{
 "metadata": {
  "name": "More hacking with PyMC"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize( 12.5 ,4)\n",
      "import scipy.stats as stats"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Chapter 11 \n",
      "___________\n",
      "## More Hacking with PyMC\n",
      "\n",
      "This chapter introduces useful or advanced techniques with PyMC including building your own stochastic variables, user-defined steps etc."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\n",
      "##### Example: Real-time Github Popularity Measures\n",
      "\n",
      "\n",
      "Most of you are likely familar with the git-repository website Github. An observed phenomenon on Github is the *scale-ness* of the popularity of repositories. Here, for lack of a better measure, we use the numbers of *stars* and *forks* to measure popularity. This is not a bad measure, but it can ignore page-views, downloads and tends to overemphasize older repositories. Since we will be studying *all* repositories and not a single one, the absense of these measures is not as relevant. \n",
      "\n",
      "Contained in this folder is a Python script for scrapping data from Github on the popularity of repos. The script requires the `Requests` and `BeautifulSoup` libraries, but if you don't have that installed, provided in the `./data` folder is the same data from a previous date (Feburary 18, 2013 at last pull). The data is the fraction of repositories with stars equal to or greater than $2^k,\\; k = 0,...,15$ and the fraction of repositories with forks equal to or than $2^k,\\; k = 0,...,15$.\n",
      "    "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "run github_datapull.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Scrapping data from Github. Sorry Github...\n",
        "The data is contained in variables `foo_to_explore` and `repo_with_foo`\n",
        "\n",
        "stars first...\n",
        "number of repos with greater than or equal to 0 stars: 2738541"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 1 stars: 1704779"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 2 stars: 493529"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 4 stars: 212099"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 8 stars: 106973"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 16 stars: 58101"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 32 stars: 31877"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 64 stars: 17370"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 128 stars: 9239"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 256 stars: 4578"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 512 stars: 2150"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 1024 stars: 872"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 2048 stars: 286"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 4096 stars: 84"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 8192 stars: 22"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 16384 stars: 5"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 32768 stars: 1"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "\n",
        "forks second...\n",
        "number of repos with greater than or equal to 0 forks: 2738548"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 1 forks: 334539"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 2 forks: 159206"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 4 forks: 74836"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 8 forks: 36532"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 16 forks: 17948"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 32 forks: 8394"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 64 forks: 3841"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 128 forks: 1580"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 256 forks: 605"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 512 forks: 222"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 1024 forks: 69"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 2048 forks: 17"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 4096 forks: 4"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 8192 forks: 2"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 16384 forks: 0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "number of repos with greater than or equal to 32768 forks: 0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot( ( stars_to_explore), repo_with_stars, label = \"stars\" )\n",
      "plt.plot( ( forks_to_explore), repo_with_forks, label = \"forks\" )\n",
      "plt.legend(loc = \"lower right\")\n",
      "plt.title(\"Popularity of Repos (as measured by stars and forks)\" )\n",
      "plt.xlabel(\"$K$\")\n",
      "plt.ylabel(\"number of repos with stars/forks  $K$\" )\n",
      "plt.xlim( -200, 35000 )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "(-200, 35000)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Kzz//fK0BlQ87MBMA3njjDezevRvXr1/HqlWr8OKLL2p0l7mf+/2C9TC/gALV42ecnZ3R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\nRERERGbzX8VMdv/FLvLEAAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Clearly, we need to adjust the scale of this plot as most of the action is hidden. The number of repos falls very quickly. We will put it on a log-log plot."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot( log2( stars_to_explore+1), log2(repo_with_stars+1), 'o-', label = \"stars\" )\n",
      "plt.plot( log2( forks_to_explore+1), log2(repo_with_forks+1), 'o-', label = \"forks\",  )\n",
      "plt.legend(loc = \"upper right\")\n",
      "plt.title(\"Log-Log plot of Popularity of Repos (as measured by stars and forks)\" )\n",
      "plt.xlabel(\"$\\log{K}$\")\n",
      "plt.ylabel(\"$\\log$(number of repos with stars/forks  < K )\" )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "<matplotlib.text.Text at 0x5d64590>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Tg3379mHu3Lkqj9d8EwkJCdiwYQPu3buHhw8fYvXq1fD3969y5gagYT9Vkagu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OCBB2hqauLq1asEg0H27NmD3W43OlZMWbRoEdu3bwdg+/btmkCJsIaGBsrKyti1axfjx483Ok7M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\n8iIiIiIiUeg/wIs+PAyzB70AAAAASUVORK5CYII=\n"
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Both characteristics look like a straight line plotted on a log-log plot. What does this mean? Denote the fraction of repos with greater than or equal to $k$ stars (or forks) $P(k)$. So in the above plot, $\\log{P(k)}$ on the y-axis and $\\log{k}$ is on the x-axis. The above linear relationship can be written as:\n",
      "\n",
      "$$ \\log_2{P(k)} = \\beta\\log_2{k} + \\alpha$$\n",
      "\n",
      "rearranging by taking both sides to the power of 2:\n",
      "\n",
      "$$ P(k) = 2^\\alpha k^{\\beta} = C k^{\\beta}, \\;\\; C = 2^{\\alpha}$$\n",
      "\n",
      "This relationship is very interesting. It is called a *power-law*, and occurs very freqently in social datasets. Why does it occur so frequently in social datasets? It has much to do with a \"winner-take-all\" or \"winner-take-most\" effect. Winners in a power-law enviroment are components that seem take a disproportiante amount of the popularity, and keep winning. In term of popularity of repos, *winning repos* are repos that are very good quailty (intially are winners), and are shared/talked about often (keep winning). \n",
      "\n",
      "\n",
      "The above plot is also telling us that the majority of repos have very few stars and forks, only a handful have hundreds, and an incredibly small number have thousands. This is not-so obvious after browsing Github's website, where you see some repos with 36000+ stars, but fail to see the millions that do not have any stars (as they are not popular, they won't be common on your tour of the site.)\n",
      "\n",
      "Distributions like this are also said to have *fat-tails*, i.e. the probability does not drop quickly as we extend into the tail of the dataset, but most of the probability is still centered near zero. \n",
      "\n",
      "\n",
      "The heaviness of the tail and strength of \"winner-take-all\" effect are both influenced by the $\\beta$ parameter. The small the $\\beta$, the more pronounced these effects. Below is a list of distributions that follow a power-law and an approximate $\\beta$ exponent [1]. Recall though that *we never observe these numbers*, we must infer them from the data.\n",
      "\n",
      "\n",
      "<table style=\"margin:40px auto\"><tbody><tr><th>Phenomenon</th><th>Assumed Exponent</th><th> </th></tr><tr><td>Frequency of word use</td><td>-1.2</td><td> </td></tr><tr><td>Number of hits on website</td><td>-1.4</td><td> </td></tr><tr><td>US book sales</td><td>-1.5</td><td> </td></tr><tr><td>Intensity of wars</td><td>-0.8</td><td> </td></tr><tr><td>New worth of Americans</td><td>-1.1</td><td> </td></tr><tr><td>Github Stars</td><td>??</td><td> </td></tr></tbody></table>\n",
      "\n",
      "\n",
      "\n",
      "### The estimation problem\n",
      "\n",
      "It is very easy to *overestimate* the true paramter $\\beta$. This is because the tail events (the events of 500+ stars) are very rare. For example, suppose in our Github dataset we only observe 100 samples. With very high probability (about 30%), all of these samples will have less than 31 stars. This is because\n",
      "approximately 99% ( Number of all repos - Number of repos with greater than 31 stars)/(Number of all repos) of all repos have less than 31 stars. Thus, we would have no samples in our dataset from the *tail* of the distribution. If I then told you that there existed a repo with 36000+ stars, you would call me crazy, as it would be about 1000 times larger than your observed most popular repo. You would assign a very large $\\beta$ exponent to your dataset (recall large $\\beta$ means thinner tails). Similarly, with the same 30% probability we would not see repos more popular than 64 stars if we had a sample of 1000.  Taking this to its logical conclusion, how confident should we be that there might not exist a theoretical repo that can attain 72000+ stars, or 150000+ stars, one which would push an estimated $\\beta$ down even more. \n",
      "\n",
      "\n",
      "### Yule-Simon distribution\n",
      "\n",
      "The \n",
      "\n",
      "\n",
      "\n",
      "\n",
      "\n"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.special import beta\n",
      "import pymc as pm\n",
      "\n",
      "\n",
      "param = pm.Exponential(\"param\", 1 )\n",
      "\n",
      "\n",
      "\n",
      "@pm.stochastic( dtype = int, observed = True )\n",
      "def yule_simon( value = repo_with_stars, rho = param ):\n",
      "    \"\"\"test\"\"\"\n",
      "    \n",
      "    def logp( value, rho):\n",
      "        return np.log( rho ) + np.log( beta( value, rho+1) )\n",
      "    \n",
      "    def random(rho):\n",
      "        W = stats.expon.rvs(scale=1./rho)\n",
      "        return stats.geom.rvs( np.exp( -W ) )\n",
      "    \n",
      "\n",
      "model = pm.Model( [param, yule_simon] )\n",
      "mcmc = pm.MCMC( model )\n",
      "\n",
      "mcmc.sample( 10000, 8000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "ename": "TypeError",
       "evalue": "yule_simon: computed log-probability [-20.51503062 -19.93158602 -18.31405136 -17.21386783 -16.32349938\n -15.53050299 -14.75010755 -13.96101721 -13.13877723 -12.2264853\n -11.23694781 -10.06769225  -8.63087616  -7.0237458   -5.33941252\n  -3.44559118  -1.4738842 ] cannot be cast to float",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
        "\u001b[1;32m<ipython-input-83-fe84742cff9d>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[0;32m      8\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      9\u001b[0m \u001b[1;33m@\u001b[0m\u001b[0mmc\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mstochastic\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mdtype\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mobserved\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mTrue\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 10\u001b[1;33m \u001b[1;32mdef\u001b[0m \u001b[0myule_simon\u001b[0m\u001b[1;33m(\u001b[0m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mrepo_with_stars\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mrho\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mparam\u001b[0m \u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     11\u001b[0m     \u001b[1;34m\"\"\"test\"\"\"\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     12\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\InstantiationDecorators.pyc\u001b[0m in \u001b[0;36minstantiate_p\u001b[1;34m(__func__)\u001b[0m\n\u001b[0;32m    147\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0minstantiate_p\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__func__\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    148\u001b[0m         \u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparents\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0m_extract\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m__func__\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkwds\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mkeys\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'Stochastic'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 149\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0m__class__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mvalue\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mparents\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mparents\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    150\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    151\u001b[0m     \u001b[0mkeys\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;34m'logp'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'random'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;34m'rseed'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36m__init__\u001b[1;34m(self, logp, doc, name, parents, random, trace, value, dtype, rseed, observed, cache_depth, plot, verbose, isdata, check_logp, logp_partial_gradients)\u001b[0m\n\u001b[0;32m    714\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mcheck_logp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    715\u001b[0m             \u001b[1;31m# Check initial value\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 716\u001b[1;33m             \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    717\u001b[0m                 \u001b[1;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;34m\"Stochastic \"\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m\"'s initial log-probability is %s, should be a float.\"\u001b[0m \u001b[1;33m%\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__repr__\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    718\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;32mc:\\Python27\\lib\\site-packages\\pymc\\PyMCObjects.pyc\u001b[0m in \u001b[0;36mget_logp\u001b[1;34m(self)\u001b[0m\n\u001b[0;32m    833\u001b[0m             \u001b[0mlogp\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mfloat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    834\u001b[0m         \u001b[1;32mexcept\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 835\u001b[1;33m             \u001b[1;32mraise\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m': computed log-probability '\u001b[0m \u001b[1;33m+\u001b[0m \u001b[0mstr\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mlogp\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;34m' cannot be cast to float'\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    836\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    837\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mlogp\u001b[0m \u001b[1;33m!=\u001b[0m \u001b[0mlogp\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
        "\u001b[1;31mTypeError\u001b[0m: yule_simon: computed log-probability [-20.51503062 -19.93158602 -18.31405136 -17.21386783 -16.32349938\n -15.53050299 -14.75010755 -13.96101721 -13.13877723 -12.2264853\n -11.23694781 -10.06769225  -8.63087616  -7.0237458   -5.33941252\n  -3.44559118  -1.4738842 ] cannot be cast to float"
       ]
      }
     ],
     "prompt_number": 83
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def logp( value, rho):\n",
      "        return np.log( rho ) + np.log( beta( value, rho+1) )\n",
      "\n",
      "beta( repo_with_stars, 1.3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 84,
       "text": [
        "array([  3.96781274e-09,   7.12048348e-09,   3.60230434e-08,\n",
        "         1.08508004e-07,   2.64859823e-07,   5.86390404e-07,\n",
        "         1.28195491e-06,   2.82711390e-06,   6.44529816e-06,\n",
        "         1.60819963e-05,   4.33570545e-05,   1.39960612e-04,\n",
        "         5.90762159e-04,   2.95765600e-03,   1.59980669e-02,\n",
        "         1.06728840e-01,   7.69230769e-01])"
       ]
      }
     ],
     "prompt_number": 84
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Exercises:\n",
      "1. Distributions like the Normal distribution have very skinny tails. Compare the PDFs of the Normal versus a power-law distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace( 1, 50, 200 )\n",
      "plt.plot( x, exp( -(x-1)**2 ), label = \"Normal distribution\" )\n",
      "plt.plot( x, x**(-2), label = r\"Power law, $\\beta = -2$\" )\n",
      "plt.plot( x, x**(-1), label = r\"Power law, $\\beta = -1$\" )\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<matplotlib.legend.Legend at 0x1487d518>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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oImJiYrztJHFxcWRkZDB27FjvaK7JZGL58uXs2LGD0aNHk5WVxaOPPkp1dbXf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\n"
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### References\n",
      "1. Taleb, Nassim. The Black Swan. 1st edition. New York: Random House, 2007. Print."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.core.display import HTML\n",
      "def css_styling():\n",
      "    styles = open(\"../styles/custom.css\", \"r\").read()\n",
      "    return HTML(styles)\n",
      "css_styling()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<style>\n",
        "    @font-face {\n",
        "        font-family: \"Computer Modern\";\n",
        "        src: url('http://9dbb143991406a7c655e-aa5fcb0a5a4ec34cff238a2d56ca4144.r56.cf5.rackcdn.com/cmunss.otf');\n",
        "    }\n",
        "    div.cell{\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    h1 {\n",
        "        font-family: \"Charis SIL\", Palatino, serif;\n",
        "    }\n",
        "    h4{\n",
        "        margin-top:12px;\n",
        "        margin-bottom: 3px;\n",
        "       }\n",
        "    div.text_cell_render{\n",
        "        font-family: Computer Modern, \"Helvetica Neue\", Arial, Helvetica, Geneva, sans-serif;\n",
        "        line-height: 145%;\n",
        "        font-size: 120%;\n",
        "        width:800px;\n",
        "        margin-left:auto;\n",
        "        margin-right:auto;\n",
        "    }\n",
        "    .CodeMirror{\n",
        "            font-family: \"Source Code Pro\", source-code-pro,Consolas, monospace;\n",
        "    }\n",
        "    .prompt{\n",
        "        display: None;\n",
        "    }\n",
        "    .text_cell_render h5 {\n",
        "        font-weight: 300;\n",
        "        font-size: 16pt;\n",
        "        color: #4057A1;\n",
        "        font-style: italic;\n",
        "        margin-bottom: .5em;\n",
        "        margin-top: 0.5em;\n",
        "        display: block;\n",
        "    }\n",
        "    \n",
        "    .warning{\n",
        "        color: rgb( 240, 20, 20 )\n",
        "        }\n",
        "</style>\n",
        "<script>\n",
        "    MathJax.Hub.Config({\n",
        "                        TeX: {\n",
        "                           extensions: [\"AMSmath.js\"]\n",
        "                           },\n",
        "                tex2jax: {\n",
        "                    inlineMath: [ ['$','$'], [\"\\\\(\",\"\\\\)\"] ],\n",
        "                    displayMath: [ ['$$','$$'], [\"\\\\[\",\"\\\\]\"] ]\n",
        "                },\n",
        "                displayAlign: 'center', // Change this to 'center' to center equations.\n",
        "                \"HTML-CSS\": {\n",
        "                    styles: {'.MathJax_Display': {\"margin\": 4}}\n",
        "                }\n",
        "        });\n",
        "</script>"
       ],
       "output_type": "pyout",
       "prompt_number": 1,
       "text": [
        "<IPython.core.display.HTML at 0x58ac110>"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "beta = pm.Uniform(\"beta\", -100, 100)\n",
      "\n",
      "@pm.observed\n",
      "def survival( value = y_, beta = beta):\n",
      "    return np.sum( [ value[i-1]*np.log( (i+0.)**beta - (i+1.)**beta ) for i in range(1,99) ] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 167
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model( [survival, beta] )\n",
      "#map_ = pm.MAP( model )\n",
      "#map_.fit()\n",
      "\n",
      "mcmc = pm.MCMC( model )\n",
      "mcmc.sample( 50000, 40000 )\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  50000 of 50000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 168
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc.Matplot import plot as mcplot\n",
      "mcplot(mcmc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting beta\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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AE++CeL8pbY8fP15v5/cLicCfDl6De0MB/jyaL7P/xt0WJNUNQtLN+7hxJQOhHg4mMR76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\nASbVHLIz52r8AAAAAElFTkSuQmCC\n"
      }
     ],
     "prompt_number": 155
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "stars_to_explore[1:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([    1,     2,     4,     8,    16,    32,    64,   128,   256,\n",
        "         512,  1024,  2048,  4096,  8192, 16384, 32768])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = stats.pareto.rvs( 2.5, size = (50000,1) )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 149
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hist(a, bins = 100)\n",
      "print"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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8kmMPzg5t7dDWFn3t0NYObe3Q1t0Y5gEAAACPYphPcuzB2aGtHdraoq8d2tqh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\n"
      }
     ],
     "prompt_number": 150
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = [ (a >= i).sum() for i in range(1,100 ) ]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 165
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_ = -np.diff(y)\n",
      "print y_\n",
      "\n",
      "print y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[41264  5572  1638   646   313   181   101    70    48    47    22    14\n",
        "    14    14     7    11     4     6     4     0     1     0     2     0\n",
        "     0     1     2     1     3     0     2     2     1     0     1     1\n",
        "     2     1     0     1     0     0     0     0     0     0     0     0\n",
        "     1     1     0     0     0     0     0     0     0     0     0     0\n",
        "     0     0     0     0     0     0     0     0     0     0     0     0\n",
        "     0     0     0     0     0     0     0     0     0     0     0     0\n",
        "     0     0     0     0     0     0     0     0     0     0     0     0\n",
        "     0     0]\n",
        "[50000, 8736, 3164, 1526, 880, 567, 386, 285, 215, 167, 120, 98, 84, 70, 56, 49, 38, 34, 28, 24, 24, 23, 23, 21, 21, 21, 20, 18, 17, 14, 14, 12, 10, 9, 9, 8, 7, 5, 4, 4, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]\n"
       ]
      }
     ],
     "prompt_number": 166
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b = -2.3"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 112
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.sum( [ y_[i-1]*np.log( (i+0.)**b - (i+1.)**b ) for i in range(1,7) ] ) + y[-1]*np.log(7) "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 113,
       "text": [
        "-13526.483069774908"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 114,
       "text": [
        "array([48930,   940,   103,    19,     7,     1])"
       ]
      }
     ],
     "prompt_number": 114
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.append( y_, y[-1] )"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 116,
       "text": [
        "array([48930,   940,   103,    19,     7,     1,     0])"
       ]
      }
     ],
     "prompt_number": 116
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mc.Uninformative?"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 129
    }
   ],
   "metadata": {}
  }
 ]
}