Planecrash.ipynb

{
 "metadata": {
  "name": "",
  "signature": "sha256:043fa6be32642db671590678adc2aa7175344b904b261a89605efaccd04738f0"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import scipy as sp\n",
      "import matplotlib.pyplot as plt\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's verify some of the claims made in [this BBC article](http://www.bbc.com/news/magazine-28481060)"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's adjust our plane crash rate to agree with the observation that there have been 45 times since 1990 that two or more crashes\n",
      "have happened on the same day."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rate = 39./365\n",
      "years = (2014-1990)*100\n",
      "N = 365*years\n",
      "crashes = sp.random.poisson(rate,N)\n",
      "\n",
      "print \"Average number of crashes in a year: \", crashes.mean()*365\n",
      "print \"Average number of observed (2014-1990) days with 2 or more crashes: \", (crashes>1).mean()*365 * (2014-1990)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Average number of crashes in a year:  39.1579166667\n",
        "Average number of observed (2014-1990) days with 2 or more crashes:  46.32\n"
       ]
      }
     ],
     "prompt_number": 118
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Look at how many crashes appear in a given year."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "top = 70\n",
      "fig,axs = plt.subplots(figsize=(30,2));\n",
      "axs.hist( [ x.sum() for x in np.split(crashes,years)], np.arange(top), histtype='stepfilled', normed=True, alpha=0.5);\n",
      "plt.xticks(np.arange(top)+0.5, np.arange(top));\n",
      "plt.title(\"Observed occurance of n crashes in a year\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SJEmSJEmSJEkaduo9J5YkSZI0Ym3atInHHnussPxt27YWli1Jkg6t7du3093d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\n/i2tD3gmAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e09efd0>"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next let's look at the average time between crashes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig,axs = plt.subplots(figsize=(30,2));\n",
      "axs.hist( np.diff(np.arange(N)[crashes > 0]), np.arange(50), histtype='stepfilled', alpha=0.5, normed=True);\n",
      "axs.set_xlim((1,50))\n",
      "plt.xticks(np.r_[1:11,15,20,30,40,50]+0.5, np.r_[1:11,15,20,30,40,50]);\n",
      "plt.title(\"Observed fraction of times next crash happens n days later\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e4ae510>"
       ]
      }
     ],
     "prompt_number": 115
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print \"Number of times you expect to see crashes the next day since 1990:\", (np.diff(np.arange(N)[crashes > 0])==1).sum()/(100+0.)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Number of times you expect to see crashes the next day since 1990: 91.72\n"
       ]
      }
     ],
     "prompt_number": 122
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This is close to the 105 times they say they got in the article"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's try to replicate the last statement, the probability we would observe 3 (or more) crashes in 8 days."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.ndimage import convolve\n",
      "eightdays = convolve(crashes, np.ones(8))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 166
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ps = [ (np.array( [ x.sum() for x in np.split(eightdays==i, N/365/10)] ) > 0 ).mean() for i in xrange(10) ]\n",
      "plt.plot(ps);\n",
      "plt.title(\"Probability of observing n crashes in an 8 day span in 10 years\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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MMI2ShIiExtKl8Mc/wgMPwAknwFlnQZcucOih0LEjfOMbsI/jupcoVDc1AW7D\nEsXRwCigV9o0ZwA9gCOAS4A7Ghlj0cTjcdch1KKY6ieMMUE441JMmfXqZQMgrVsH558PTz4Z59Zb\n4cILbajVli2hc2cb/2LECLj0Upg0Ce6+G2bPhoUL4cMPobra9ZLkV9OA0/cHVgKrvNezgBHAUt80\n/wLc5z1fALQFOgAfNjjKIonH48RiMddhpFBM9RPGmCCccSmm3Fq2tCSxcmWcqqrY3v/v3AmbNsGG\nDbBxY/LvK6+k/m/LFhtxr2PHZCnE/zxMJZP6CJokOgFrfa/XAd+qxzSdiUCSEBHJpnlz6NrVHrk0\nJplkSiquk0nQJFHfRoT0OjM1PohIWQiaTBJJw59M/P/zJxMXgjaADACqsDYJgGuBalIbr+8E4lhV\nFMAy4BRqlyRWAt0Dfr+ISDl7D2vzDa2mWJCVQHNgEZkbrmd7zwcArxYrOBERcW8osBwrCVzr/W+8\n90i4zXv/LaBfUaMTEREREZHSNARrp1gBTHAcS8K9WJvJO64D8ekCzAPeBRYDV7gNB4CWWLfmRcAS\n4Aa34aRogt20+bTrQDyrgLexmF5zG8pebYFHsS7rS7DqYNeOwtZR4rGFcOzr12LH3jvAn4EWbsMB\n4EosnsXe85LUBKuGqgSakblNw4WBwHGEK0kcAnzTe94Gq+ILw7pq5f1tirU3newwFr+fAX8CnnId\niOcD4CDXQaS5D7jYe94UOMBhLJnsA2zELpBcqgTeJ5kYHgLGOIvG9MbOTy2x8+gLFKnjT7F73/pv\nxttF8mY81/4X+Mx1EGk2YUkU4Avs6s9RJ7gU272/zbGd9VOHsSR0xjpM3I3b3yNLF6ZYDsAuhu71\nXu/GrtrD5HSsY8zauiYssK3Y+akVlkxbAeudRgQ9sVL8DmAP8Ffg7GJ8cbGTRKYb7ToVOYYoqsRK\nOgscxwG2zyzCqufmYdUWrk0FfoF1xw6LGmAu8AYwznEsAIcBHwPTgTeBaSRLhWFxLla149qnwO+B\nNcAG4HNsW7q0GEvyB2HbbRh2cVRwxU4SuqkuuDZYPfKVWInCtWqsGqwz8G0g5jQaGA58hNVnh+nK\n/SQssQ8FLscOcJeaYj0N/9v7+yVwjdOIUjUHvgs84joQrBrnJ9jFWUfsGBztMiCsHXcK8DzwLLa/\nF+WiqNhJYj2p9Y1dsNKEZNYMeAx4EHjScSzptgB/AU5wHMc/Y78X9gEwExgE3O80IrPR+/sx8ARW\n1erSOu+TFrL6AAABB0lEQVTxuvf6UcLVPX0o8Hdsfbl2AvAKsBmrlnsc289cuxeL7RSsdLPcbTiF\nUZ+b8VypJFwN1xXYyW6q60B82mE9ZAD2BeYDp7kLp5ZTCEfvplbAft7z1sDLwGB34ew1HzjSe15F\n5p/5d2UW7huHE/pi1Tv7YsfhfVhp0LX23t+uWBvl/g5jKahMN+O5NhOre/waazO5yG04gPUaqsYS\naaJ74JCcnyi8Plh99iKse+cv3IZTyymEo3fTYdg6WoSdbMKyn/fFShJvYVfHYend1Br4hGRiDYOr\nSXaBvQ8r1bs2H4tpEXCq41hERERERERERERERERERERERERERERERERERERKx/8DdveG51mlRHUA\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x112eb6410>"
       ]
      }
     ],
     "prompt_number": 173
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist( [ x.max() for x in np.split(eightdays,N/365/10) ], np.arange(12), histtype='stepfilled', alpha=0.5, normed=True);\n",
      "plt.xticks(np.arange(12)+0.5, np.arange(12));\n",
      "plt.title(\"Probability of n being the max number of crashes in 8 day span over 10 years\");"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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16ve2wM+APwDXEOe0nem9hzimz+CIosagicSQeCcwmfr3s0fSa4G/Ir+gvCPw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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e0fe550>"
       ]
      }
     ],
     "prompt_number": 174
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So it would seem that the second part of the article is going by a different definition of crash than the first part of the article."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}