{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bayesian Statistics Seminar\n",
    "===\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "\n",
    "from thinkbayes2 import Pmf, Suite\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Working with Pmfs\n",
    "---\n",
    "Create a Pmf object to represent a six-sided die."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d6 = Pmf()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A Pmf is a map from possible outcomes to their probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "for x in [1,2,3,4,5,6]:\n",
    "    d6[x] = 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Initially the probabilities don't add up to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 1\n",
      "2 1\n",
      "3 1\n",
      "4 1\n",
      "5 1\n",
      "6 1\n"
     ]
    }
   ],
   "source": [
    "d6.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Normalize` adds up the probabilities and divides through.  The return value is the total probability before normalizing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6.Normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now the Pmf is normalized."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1 0.166666666667\n",
      "2 0.166666666667\n",
      "3 0.166666666667\n",
      "4 0.166666666667\n",
      "5 0.166666666667\n",
      "6 0.166666666667\n"
     ]
    }
   ],
   "source": [
    "d6.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can compute its mean (which only works if it's normalized)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.5"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`Random` chooses a random value from the Pmf."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d6.Random()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`thinkplot` provides methods for plotting Pmfs in a few different styles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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qOINekjrOoJekjjPoJanjDHpJ6rhWQZ9kU5KjSY4leeAiNY8kOZ7kcJIbm7E1SZ5N8mqS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\nUscZ9JLUcQa9JHXc/wfKPgVBfzMnfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eedd1fdd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Hist(d6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 1:**  The Pmf object provides `__add__`, so you can use the `+` operator to compute the Pmf of the sum of two dice.\n",
    "\n",
    "Compute and plot the Pmf of the sum of two 6-sided dice."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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PAGuH2h4Y2t86xxw/BX46aoGSpPHxjlxJahFDX5JaxNCXpBYx9CWpRQx9SWoRQ1+SWsTQ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\nHyNPMQvJFWOvAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb60bc550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "thinkplot.Hist(d6+d6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 2:** Suppose I roll two dice and tell you the result is greater than 3.\n",
    "\n",
    "Plot the Pmf of the remaining possible outcomes and compute its mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.393939393939394"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Gf34/3+uQczjO/KOKDpd3vDlLkhrS9+UdSdIyMvqS1BCjL0kNMfqS1BCjL0kNMfqS1BCj\nL0kNMfqS1JD/BRvbyHla71dWAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5df9c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf = d6 + d6\n",
    "pmf[2] = 0\n",
    "pmf[3] = 0\n",
    "pmf.Normalize()\n",
    "thinkplot.Hist(pmf)\n",
    "pmf.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The cookie problem\n",
    "---\n",
    "Create a Pmf with two equally likely hypotheses.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.5\n",
      "Bowl 2 0.5\n"
     ]
    }
   ],
   "source": [
    "cookie = Pmf(['Bowl 1', 'Bowl 2'])\n",
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Update each hypothesis with the likelihood of the data (a vanilla cookie)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.625"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cookie['Bowl 1'] *= 0.75\n",
    "cookie['Bowl 2'] *= 0.5\n",
    "cookie.Normalize()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print the posterior probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.6\n",
      "Bowl 2 0.4\n"
     ]
    }
   ],
   "source": [
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 3:** Suppose we put the first cookie back, stir, choose again from the same bowl, and get a chocolate cookie.\n",
    "\n",
    "Hint: The posterior (after the first cookie) becomes the prior (before the second cookie)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.428571428571\n",
      "Bowl 2 0.571428571429\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "cookie['Bowl 1'] *= 0.25\n",
    "cookie['Bowl 2'] *= 0.5\n",
    "cookie.Normalize()\n",
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 4:** Instead of doing two updates, what if we collapse the two pieces of data into one update?\n",
    "\n",
    "Re-initialize `Pmf` with two equally likely hypotheses and perform one update based on two pieces of data, a vanilla cookie and a chocolate cookie.\n",
    "\n",
    "The result should be the same regardless of how many updates you do (or the order of updates)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bowl 1 0.428571428571\n",
      "Bowl 2 0.571428571429\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "cookie = Pmf(['Bowl 1', 'Bowl 2'])\n",
    "cookie['Bowl 1'] *= 0.75 * 0.25\n",
    "cookie['Bowl 2'] *= 0.5 * 0.5\n",
    "cookie.Normalize()\n",
    "cookie.Print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## STOP HERE"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Euro problem\n",
    "\n",
    "\n",
    "**Exercise 5:**  Write a class definition for `Euro`, which extends `Suite` and defines a likelihood function that computes the probability of the data (heads or tails) for a given value of `x` (the probability of heads).\n",
    "\n",
    "Note that `hypo` is in the range 0 to 100.  Here's an outline to get you started."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class Euro(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\" \n",
    "        hypo is the prob of heads (0-100)\n",
    "        data is a string, either 'H' or 'T'\n",
    "        \"\"\"\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class Euro(Suite):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\" \n",
    "        hypo is the prob of heads (0-100)\n",
    "        data is a string, either 'H' or 'T'\n",
    "        \"\"\"\n",
    "        x = hypo / 100\n",
    "        if data == 'H':\n",
    "            return x\n",
    "        else:\n",
    "            return 1-x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We'll start with a uniform distribution from 0 to 100."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5c99cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Euro(range(101))\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can update with a single heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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18An8CDAGSL1im/nAOGBmsEzOOueOmdnJ693WzBo45356Y/1IYPOt7oSE2rX/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\nERG5ispBRESuonIQEZGrqBxEROQq/x/8+g7JrjO2aAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5cd2290>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.Update('H')\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Another heads:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rQpWJRBeFg8SEfQePMn7SfOYu3XRWf5MGtRhxaz8u75wUocpEopPCQSq0UxmZ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\n/H/cYFpqrQd1cQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5b98650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.Update('H')\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And a tails:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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nyhE9XI3JGDeM6F909bB8ffDtEGfJwVSpd/+1kgOHPZud1KkdY91JJmwN69vB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\n81hyMMYYcx5LDsYYY87z/wE3Qcameo1YXAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5aa4bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro.Update('T')\n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Starting over, here's what it looks like after 7 heads and 3 tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "70"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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FhDFDATDAweMF9gbk5zQ5KOWDGhub2Lyr+ZLSCm01eGT25OZeS/u011KXaHJQygcdOH6e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\nA6VVsMR4XJ9KAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb615c590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Euro(range(101))\n",
    "\n",
    "for outcome in 'HHHHHHHTTT':\n",
    "    euro.Update(outcome)\n",
    "\n",
    "thinkplot.Pdf(euro)\n",
    "euro.MaximumLikelihood()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The maximum posterior probability is 70%, which is the observed proportion.\n",
    "\n",
    "Here are the posterior probabilities after 140 heads and 110 tails."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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B1T9RrJRbAlYPDgGzCiWXkXZLwBYqh4BZhZITxTwmYAuVQ8CsQrV6oMykbj9i0urAIWBW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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5931bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro = Euro(range(101))\n",
    "\n",
    "evidence = 'H' * 140 + 'T' * 110\n",
    "for outcome in evidence:\n",
    "    euro.Update(outcome)\n",
    "    \n",
    "thinkplot.Pdf(euro)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior mean s about 56%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55.952380952380956"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So is the value with maximum aposteriori probability (MAP)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "56"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.MAP()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior credible interval has a 90% chance of containing the true value (provided that the prior distribution truly represents our background knowledge)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(51, 61)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "euro.CredibleInterval(90)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise 6** The following function makes a `Euro` object with a triangle prior."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def TrianglePrior():\n",
    "    \"\"\"Makes a Suite with a triangular prior.\"\"\"\n",
    "    suite = Euro(label='triangle')\n",
    "    for x in range(0, 51):\n",
    "        suite.Set(x, x)\n",
    "    for x in range(51, 101):\n",
    "        suite.Set(x, 100-x) \n",
    "    suite.Normalize()\n",
    "    return suite"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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bvjqCvDbBIdbyA0eZs7yEg0eOp7hnmU3FIU1tLa/kgZWldWE9p3Rpx21FBQrr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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb59a6ad0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "euro1 = Euro(range(101), label='uniform')\n",
    "euro2 = TrianglePrior()\n",
    "thinkplot.Pdfs([euro1, euro2])\n",
    "thinkplot.Config(title='Priors')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Update `euro1` and `euro2` with the same data we used before (140 heads and 110 tails) and plot the posteriors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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BYD+wNvB8TfpYbpmTpyiz191/nn78LWDSgWWYGAREFqqeofj44nEUPkcgo6E6\nEggCppaAvOjH8ebNm+d9zXy6gx4H1ptZu5lVAFcBW3LKbAGuBTCzC4Aedz/s7oeBvWZ2errc64Bn\n5l1rkTIK5ghESNJYX5zuoPqcpSPUEpBimLEl4O4JM7sR2EoqaNzt7tvM7IbUy36Xuz9oZleY2XPA\nIHB94BLvB75qZlFgV85rIotObndQY4HXDcpoqAosImcherV0hBRBXmMC7v4QcEbOsTtznt84xbm/\nAl491wqKLDQ9Q3HGEuN7CTQVIVsYoDIaprYq9Sfq2ITcBJFCUcawyCz1DseJx1O7ikVI0lSkKaIA\nTTXjOQhdGhOQIlAQEJmlnsHR7AqiEZI0FWlgGKC1IRgEtH6QFJ6CgMgsHQ10yzTVVWRn8BRDa30V\nmRUpBkcTjMbiRXsvWZoUBERmIZl0ugJLRiwvYlcQpDeXCeww1tWrGUJSWAoCIrMwMDpGLD6eLby8\nqbao79dQHSUaDWwu06cgIIWlICAyCz1DcWKB6aHNjcVuCUSoCGQNdykISIEpCIjMQu/Q+MygUgSB\n3KUjunoGi/p+svQoCIjMQs9QbEK2cEtDcbuD6qsjVERTuQIJjB5lDUuBKQiIzELf8NiEbOGWUowJ\nBJaO6OpVS0AKS0FAZBZ6h+ITBoZbijw7qL4qQjSSaQkoCEjhKQiIzEJud1BzY5G7g6oiVFWmgkDS\nQnT1av0gKSwFAZFZ6B6MZdcNiprTWIQN5oPMjGX141nDRxQEpMAUBERm4WjveLZwc10loVDx/4SW\nN1Zns4b7lTUsBaYgIJInd+dYYMmI5UXaVjJXc21FdsP5MWUNS4EpCIjkaSSeZDg2vsH88qbiDgpn\nNNdEs0EgQYhuJYxJASkIiOQplSiWHhT2JK1NdSV536baimzW8JgpCEhhKQiI5KlnKDZhyYimhuIt\nIR3UXDOeNTxGWFnDUlAKAiJ56hsey7YEwiRpLXKiWEZTbUUgazhEd5+CgBSOgoBInnpzNphvLvKS\nERnNtdEJA8PqDpJCUhAQyVPPUGxCS6ClyIvHZTTVjM8OSliI4+oOkgJSEBDJU+9QnNhYegVRT5Ss\nJVARCdFYWwGkNpw/qoQxKSAFAZE8dfWPkkg6ABVhaChytnBQMCchuL2lyHwpCIjkKbhkQ0tdJZZJ\n4y2BtqbxrOEBZQ1LAeUVBMzsMjPbbmY7zOzmKcp8xsx2mtmTZnZOzmshM/ulmW0pRKVFyuFYf+mz\nhTOC4wIr14pRAAAQ/klEQVTKGpZCmjEImFkIuAO4FDgbuNrMNuSUuRw41d1PA24APp9zmZuAZwpS\nY5EyiCeS9A2NZwuvLFG2cEZTYIZQQgljUkD5tATOA3a6+253jwP3AxtzymwE7gNw90eBRjNrAzCz\nNcAVwBcLVmuREusLTA8Ne5KWEmULZzTXBLKGCWtfASmYfILAamBv4Pm+9LHpyuwPlPk74IOAz7GO\nImXXPRifMD202HsL52qqjRKNBnIF1B0kBRIp5sXN7I3AYXd/0sw6gGlH0jZt2pR93NHRQUdHRzGr\nJ5K34/2j2emhpdhbOFdqJVFlDS91nZ2ddHZ2FvSa+QSB/cDawPM16WO5ZU6epMyVwFvM7AqgGqg3\ns/vc/drJ3igYBEQWkmMD44liURJF31s4V1ONsoblxT+ON2/ePO9r5tMd9Diw3szazawCuArIneWz\nBbgWwMwuAHrc/bC7f8jd17r7S9Ln/XCqACCykB3rHx1fMsITNBd5b+Fc9VURqirGt5k82q2WgBTG\njC0Bd0+Y2Y3AVlJB425332ZmN6Re9rvc/UEzu8LMngMGgeuLW22R0jrWP5rdYD5CkpYi7y2cy8xo\nDWwzebhHWcNSGHmNCbj7Q8AZOcfuzHl+4wzXeBh4eLYVFFkIDveMkPTU3IbqMNRWV5S8Disax3MT\njg+Mlvz95cSkjGGRGSSTzqHAbJwVjVUlzRbOyM0aHhlV1rDMn4KAyAx6huIMj6S+cMOepK2ltDkC\nGc21lRocloJTEBCZwfGBUUZjmemhCdpaG8pSj+AMoYSFFQSkIBQERGZwrD+WDQJREqxcXp4g0FwX\nzBoOcbSrvyz1kBOLgoDIDI5NaAkkWbmssSz1aK6JUlkRBVJB4NCxvrLUQ04sCgIiMzgeaAlEPMHK\ncnUH1VZQWTGeNXzoWG9Z6iEnFgUBkRkc7R9lNJ4aGC5nd1BTTXQ8CFiIQ8fUHSTzpyAgMoMDXYOk\nNxSjsTpCbXXl9CcUSTQcoqU+lSvgGPvUHSQFoCAgMo1k0jnUMz4LZ01reaaHZrQ1VWdXYewaiClX\nQOZNQUBkGt1DMYZHMpvLJzlpRXkGhTNa6yqpSHcJjRHi8HG1BmR+FAREppGaHhoYDyjToHDGiobK\n7EJyccIcPKrBYZkfBQGRaRzrH2U0Pp4otnJZeYNAW2MVFdF0ELAIh49rcFjmR0FAZBrHB2KMjo7n\nCLQtgCBQVZnKFYgT1jRRmTcFAZFpBFsCUV8ILYHK7DTROGEOHdWYgMyPgoDINA71DDGWSAJQFabk\n+wjkaqmtoLYqtYx1wkLs1zRRmScFAZFp7Ds2voPXquaasiwhHWRmrF02HogOdg+TSAcpkblQEBCZ\nQiLpHOkdyT5fu6K8OQIZJ7XUZFcTHfUQR7sHylwjWcwUBESm0D0YYzidjBXxBCctL2+OQMbKxqrx\ncQELK1dA5kVBQGQKx/pHszkCEZJl20cg14qG3MFhzRCSuVMQEJnCsYHYgsoRyFjZWEVlJleAiJaU\nlnlREBCZQqolENxMZmF0B7U1VlGV3lcgbsoVkPlREBCZwt5jQ8TiCSCVI7Ciub7MNUqpq4rQVJea\nJprE2H1ELQGZOwUBkSk8d2j8y7WtsZJoNFzG2ky0dvn4TKX9XcO4exlrI4tZXkHAzC4zs+1mtsPM\nbp6izGfMbKeZPWlm56SPrTGzH5rZ02b2lJm9v5CVFymWkViCA12pHAHDWbd8YUwPzVi7rJZwKJWz\nMBh3egeGy1wjWaxmDAJmFgLuAC4FzgauNrMNOWUuB05199OAG4DPp18aAz7g7mcDrwHem3uuyEK0\nv3t4fDzAE6xaIIPCGW2N1dn9huOm5SNk7vJpCZwH7HT33e4eB+4HNuaU2QjcB+DujwKNZtbm7ofc\n/cn08QFgG7C6YLUXKZJ9XcPZHIEKxsq2ufxUJuQKoFwBmbt8gsBqYG/g+T5e/EWeW2Z/bhkzWwec\nAzw620qKlNreriEGh2MAVPgYp65dXuYaTTRxIbkIBzVDSOYoUoo3MbM64FvATekWwaQ2bdqUfdzR\n0UFHR0fR6yYymT3HBhkeSQWBSsZYv8CCwIqG8ZbAmIXYd7inzDWSUujs7KSzs7Og18wnCOwH1gae\nr0kfyy1z8mRlzCxCKgB82d3/ebo3CgYBkXJxd3Yc6CUz32Zta23ZNpefSkUkxKrmGnYf6MIxntl9\nrNxVkhLI/XG8efPmeV8zn+6gx4H1ZtZuZhXAVcCWnDJbgGsBzOwCoMfdD6dfuwd4xt0/Pe/aipTA\n8YEYXX2p2TZhT3LmumVlrtHkTl3ZSGZR0wNdw/RphpDMwYxBwN0TwI3AVuBp4H5332ZmN5jZf0uX\neRB43syeA+4E/hTAzC4C3gm81syeMLNfmtllRfosIgWxr2t4fDyAMU5rbytzjSZ3Uks1Nem9BeKE\n2bn7SJlrJItRXmMC7v4QcEbOsTtznt84yXn/ASycDBuRPOzrGmJweBTIBIEVZa7R5FY2VlFbXcng\ncIyYhdmx+wivOru93NWSRUYZwyI5dh3pZySdI1BlSdatbi1zjSZ3UnM1tdWplsAoUZ5TS0DmQEFA\nJMcze7qzj09ZUUdFtCST6GbtJStqaayrAiBmEba9cFTLR8isKQiIBIyOJdib3VLSedkpC3NQGKAy\nEuaMkxqJhFN/xl0jSQ5obwGZJQUBkYAD3SPZ8YCoJ9iwbmGOB2Scvqo+O3112KLsfOHwDGeITKQg\nIBKwL5ApnEoSW5gzgzJOX1mfHRcYIcqOFzQuILOjICASsH1fD/Gx1B4CtWE4eWVTmWs0vVNX1FJX\nk2oJjFqEbQoCMksKAiIBz+zpyj5+ycp6QqGF/SdSUxnhjNWZQGU8e7CPWHpLTJF8LOx/4SIlNDqW\nYOeh/uzzl7UvzKmhuV56chNV6XWEhjzCrr1aQkLypyAgkvb0vj76BtNJYj7GK05bWeYa5ef0lXXZ\nweERosoclllREBBJ+9nOY/QPjQBQy+iCzRTOtX5lHbU16aQxi7Dt+UNlrpEsJgoCIsBYIknnU/vJ\n5FptaKtlRcvC2Fh+JvVVUU5ZkaqrY/zq+S4ljUneFAREgO0H+zlwPLXVRcQTXH7++jLXaHZedeoy\nQuklRQ/0x/jtnqNlrpEsFgoCIsCPnznEwFBqPKCeGL/36tPKXKPZ2bC6keaGGiA1LvCDn20rc41k\nsVAQkCUvmXT+7Vfj+yS96pRmmuprylij2Tu9rY5lzXUAjFiUzl/sYiS9R7LIdBQEZMnbebif/cdS\nU0PDnmTjRaeXuUaz11RbwcvaW6iqiOAYh2NhfvrkrnJXSxYBBQFZ8v7ll3uzS0c3RcY47+Xryluh\nOXrDy1bS2pRqDfRRzdafbi9zjWQxUBCQJc3d+eFTB7LPLzxjBZUV0TLWaO5edUozp61uxoCEhfj5\n893sP6IN6GV6CgKypP1iVxf7jqVmBYU8ydsvPmOGMxaucMh44ytX01hfDUCPVfNvP9UAsUxPQUCW\nrKHRMf72gScZSyQBWFntvOKM1WWu1fxcfPoyVi9vACBuEbb8bBdj6QXxRCajICBL1t9//xl2HUx1\nl4Q9ybtedzqWnmu/WFVVhHnLq9cSjaS29t4/HGLLj35d5lrJQqYgIEvSr3cf5x9/Mj575rw1Vbz9\nda8oY40K5z+/dCVtLakB4mGr4K7vPskT2/aWuVayUCkIyJITTyT58FceJxZPdZM0RRLc9q6ORd8K\nyGipq2Dj+adk9xk4HKpn8z2dHNTWkzKJvIKAmV1mZtvNbIeZ3TxFmc+Y2U4ze9LMzpnNuSKlsudI\nP3/0yX9jT3of4RDOh95+DssXyTpB+fqD16zlwrPXUBEJ4xi7x6r5q8//K8MjsXJXTRaYGYOAmYWA\nO4BLgbOBq81sQ06Zy4FT3f004Abg8/meKy/W2dlZ7iosCIW8D+7O3f/yNL//8R+w/UBf9njHaU28\n4YKFnxw223vRUB3lQxvP4tVnnoRZamG5J7rgDzZ9m3/60VOLerBYfx+FlU9L4Dxgp7vvdvc4cD+w\nMafMRuA+AHd/FGg0s7Y8z5Uc+keeMp/7MDIaZ+e+Lr72w228544fcclfbeGzD21nJJ6aCWQ4r15d\nze3v+r0C1ba45nIvmmor2PyOV3D2uuVAKhDsGY1y25Zn+S8f+b/8/1//CQ89upMj3QOLatVR/X0U\nViSPMquB4KjSPlJf7jOVWZ3nuVlX3v5gHtU58T3z4538Rvdiwn3IfEUFv6ySDo7jSYgnk4wlnLGE\nMxRPMpqY+kutNuL8+RVn8vaOs06YcYCpLKuv5BPXncf//PLjbNt9nNhYgiTGviH42mMH+dpjBzF+\nRcSgMmJURsJURkOEzAiHjJAZmVtkZiyEu6W/j8LKJwjMxZz+rTx3bLjQ9ViUuobiuhcU/j6EzTm3\nvZG/ve5CWptqC3bdha6tsYov/PeL+I9nj3Lvv23n6d1dJJLJ7OuOEXeIx2EgnoDhhd1VpL+PwrKZ\nmoFmdgGwyd0vSz+/BXB3/2igzOeBH7n7N9LPtwP/CThlpnMD11g87VERkQXC3efVQMunJfA4sN7M\n2oGDwFXA1TlltgDvBb6RDho97n7YzI7lcS4w/w8iIiKzN2MQcPeEmd0IbCU1kHy3u28zsxtSL/td\n7v6gmV1hZs8Bg8D1051btE8jIiKzMmN3kIiInLjKnjG8lJPJzGyNmf3QzJ42s6fM7P3p481mttXM\nnjWzfzGzxnLXtVTMLGRmvzSzLennS/JemFmjmf2jmW1L//s4fwnfiz83s9+Y2a/N7KtmVrFU7oWZ\n3W1mh83s14FjU352M/vLdNLuNjN7Qz7vUdYgoGQyxoAPuPvZwGuA96Y//y3AD9z9DOCHwF+WsY6l\ndhPwTOD5Ur0XnwYedPczgVcA21mC98LMTgLeB7zS3V9Oqgv7apbOvbiX1Pdj0KSf3czOAn4fOBO4\nHPg/lscc6HK3BJZ0Mpm7H3L3J9OPB4BtwBpS9+Af0sX+Afgv5alhaZnZGuAK4IuBw0vuXphZA3Cx\nu98L4O5j7t7LErwXaWGg1swiQDWwnyVyL9z934HunMNTffa3APen/728AOxkmrysjHIHgamSzJYc\nM1sHnAP8DGhz98OQChTAivLVrKT+Dvgg47lhsDTvxSnAMTO7N901dpeZ1bAE74W7HwA+Aewh9eXf\n6+4/YAnei4AVU3z23O/T/eTxfVruICCAmdUB3wJuSrcIckfrT/jRezN7I3A43TKargl7wt8LUl0e\nrwT+3t1fSWrG3S0szX8XTaR++bYDJ5FqEbyTJXgvpjGvz17uILAfWBt4viZ9bMlIN3G/BXzZ3f85\nffhweu0lzGwlcKRc9Suhi4C3mNku4OvAa83sy8ChJXgv9gF73f3n6ecPkAoKS/HfxeuBXe7e5e4J\n4P8CF7I070XGVJ99P3ByoFxe36flDgLZRDQzqyCVTLalzHUqtXuAZ9z904FjW4A/Tj++Dvjn3JNO\nNO7+IXdf6+4vIfXv4Ifu/kfAd1h69+IwsNfMMsubvg54miX474JUN9AFZlaVHuR8HamJA0vpXhgT\nW8dTffYtwFXp2VOnAOuBx2a8eLnzBMzsMlIzITLJZP+7rBUqITO7CPgx8BSpJp0DHyL1f9w3SUX1\n3cDvu3tPuepZamb2n4D/4e5vMbMWluC9MLNXkBogjwK7SCVghlma9+IjpH4YxIEngHcD9SyBe2Fm\nXwM6gFbgMPAR4J+Af2SSz25mfwn8V1L36iZ33zrje5Q7CIiISPmUuztIRETKSEFARGQJUxAQEVnC\nFARERJYwBQERkSVMQUBEZAlTEBARWcIUBERElrD/B/0LOtPaKCYRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f1eb5884dd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "evidence = 'H' * 140 + 'T' * 110\n",
    "for outcome in evidence:\n",
    "    euro1.Update(outcome)\n",
    "    euro2.Update(outcome)\n",
    "\n",
    "thinkplot.Pdfs([euro1, euro2])\n",
    "thinkplot.Config(title='Posteriors')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}