{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Bayes\n",
    "\n",
    "This notebook presents example code and exercise solutions for Think Bayes.\n",
    "\n",
    "Copyright 2018 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "# import classes from thinkbayes2\n",
    "from thinkbayes2 import Pmf, Beta\n",
    "import thinkplot\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The skeet problem\n",
    "\n",
    "At the 2016 Summer Olympics in the Women's Skeet event, Kim Rhode faced Wei Meng in the bronze medal match.  They each hit 15 of 25 skeets, sending the match into sudden death.  In the first round, both hit 1 of 2 skeets.  In the next two rounds, they each hit 2 skeets.  Finally, in the fourth round, Rhode hit 2 and Wei hit 1, so Rhode won the bronze medal, making her the first Summer Olympian to win an individual medal at six consecutive summer games.\n",
    "\n",
    "But after all that shooting, what is the probability that Rhode is actually a better shooter than Wei?  If the same match were held again, what is the probability that Rhode would win?\n",
    "\n",
    "As always, you will have to make some modeling decisions, but one approach is to estimate, for each shooter, the probability of hitting a skeet.  Then, to estimate the probability that Rhode is a better shooter, you can draw samples from the two posterior distributions and compare them.  To estimate the probability of winning a rematch, you could draw samples from the posterior distributions and simulate a round of 25 shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's a Beta distribution that represents Rhode's probability\n",
    "# of hitting a skeet\n",
    "\n",
    "rhode_beta = Beta(1, 1, label='Rhode')\n",
    "rhode_beta.Update((22, 11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "# And another Beta for Wei\n",
    "\n",
    "wei_beta = Beta(1, 1, label='Wei')\n",
    "wei_beta.Update((21, 12))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# Here's what the posteriors look like\n",
    "\n",
    "thinkplot.Pdf(rhode_beta.MakePmf())\n",
    "thinkplot.Pdf(wei_beta.MakePmf())\n",
    "thinkplot.Config(xlabel='x', ylabel='Probability')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.76753424, 0.68572586, 0.57222812, ..., 0.60927265, 0.69046666,\n",
       "       0.68404881])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# To estimate the probability of superiority, we can\n",
    "# draw samples from the posteriors and compare them\n",
    "\n",
    "rhode_sample = rhode_beta.Sample(10000)\n",
    "wei_sample = wei_beta.Sample(10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6076"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Rhode is a better shooter is about 60%\n",
    "\n",
    "np.mean(rhode_sample > wei_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3924"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Wei is a better shooter is about 40%\n",
    "\n",
    "np.mean(rhode_sample < wei_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# To simulate a rematch, we can draw `p` from the posterior\n",
    "# distribution and then sample from a binomial distribution\n",
    "# with parameters `p` and `n=25`.\n",
    "\n",
    "rhode_rematch = np.random.binomial(25, rhode_sample)\n",
    "thinkplot.Hist(Pmf(rhode_rematch))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.53"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Rhode wins a rematch (without going\n",
    "# to sudden death) is about 52%\n",
    "\n",
    "wei_rematch = np.random.binomial(25, wei_sample)\n",
    "np.mean(rhode_rematch > wei_rematch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3894"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that Wei wins the rematch is about 39%\n",
    "\n",
    "np.mean(rhode_rematch < wei_rematch)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0806"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# And the chance that the rematch also goes to sudden death is\n",
    "# about 9%\n",
    "\n",
    "# Assuming that sudden death is close to 50/50, the overall chance\n",
    "# that Rhode winds is about 56%\n",
    "\n",
    "np.mean(rhode_rematch == wei_rematch)"
   ]
  },
  {
   "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"
  }
 },
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}