PyMC solution to http://allendowney.blogspot.ca/2014/11/the-world-cup-problem-germany-v-brazil.html

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## The World Cup Problem: Germany v. Brazil\n",
      "\n",
      "PyMC solution to [Allen D.s soccer problem](http://allendowney.blogspot.ca/2014/11/the-world-cup-problem-germany-v-brazil.html).\n",
      "\n",
      "We'll use an exponential prior, instead of a Uniform prior, but also with mean equal to the observed sample mean goals per team per game. \n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "%pylab inline\n",
      "figsize(12,6)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "avg_goals_per_team = 1.34\n",
      "duration_of_game = 93."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 69
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#prior\n",
      "lambda_ = pm.Exponential('lambda_', duration_of_game/avg_goals_per_team)\n",
      "sample = np.array([lambda_.random() for i in range(10000)])\n",
      "hist(sample, bins=30);\n",
      "plt.title('Prior distribution: Exponential with mean equal to observed mean');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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kSarAQrrB7KXKZZ55zDKXeeYyzzxmmcs868dCWpIkSarAQrrB7KXKZZ55zDKX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\nC+kGs0c6l71pecwyl3nmMs8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       "text": [
        "<matplotlib.figure.Figure at 0x10abb21d0>"
       ]
      }
     ],
     "prompt_number": 71
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sample_points_per_team = np.random.poisson(duration_of_game*sample)\n",
      "hist(sample_points_per_team, bins=sample_points_per_team.max(), normed=True);\n",
      "plt.title('Hypothetical goals/game/team,\\ngiven homogeneous Poisson Process model assumptions')\n",
      "plt.ylabel('Probability')\n",
      "plt.xlabel('Number of goals');\n",
      "\n",
      "print sample_points_per_team.mean()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.3133\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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mmFOOOeWZVY455ZlVjjnlmFN1OlVwA1xS/JQNVWi/NbGuJEmSVHse2r0HlXcA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\nTSD1mAjIbr0AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f0baed0>"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "duration_between_goals = [11, 12]\n",
      "\n",
      "obs = pm.Exponential('obs', lambda_, observed=True, value=duration_between_goals)\n",
      "\n",
      "prediction = pm.Poisson('pred', (duration_of_game-23)*lambda_)\n",
      "\n",
      "mcmc = pm.MCMC([lambda_, obs, prediction])\n",
      "mcmc.sample(15000,5000)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 4428 of 15000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 7701 of 15000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------74%--------          ] 11211 of 15000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 14758 of 15000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 15000 of 15000 complete in 2.0 sec"
       ]
      }
     ],
     "prompt_number": 73
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prediction_trace = mcmc.trace('pred')[:]\n",
      "hist(prediction_trace,bins=max(prediction_trace), normed=True);\n",
      "plt.title(\"Predictive distribution of Germany's goals in the next 70 minutes\")\n",
      "plt.ylabel('Probability')\n",
      "plt.xlabel('Number of goals');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2cOeydy6PWeYyz1zmmccsc5lns6aP0/VsGuP2LwTWAk8HriR6wX8w1kFJkiRJ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\nJEmSJGk8/X94ASQ+NASrEgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10aaed5d0>"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(prediction_trace >= 5).mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 76,
       "text": [
        "0.128"
       ]
      }
     ],
     "prompt_number": 76
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We get more than twice the probability that Germany scores 5 or more goals. Why such a large difference? Since we have very few data points (only two), our prior still has lots of influence on the posterior, so our results are very depenedent on prior chosen - and Allen and I choose different priors (uniform vs. exponential). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}