Group 4 02-05-15 In-class activities.ipynb

{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "The heading for each part of the activity briefly describes the part. For full details, see:\n",
      "http://granite.ices.utexas.edu/coursewiki/images/2/2e/ClassActivity20130204.pdf"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt\n",
      "import scipy.stats"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Part 1: Read the events from the file."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Load the data.\n",
      "events = [float(line.strip()) for line in open('data/Events20130204.txt').readlines()]\n",
      "print '{0} independent measurements. First 10:'.format(len(events))\n",
      "print events[:10]\n",
      "\n",
      "# Take a peek.\n",
      "plt.hist(events, bins=100)\n",
      "sample_mean = np.mean(events)\n",
      "sample_stdev = np.std(events)\n",
      "print 'Sample mean: {}'.format(sample_mean)\n",
      "print 'Sample stdev: {}'.format(sample_stdev)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000 independent measurements. First 10:\n",
        "[6.1355644, 2.9098908, 3.9025586, 2.8688229, 2.6472936, 5.9071974, 0.21227957, 1.293517, 2.9736624, -0.22960726]\n",
        "Sample mean: 2.23679165769"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "Sample stdev: 2.23531606892\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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QEI4BAKAgHAMAQEE4BgCAgnAMAAAF4Rg4xB14hzYOJT3fYc+dD4FaGV/rAgAG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\nn81S82CUe2EAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9935d0c>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Part 2: Compute the probability of the data assuming it is normally distributed."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Get a PDF for a normal distribution with the sample mean/stdev.\n",
      "normal_pdf = scipy.stats.norm(loc=sample_mean, scale=sample_stdev).pdf\n",
      "print 'Probability of the first data point: p({0}) = {1}'.format(events[0], normal_pdf(events[0]))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Probability of the first data point: p(6.1355644) = 0.0389924654454\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def log_prob_data(data, pdf):\n",
      "    \"\"\"Computes the (log) probability of the data with the given PDF.\"\"\"\n",
      "    return np.sum(np.log(pdf(data)))\n",
      "\n",
      "normal_prob = log_prob_data(events, normal_pdf)\n",
      "print 'Log probability of the data (normal): {0}'.format(normal_prob)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Log probability of the data (normal): -2223.32116913\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Part 3: Now suppose the events are from a Student t distribution..."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_mu = 2.0\n",
      "t_sigma = 1.2\n",
      "t_nu = 5.0\n",
      "student_t_pdf = scipy.stats.t(t_nu, loc=t_mu, scale=t_sigma).pdf\n",
      "\n",
      "student_t_prob = log_prob_data(events, student_t_pdf)\n",
      "print 'Log probability of the data (Student t): {0}'.format(student_t_prob)\n",
      "print '{0} times more probable than with the normal distribution'.format(np.exp(student_t_prob - normal_prob))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Log probability of the data (Student t): -2208.17899194\n",
        "3768460.75583 times more probable than with the normal distribution\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Part 4: Find the MAP estimates for the Student t parameters."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def func_to_minimize(params):\n",
      "    \"\"\"Returns the negative log probability of the data from a student t\n",
      "    distribution with the provided parameters.\"\"\"\n",
      "    mu, sigma, nu = params\n",
      "    pdf = scipy.stats.t(nu, loc=mu, scale=sigma).pdf\n",
      "    return -log_prob_data(events, pdf)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "initial_guess = [t_mu, t_sigma, t_nu]\n",
      "best_params = scipy.optimize.fmin(func_to_minimize, initial_guess)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Optimization terminated successfully.\n",
        "         Current function value: 2133.607855\n",
        "         Iterations: 58\n",
        "         Function evaluations: 109\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "t_map_mu, t_map_sigma, t_map_nu = best_params\n",
      "for name, value in [('mu', t_map_mu), ('sigma', t_map_sigma), ('nu', t_map_nu)]:\n",
      "    print 'MAP {0}: {1}'.format(name, value)\n",
      "\n",
      "map_student_t_pdf = scipy.stats.t(t_map_nu, loc=t_map_mu, scale=t_map_sigma).pdf\n",
      "map_student_t_prob = log_prob_data(events, map_student_t_pdf)\n",
      "print 'Log probability of the data (Student t w/ MAP params): {0}'.format(map_student_t_prob)\n",
      "print '{0} times more probable than with our initial student t parameters'.format(np.exp(map_student_t_prob - student_t_prob))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "MAP mu: 2.22092512454\n",
        "MAP sigma: 1.52345938155\n",
        "MAP nu: 3.59467140035\n",
        "Log probability of the data (Student t w/ MAP params): -2133.60785489\n",
        "2.43127079087e+32 times more probable than with our initial student t parameters\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Part 5: Fixing parameters at their MAP values, allow one parameter at a time to vary, and graph its Bayes posterior probability."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = np.linspace(1, 5, num=1000)\n",
      "\n",
      "def scaled_posterior(nu, mu, sigma):\n",
      "    \"\"\"Returns something like the posterior probabilty of the data from a\n",
      "    Student t distribution with the provided parameters, but scaled\n",
      "    relative to map_student_t_prob.\"\"\"\n",
      "    pdf = scipy.stats.t(nu, loc=mu, scale=sigma).pdf\n",
      "    prob = log_prob_data(events, pdf)\n",
      "    return np.exp(prob - map_student_t_prob)\n",
      "                            \n",
      "vectorized_scaled_posterior = np.vectorize(scaled_posterior)\n",
      "                            \n",
      "y_varied_nu = vectorized_scaled_posterior(xs, t_map_mu, t_map_sigma)\n",
      "y_varied_mu = vectorized_scaled_posterior(t_map_nu, xs, t_map_sigma)\n",
      "y_varied_sigma = vectorized_scaled_posterior(t_map_nu, t_map_mu, xs)\n",
      "\n",
      "plt.plot(xs, y_varied_nu, label='nu')\n",
      "plt.plot(xs, y_varied_mu, label='mu')\n",
      "plt.plot(xs, y_varied_sigma, label='sigma')\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.legend.Legend at 0x99443cc>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sUX5+vi677DIWiQelqiqxjnMsxriGBTq6xzkzLVPxeFx1DXUBVgVEB/PN7eOA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\nzkREREREdvh/d8tifQ9T10UAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x99558cc>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Part 6: Instead of fixing any parameter values, graph the Bayes posterior of each if you marginalize over the other two."
     ]
    },
    {
     "cell_type": "raw",
     "metadata": {},
     "source": [
      "Out of time..."
     ]
    }
   ],
   "metadata": {}
  }
 ]
}