{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "import thinkbayes2\n",
    "import thinkplot\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Socks(thinkbayes2.Suite):\n",
    "    \n",
    "    def __init__(self, hypos):\n",
    "        \"\"\"Inits a Sock object.\n",
    "        \n",
    "        hypos: sequence or map of number of pairs in the drawer\n",
    "        \n",
    "        matched: number of matched socks that have been picked\n",
    "        unmatched: number of unmatched socks that have been picked\n",
    "        \"\"\"\n",
    "        thinkbayes2.Suite.__init__(self, hypos)\n",
    "        self.matched = 0\n",
    "        self.unmatched = 0\n",
    "        \n",
    "    def Update(self, data):\n",
    "        \"\"\"Updates the suite based on data.\n",
    "        \n",
    "        data: 'u' if we picked an unmatched sock, 'm' otherwise\n",
    "        \"\"\"\n",
    "        thinkbayes2.Suite.Update(self, data)\n",
    "        if data == 'u':\n",
    "            self.unmatched += 1\n",
    "        else:\n",
    "            self.matched += 1\n",
    "            \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "        \n",
    "        data: 'u' if we picked an unmatched sock, 'm' otherwise\n",
    "        hypo: hypothetical number of pairs\n",
    "        \"\"\"\n",
    "        n_pairs = hypo\n",
    "        n_socks = 2 * n_pairs - self.matched - self.unmatched\n",
    "        if n_socks <= 0:\n",
    "            return 0\n",
    "        \n",
    "        n_singletons = self.unmatched - self.matched\n",
    "        p = n_singletons / n_socks\n",
    "\n",
    "        like = 1-p if data == 'u' else p\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4Frglri/KOax3fD2M/XN4DuHRg13AHuCLcX1Rzl3SBMIlqS5gIsW8h/HfhJNZBB8lPHWf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2568e8e910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior_n_pairs = thinkbayes2.MakePoissonPmf(12, 30)\n",
    "suite = Socks(prior_n_pairs)\n",
    "thinkplot.Hist(suite)\n",
    "thinkplot.Config(xlabel='# pairs', ylabel='PMF', xlim=[0, 30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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nq/0jur+/v6X6uYPiGCEEthCugFpHOBm9Im4fAO4lXPk0BDwNXBu3vRp4O/AQsD2uuxm4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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2568f44950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "suite = Socks(hypos)\n",
    "for datum in 'u' * 11:\n",
    "    suite.Update('u')\n",
    "thinkplot.Hist(suite)\n",
    "thinkplot.Config(xlabel='# pairs', ylabel='PMF', xlim=[0, 30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Socks2(Socks, thinkbayes2.Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"Computes the likelihood of the data under the hypothesis.\n",
    "        \n",
    "        data: 'u' if we picked an unmatched sock, 'm' otherwise\n",
    "        hypo: hypothetical number of pairs, number of odds\n",
    "        \"\"\"\n",
    "        n_pairs, n_odds = hypo\n",
    "        n_socks = 2 * n_pairs + n_odds - self.matched - self.unmatched\n",
    "        if n_socks <= 0:\n",
    "            return 0\n",
    "        \n",
    "        n_singletons = self.unmatched - self.matched\n",
    "        p = n_singletons / n_socks\n",
    "\n",
    "        like = 1-p if data == 'u' else p\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dMX0dE/84q+Ls0vT7GezjN0Q69fI94Mul5VU5hu32rwrH8KeZOGV2CvBe0hVcVTl2k6ry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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2568f86a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "prior_n_odds = thinkbayes2.MakePoissonPmf(3, 30)\n",
    "thinkplot.Hist(prior_n_odds)\n",
    "thinkplot.Config(xlabel='# odds', ylabel='PMF', xlim=[0, 30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [],
   "source": [
    "joint = thinkbayes2.MakeJoint(prior_n_pairs, prior_n_odds)\n",
    "suite = Socks2(joint)\n",
    "for datum in 'u' * 11:\n",
    "    suite.Update('u')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oJElnqv0jur+/v6X6qYNilBACWwlXQG0gDEqvzrYPAA8QrnwaBl4Ers+2vRW4DngM2JGt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2568f07690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "post_n_pairs = suite.Marginal(0)\n",
    "thinkplot.Hist(post_n_pairs)\n",
    "thinkplot.Config(xlabel='# pairs', ylabel='PMF', xlim=[0, 30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2568cbd410>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "post_n_odds = suite.Marginal(1)\n",
    "thinkplot.Hist(post_n_odds)\n",
    "thinkplot.Config(xlabel='# odds', ylabel='PMF', xlim=[0, 30])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}