CamDavidsonPilon/world_cup_II.ipynb Secret

## world_cup_II.ipynb
{
 "metadata": {
  "name": "",
  "signature": "sha256:99d41acf9c19016529f85de0da8e3382f667f72b191b271630a758a6412d5337"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### The World Cup: Germany vs. Argentina\n",
      "\n",
      "This is a continuation of the Bayesian World Cup series: Allen Downey. has been posting neat little Bayesian problems and suggesting others replicating the solution in their frameworks of choice:\n",
      "\n",
      "1. [Part 1: The World Cup Problem: Germany v. Brazil ](http://allendowney.blogspot.ca/2014/11/the-world-cup-problem-germany-v-brazil.html)\n",
      "2. [Part 2: The World Cup Problem Part 2: Germany v. Argentina](http://allendowney.blogspot.ca/2014/11/the-world-cup-problem-part-2-germany-v.html)\n",
      "\n",
      "My other solution to the first problem is [available here](http://nbviewer.ipython.org/gist/CamDavidsonPilon/7bcdebce13959964269f). "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "%pylab inline\n",
      "figsize(12,6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "avg_goals_per_team = 1.34\n",
      "duration_of_game = 93."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "german_prior = pm.Exponential('german_prior', duration_of_game/avg_goals_per_team)\n",
      "arg_prior = pm.Exponential('arg_prior', duration_of_game/avg_goals_per_team)\n",
      "\n",
      "sample = np.array([german_prior.random() for i in range(10000)])\n",
      "hist(sample, bins=30, normed=True, histtype='stepfilled');\n",
      "plt.title('Prior distribution: Exponential with mean equal to observed mean');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SJEnYYzwt7DGWJEnqH3uMJUmSpBJZGNeUfU65zD+X+ecx+1zmn8v8q8/CWJIk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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x117722050>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "germany = pm.Poisson('germany_obs', german_prior, observed=True, value=[1])\n",
      "argentina = pm.Poisson('arg_obs', arg_prior, observed=True, value=[0])\n",
      "\n",
      "germany_predictive = pm.Poisson('germany_predictive', duration_of_game*german_prior)\n",
      "arg_predictive = pm.Poisson('arg_predictive', duration_of_game*arg_prior)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc = pm.MCMC([germany, argentina, german_prior, arg_prior, germany_predictive, arg_predictive])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.sample(20000, 5000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 1963 of 20000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 4183 of 20000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 6165 of 20000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  39%                  ] 7941 of 20000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 9795 of 20000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------57%-                 ] 11557 of 20000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------67%-----             ] 13421 of 20000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------74%--------          ] 14976 of 20000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------83%-----------       ] 16731 of 20000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------92%---------------   ] 18463 of 20000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 20000 of 20000 complete in 5.5 sec"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "german_lambda_trace = mcmc.trace('german_prior')[:]\n",
      "arg_lambda_trace = mcmc.trace('arg_prior')[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(german_lambda_trace, bins=45, histtype='stepfilled', label='Germany', alpha=0.9, normed=True);\n",
      "hist(arg_lambda_trace, bins=45, histtype='stepfilled', label='Argentina', alpha=0.8, normed=True);\n",
      "plt.legend();\n",
      "plt.title('Posteriors of average goals/minute of the two teams');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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2tpYRI0ZQV1fHwoUL25arr69nzpw59IZCJ0J+FJgDLAYuB6ozt68GriKMII+h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\nJ7JTdXXOxal4GZ+KlbGppHM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       "text": [
        "<matplotlib.figure.Figure at 0x1174819d0>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "german_post_trace = mcmc.trace('germany_predictive')[:]\n",
      "arg_post_trace = mcmc.trace('arg_predictive')[:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(german_post_trace, bins=10, histtype='stepfilled', label='Germany', alpha=0.9, normed=True);\n",
      "hist(arg_post_trace, bins=10, histtype='stepfilled', label='Argentina', alpha=0.8, normed=True);\n",
      "plt.legend();\n",
      "plt.title('Posteriors of Goals per Team for a 93 minute game');\n",
      "plt.ylabel('probability')\n",
      "plt.xlabel('Number of goals')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "<matplotlib.text.Text at 0x117710450>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Vg8sJn1fSxuj/CDsjksqsK2G0bzjhZ7gXCD+Jx5b7C6G28oROritJ1eJyTLi1cdiK8AvC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\npBIy4VZN8wwlium704cr3QVVIWt1FWN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       "text": [
        "<matplotlib.figure.Figure at 0x1175e4790>"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Probability of Germany winning: %.3f\"%(german_post_trace > arg_post_trace).mean()\n",
      "print \"Probability of Argentina winning: %.3f\"%(german_post_trace < arg_post_trace).mean()\n",
      "print \"Probability of tie: %.3f\"%(german_post_trace == arg_post_trace).mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Probability of Germany winning: 0.728\n",
        "Probability of Argentina winning: 0.159\n",
        "Probability of tie: 0.113\n"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Again, the differences between my solution and Allen's is due to the differences in our priors =)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}