian_probability#Justification).\n",
    "\n",
    "As discussed in [Cox's theorem § Interpretation and further discussion](https://en.wikipedia.org/wiki/Cox%27s_theorem#Interpretation_and_further_discussion), there's plenty of reason to doubt this justification.\n",
    "\n",
    "An arguably better justification is the [Dutch book theorems](https://en.wikipedia.org/wiki/Dutch_book_theorems); see [Dutch Book Arguments (Stanford Encyclopedia of Philosophy)](https://plato.stanford.edu/entries/dutch-book/) and [Notes on the Dutch Book Argument](https://www.stat.berkeley.edu/~freedman/dutchdef.pdf) (by David A Freedman) for some more rigorous mathematics going back to the original person to make the argument (De Finetti). This justification remains completely finite, which seems desirable, not only if you have prior commitments to finitism but based on the following research (quoting from [David A. Freedman](https://en.wikipedia.org/wiki/David_A._Freedman)):\n",
    "\n",
    "> In particular, the 1965 paper with the innocent title \"On the asymptotic behaviour of Bayes estimates in the discrete case II\" finds the rather disappointing answer that when sampling from a countably infinite population the [Bayesian procedure](https://en.wikipedia.org/wiki/Bayesian_inference \"Bayesian inference\") fails almost everywhere, i.e., one does not obtain the true distribution asymptotically. This situation is quite different from the finite case when the (discrete) random variable takes only finite many values and the Bayesian method is consistent in agreement with earlier findings of Doob (1948)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "74d04ea9-05ad-45f2-a209-3da63cc78420",
   "metadata": {},
   "source": [
    "From [Bayesian inference § Alternatives to Bayesian updating](https://en.wikipedia.org/wiki/Bayesian_inference#Alternatives_to_Bayesian_updating):"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "148e3c0e-eaa3-4432-ab83-267e8bcf00f9",
   "metadata": {},
   "source": [
    "> [Ian Hacking](https://en.wikipedia.org/wiki/Ian_Hacking \"Ian Hacking\") noted that traditional \"[Dutch book](https://en.wikipedia.org/wiki/Dutch_book \"Dutch book\")\" arguments did not specify Bayesian updating: they left open the possibility that non-Bayesian updating rules could avoid Dutch books. Hacking wrote: \"And neither the Dutch book argument nor any other in the personalist arsenal of proofs of the probability axioms entails the dynamic assumption. Not one entails Bayesianism. So the personalist requires the dynamic assumption to be Bayesian. It is true that in consistency a personalist could abandon the Bayesian model of learning from experience. Salt could lose its savour.\"\n",
    ">\n",
    "> Indeed, there are non-Bayesian updating rules that also avoid Dutch books (as discussed in the literature on \"[probability kinematics](https://en.wikipedia.org/wiki/Probability_kinematics \"Probability kinematics\")\") following the publication of [Richard C. Jeffrey](https://en.wikipedia.org/wiki/Richard_C._Jeffrey \"Richard C. Jeffrey\")'s rule, which applies Bayes' rule to the case where the evidence itself is assigned a probability. The additional hypotheses needed to uniquely require Bayesian updating have been deemed to be substantial, complicated, and unsatisfactory."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6e2d6e6-06ab-4cd4-8637-f5d03bca03ce",
   "metadata": {},
   "source": [
    "### 2.1.2 Combining other information"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cc3f9ec-3906-4477-867c-8ac436f94b64",
   "metadata": {},
   "source": [
    "### 2.1.3 From counts to probability"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8317cee9-6e26-4a1f-840e-9eaf5c1350ab",
   "metadata": {},
   "source": [
    "The author uses the term \"plausibility\" as a synonym for probability; it's not clear why the word is being introduced."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0498e39a-68ff-4bed-966f-4791ff6ebe66",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<style>\n",
       ".list-inline {list-style: none; margin:0; padding: 0}\n",
       ".list-inline>li {display: inline-block}\n",
       ".list-inline>li:not(:last-child)::after {content: \"\\00b7\"; padding: 0 .5ex}\n",
       "</style>\n",
       "<ol class=list-inline><li>0</li><li>0.15</li><li>0.4</li><li>0.45</li><li>0</li></ol>\n"
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       "\\begin{enumerate*}\n",
       "\\item 0\n",
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       "\\item 0.4\n",
       "\\item 0.45\n",
       "\\item 0\n",
       "\\end{enumerate*}\n"
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       "1. 0\n",
       "2. 0.15\n",
       "3. 0.4\n",
       "4. 0.45\n",
       "5. 0\n",
       "\n",
       "\n"
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       "[1] 0.00 0.15 0.40 0.45 0.00"
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   ],
   "source": [
    "ways <- c(0, 3, 8, 9, 0)\n",
    "ways / sum(ways)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68feccc4-34e2-49f1-8947-0dbb03951bed",
   "metadata": {},
   "source": [
    "The following sentence seems to accidentally italicize the word *they* (📌):"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fec6a37d-5a73-4727-a10c-8e91e79fab7a",
   "metadata": {},
   "source": [
    "> These plausibilities are also *probabilities—they* are ..."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4645f8e8-c0b0-42d4-8237-c0e0c5d98ad0",
   "metadata": {},
   "source": [
    "## 2.2. Building a model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e9b39c4-7043-417b-96c1-a253fab15803",
   "metadata": {},
   "source": [
    "The three steps the author introduces in this section are almost surely coming directly from his reading of [BDA3](https://stat.columbia.edu/~gelman/book/BDA3.pdf) section **The three steps of Bayesian data analysis**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bca40c5-bab2-45f1-be35-88f3e0afd56c",
   "metadata": {},
   "source": [
    "### 2.2.1. A data story"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "596baf99-e911-4e71-ad8c-a099bdd67095",
   "metadata": {},
   "source": [
    "### 2.2.2. Bayesian updating"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f3d7c62-e231-47bb-8e2d-7cae9bfcacbd",
   "metadata": {},
   "source": [
    "### 2.2.3. Evaluate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "640ce52e-4dfe-4fbc-8daa-53ca9dc9d385",
   "metadata": {},
   "source": [
    "## 2.3. Components of the model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4870e352-2428-4690-be39-2f585e6a4cfa",
   "metadata": {},
   "source": [
    "### 2.3.1. Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a8a7d733-5fdb-4dd1-95cb-267bcfbae1ef",
   "metadata": {},
   "source": [
    "### 2.3.2. Definitions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d23d3e5f-d0f2-4b6c-950c-2b1b6b66a1a1",
   "metadata": {},
   "source": [
    "By far the most confusing definition given here is for the likelihood. In this book, a 'likelihood' will refer to a distribution function assigned to an observed variable. In this section, for example, the 'likelihood' is the binomial distribution. According to the author, this is the language used in 'conventional' statistics as well. The author often calls this the 'likelihood' but it is a function, of course, because any probability distribution is a function.\n",
    "\n",
    "In non-Bayesian statistics and in particular on Wikipedia the definition of the likelihood function is completely different and denoted with $\\mathcal{L}$. See the author's footnote and [Likelihood function](https://en.wikipedia.org/wiki/Likelihood_function)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2dd2f871-58aa-4b09-ae4c-25cb72284306",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.1640625"
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       "0.1640625"
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       "0.1640625"
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      "text/plain": [
       "[1] 0.1640625"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "dbinom(6, size = 9, prob = 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7adf0104-0e79-410d-b460-5386625879d7",
   "metadata": {},
   "source": [
    "## 2.4. Making the model go"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac690714-9cd1-4553-8ac9-946ce1ea203a",
   "metadata": {},
   "source": [
    "### 2.4.3 Grid Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2cd28890",
   "metadata": {},
   "outputs": [
    {
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       "<ol class=list-inline><li>0</li><li>0.0526315789473684</li><li>0.105263157894737</li><li>0.157894736842105</li><li>0.210526315789474</li><li>0.263157894736842</li><li>0.315789473684211</li><li>0.368421052631579</li><li>0.421052631578947</li><li>0.473684210526316</li><li>0.526315789473684</li><li>0.578947368421053</li><li>0.631578947368421</li><li>0.684210526315789</li><li>0.736842105263158</li><li>0.789473684210526</li><li>0.842105263157895</li><li>0.894736842105263</li><li>0.947368421052632</li><li>1</li></ol>\n"
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       "\\begin{enumerate*}\n",
       "\\item 0\n",
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       "\\item 0.263157894736842\n",
       "\\item 0.315789473684211\n",
       "\\item 0.368421052631579\n",
       "\\item 0.421052631578947\n",
       "\\item 0.473684210526316\n",
       "\\item 0.526315789473684\n",
       "\\item 0.578947368421053\n",
       "\\item 0.631578947368421\n",
       "\\item 0.684210526315789\n",
       "\\item 0.736842105263158\n",
       "\\item 0.789473684210526\n",
       "\\item 0.842105263157895\n",
       "\\item 0.894736842105263\n",
       "\\item 0.947368421052632\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
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       "1. 0\n",
       "2. 0.0526315789473684\n",
       "3. 0.105263157894737\n",
       "4. 0.157894736842105\n",
       "5. 0.210526315789474\n",
       "6. 0.263157894736842\n",
       "7. 0.315789473684211\n",
       "8. 0.368421052631579\n",
       "9. 0.421052631578947\n",
       "10. 0.473684210526316\n",
       "11. 0.526315789473684\n",
       "12. 0.578947368421053\n",
       "13. 0.631578947368421\n",
       "14. 0.684210526315789\n",
       "15. 0.736842105263158\n",
       "16. 0.789473684210526\n",
       "17. 0.842105263157895\n",
       "18. 0.894736842105263\n",
       "19. 0.947368421052632\n",
       "20. 1\n",
       "\n",
       "\n"
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       " [1] 0.00000000 0.05263158 0.10526316 0.15789474 0.21052632 0.26315789\n",
       " [7] 0.31578947 0.36842105 0.42105263 0.47368421 0.52631579 0.57894737\n",
       "[13] 0.63157895 0.68421053 0.73684211 0.78947368 0.84210526 0.89473684\n",
       "[19] 0.94736842 1.00000000"
      ]
     },
     "metadata": {},
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    }
   ],
   "source": [
    "p_grid <- seq(from=0, to=1, length.out=20)\n",
    "p_grid"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1d38e72c",
   "metadata": {},
   "outputs": [
    {
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       "<ol class=list-inline><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li><li>1</li></ol>\n"
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       "1. 1\n",
       "2. 1\n",
       "3. 1\n",
       "4. 1\n",
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       "6. 1\n",
       "7. 1\n",
       "8. 1\n",
       "9. 1\n",
       "10. 1\n",
       "11. 1\n",
       "12. 1\n",
       "13. 1\n",
       "14. 1\n",
       "15. 1\n",
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   ],
   "source": [
    "prior <- rep(1, 20)\n",
    "prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "3b511280",
   "metadata": {},
   "outputs": [
    {
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BBCTxHyG4LEQc3EyY7/Kw/e8D11p4GdleQSEYL7I/kBQeJgwWbXcuT5MNpGdLVy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\nKzH3zLf9ovbm3/RBuj/ZPe3NoMO0jQSRO8fMieuo20dOkUHqyPp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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compute likelihood at each value in grid\n",
    "likelihood <- dbinom(6, size=9, prob=p_grid)\n",
    "plot(p_grid, likelihood, type=\"b\", xlab=\"probability of water\", ylab=\"likelihood\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "f485a438",
   "metadata": {},
   "outputs": [
    {
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InV1OzbLzoDuNCHugNXGoP0NssgWnXjRyfd9QmCJNSH26k74O4nqU7JagxS98Ux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\n2N9phxpS4l7l1ZKCIIF282OEltMYpMBgu5Idd3fl1ZENggRavXR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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
       "width": 420
      },
      "image/svg+xml": {
       "height": 420,
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       "width": 420
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     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compute product of likelihood and prior\n",
    "unstd.posterior <- likelihood * prior\n",
    "plot(p_grid, unstd.posterior, type=\"b\", xlab=\"probability of water\", ylab=\"unstandardized posterior\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "21420972",
   "metadata": {},
   "outputs": [
    {
     "data": {
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b1TsgqDNCnRMRl7wP0JPMpxQJDU0T2W5+cGOho8JaswSK/eTVm73t/9VxVpVEp+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\nRszbQNMvpymLH6ng3nYY2KeOiIfPUJegEb3uBJD0qzxIQVVbtKj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      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
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   ],
   "source": [
    "# standardize the posterior, so it sums to 1\n",
    "posterior <- unstd.posterior / sum(unstd.posterior)\n",
    "plot(p_grid, posterior, type=\"b\", xlab=\"probability of water\", ylab=\"posterior probability\")\n",
    "mtext( \"20 points\" )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b13c554-d37f-485b-a052-9aca8ae5b1f9",
   "metadata": {},
   "source": [
    "### 2.4.4 Quadratic Approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "28108196",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: rstan\n",
      "\n",
      "Loading required package: StanHeaders\n",
      "\n",
      "\n",
      "rstan version 2.32.6 (Stan version 2.32.2)\n",
      "\n",
      "\n",
      "For execution on a local, multicore CPU with excess RAM we recommend calling\n",
      "options(mc.cores = parallel::detectCores()).\n",
      "To avoid recompilation of unchanged Stan programs, we recommend calling\n",
      "rstan_options(auto_write = TRUE)\n",
      "For within-chain threading using `reduce_sum()` or `map_rect()` Stan functions,\n",
      "change `threads_per_chain` option:\n",
      "rstan_options(threads_per_chain = 1)\n",
      "\n",
      "\n",
      "Loading required package: parallel\n",
      "\n",
      "rethinking (Version 2.13)\n",
      "\n",
      "\n",
      "Attaching package: ‘rethinking’\n",
      "\n",
      "\n",
      "The following object is masked from ‘package:stats’:\n",
      "\n",
      "    rstudent\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(rethinking)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "f6d9971b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A precis: 1 × 4</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>mean</th><th scope=col>sd</th><th scope=col>5.5%</th><th scope=col>94.5%</th></tr>\n",
       "\t<tr><th></th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th><th scope=col>&lt;dbl&gt;</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>p</th><td>0.6666669</td><td>0.1571337</td><td>0.4155369</td><td>0.917797</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A precis: 1 × 4\n",
       "\\begin{tabular}{r|llll}\n",
       "  & mean & sd & 5.5\\% & 94.5\\%\\\\\n",
       "  & <dbl> & <dbl> & <dbl> & <dbl>\\\\\n",
       "\\hline\n",
       "\tp & 0.6666669 & 0.1571337 & 0.4155369 & 0.917797\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A precis: 1 × 4\n",
       "\n",
       "| <!--/--> | mean &lt;dbl&gt; | sd &lt;dbl&gt; | 5.5% &lt;dbl&gt; | 94.5% &lt;dbl&gt; |\n",
       "|---|---|---|---|---|\n",
       "| p | 0.6666669 | 0.1571337 | 0.4155369 | 0.917797 |\n",
       "\n"
      ],
      "text/plain": [
       "  mean      sd        5.5%      94.5%   \n",
       "p 0.6666669 0.1571337 0.4155369 0.917797"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "globe.qa <- quap(\n",
    "    alist(\n",
    "        W ~ dbinom(W+L, p), # binomial likelihood\n",
    "        p ~ dunif(0, 1)     # uniform prior\n",
    "    ),\n",
    "    data=list(W=6,L=3) )\n",
    "precis(globe.qa)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "509c8a50",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/pdf": 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lUhSKr4fL9kdfZuPmXQcPRD05eQ6Md515ELVzb4kLMfiNf8rqpwJxkrllOywint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\njozJ1Q4Kg1T2CXdabyRHPuzcpF6TrpPOEdkBZREkd3VLEv+LdUz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       "<path fill=\"none\" stroke-width=\"0.75\" stroke-linecap=\"round\" stroke-linejoin=\"round\" stroke=\"rgb(0%, 0%, 0%)\" stroke-opacity=\"1\" stroke-dasharray=\"3 3\" stroke-miterlimit=\"10\" d=\"M 74.398438 416.75 L 78.238281 416.738281 L 82.078125 416.71875 L 85.921875 416.695312 L 89.761719 416.664062 L 93.601562 416.628906 L 97.441406 416.582031 L 101.28125 416.523438 L 105.121094 416.449219 L 108.960938 416.359375 L 112.800781 416.25 L 116.640625 416.113281 L 120.480469 415.945312 L 124.320312 415.742188 L 128.160156 415.5 L 132 415.203125 L 135.839844 414.847656 L 139.679688 414.421875 L 143.519531 413.914062 L 147.359375 413.3125 L 151.199219 412.597656 L 155.039062 411.761719 L 158.878906 410.78125 L 162.71875 409.640625 L 166.558594 408.3125 L 170.398438 406.78125 L 174.238281 405.019531 L 178.078125 403 L 181.921875 400.695312 L 185.761719 398.082031 L 189.601562 395.128906 L 193.441406 391.808594 L 197.28125 388.09375 L 201.121094 383.949219 L 204.960938 379.359375 L 208.800781 374.289062 L 212.640625 368.722656 L 216.480469 362.640625 L 220.320312 356.027344 L 224.160156 348.871094 L 228 341.164062 L 231.839844 332.917969 L 235.679688 324.132812 L 239.519531 314.824219 L 243.359375 305.019531 L 247.199219 294.75 L 251.039062 284.058594 L 254.878906 272.992188 L 258.71875 261.609375 L 262.558594 249.980469 L 266.398438 238.175781 L 270.238281 226.285156 L 274.078125 214.390625 L 277.921875 202.597656 L 281.761719 191 L 285.601562 179.699219 L 289.441406 168.804688 L 293.28125 158.421875 L 297.121094 148.652344 L 300.960938 139.601562 L 304.800781 131.359375 L 308.640625 124.019531 L 312.480469 117.660156 L 316.320312 112.355469 L 320.160156 108.164062 L 324 105.136719 L 327.839844 103.304688 L 331.679688 102.691406 L 335.519531 103.304688 L 339.359375 105.136719 L 343.199219 108.164062 L 347.039062 112.355469 L 350.878906 117.660156 L 354.71875 124.019531 L 358.558594 131.359375 L 362.398438 139.601562 L 366.238281 148.652344 L 370.078125 158.421875 L 373.921875 168.804688 L 377.761719 179.699219 L 381.601562 191 L 385.441406 202.597656 L 389.28125 214.390625 L 393.121094 226.285156 L 396.960938 238.175781 L 400.800781 249.980469 L 404.640625 261.609375 L 408.480469 272.992188 L 412.320312 284.058594 L 416.160156 294.75 L 420 305.019531 L 423.839844 314.824219 L 427.679688 324.132812 L 431.519531 332.917969 L 435.359375 341.164062 L 439.199219 348.871094 L 443.039062 356.027344 L 446.878906 362.640625 L 450.71875 368.722656 L 454.558594 374.289062 L 458.398438 379.359375 \"/>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "application/pdf": {
       "height": 420,
       "width": 420
      },
      "image/jpeg": {
       "height": 420,
       "width": 420
      },
      "image/png": {
       "height": 420,
       "width": 420
      },
      "image/svg+xml": {
       "height": 420,
       "isolated": true,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# analytical calculation\n",
    "W <- 6\n",
    "L <- 3\n",
    "curve( dbeta( x , W+1 , L+1 ) , from=0 , to=1 )\n",
    "# quadratic approximation\n",
    "curve( dnorm( x , 0.67 , 0.16 ) , lty=2 , add=TRUE )"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3717d373-ac07-49e3-838d-f57fadb25870",
   "metadata": {},
   "source": [
    "### 2.4.5 Markov chain Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7ed1affc",
   "metadata": {},
   "outputs": [
    {
     "data": {
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PN99zGKwLkNDTsPRb7Z1hx5Aa5pebgs8lhkG4T3t8LG597SrIzsXra7v+0IXFg8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\naL/45IU7E26Kwy8VBz4XTjBh4qcKybPYzsOai7UWaxDrNqxTsF6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EvqdlwNPAf8L/DmThPM0K7AQqIAzMuq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\nYQ8QC0pm3Z0nSZIkSZkaDJwJLGT5IpqVvuYRC20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      "text/plain": [
       "Plot with title “”"
      ]
     },
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   ],
   "source": [
    "n_samples <- 1000\n",
    "p <- rep(NA, n_samples)\n",
    "p[1] <- 0.5\n",
    "W <- 6\n",
    "L <- 3\n",
    "for (i in 2:n_samples) {\n",
    "    p_new <- rnorm( 1 , p[i-1] , 0.1 )\n",
    "    if ( p_new < 0 ) p_new <- abs( p_new )\n",
    "    if ( p_new > 1 ) p_new <- 2 - p_new\n",
    "    q0 <- dbinom( W , W+L , p[i-1] )\n",
    "    q1 <- dbinom( W , W+L , p_new )\n",
    "    p[i] <- ifelse( runif(1) < q1/q0 , p_new , p[i-1] )\n",
    "}\n",
    "dens( p , xlim=c(0,1) )\n",
    "curve( dbeta( x , W+1 , L+1 ) , lty=2 , add=TRUE )"
   ]
  }
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