gistfile1.txt

{
 "metadata": {
  "name": "coin flip"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#this is how we make a sequence of coin tosses\n",
      "#each trial makes 40 choices between either 0 (heads) or 1 (tails) with 50/50 probability\n",
      "s = scipy.random.choice([0,1], size = 40)\n",
      "s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 23,
       "text": [
        "array([0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1,\n",
        "       1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1])"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#here we keep trying many many times until we get a random sequence where the sum of the first 20 attempts is 20. That is, we got 20 heads in a row\n",
      "s = []\n",
      "for i in range(10000000):\n",
      "    s = scipy.random.choice([0,1], size = 40)\n",
      "    prior = s[0:20]\n",
      "    if sum(prior) == 20:\n",
      "        print \"found\"\n",
      "        break"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "found\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#we got one sequence, lets have a look\n",
      "s"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0,\n",
        "       1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0])"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prior = s[:20] #prior observation: 20 heads\n",
      "future = s[20:]#future observations: 20 more random coin tosses"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "prior #as expected the prior observation is 20 tails in a row"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1])"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "future #the future observation still has a 50/50 distribution of heads and tails, it doesn't 'compensate' for prior in any way"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 36,
       "text": [
        "array([0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 0])"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#histogram of the prior observations.. 100% tails\n",
      "ax = plt.hist(prior, bins = 4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD9CAYAAACoXlzKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nhrADgDGEHQCMIewAYAxhBwBjCDsAGPM/kW7fLDFRk7gAAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#histogram of the future observations: roughly 50/50. A\n",
      "ax = plt.hist(future, bins = 4) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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OnDmqqKho9Z9Z/2Zu1uLHH3/UtGnTJF1602vTpk2KjY01d4urm7VISkpSnz591K1bN3Xr\n1k2PPPKIqqurzcXczVpUVlbqtddekyQlJydrwIABqqmpUVZWVrvOGm2euhnKRfympibn/vvvd2pr\na53z58/f8g3QHTt2mH3Tz81a/Pzzz05ycrKzY8eOKE3ZPtysxbWeeuop57PPPmvHCduPm7U4cOCA\nM3bsWKe5udk5e/ask5aW5uzbty9KE0eOm7WYP3++U1xc7DiO4xw9etRJSEhwfv/992iMG3G1tbWu\n3gB1282Qzsxvdr/5e++9J0l69tlnlZeXp40bN2rgwIHq3r27VqxYEcpLdlhu1uL111/XyZMnr1wn\njo2N1a5du6I5dkS4WYvOws1aDBkyRBMmTNCwYcPUpUsXzZkzR6mpqVGePPzcrMWrr76qwsJC+f1+\nXbx4UW+99ZZ69eoV5cnDr6CgQNu2bdPx48eVlJSkkpISNTU1SfLeTZ/jGL1YCQCdCN+KDwAMIOYA\nYAAxBwADiDkAGEDMAcAAYg4ABvw/D1OVE3zkGa8AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#histogram of the complete trial: highly skewed on tails\n",
      "ax = plt.hist(s, bins = 4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#remember this is a series of completely random coin tosses"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}