Untitled4.ipynb

{
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  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats as stats\n",
      "from IPython.core.pylabtools import figsize\n",
      "import numpy as np\n",
      "figsize(12.5, 4)\n",
      "jet = plt.cm.jet\n",
      "import matplotlib.pyplot as plt\n",
      "from mpl_toolkits.mplot3d import Axes3D"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create the observed data\n",
      "\n",
      "# sample size of data we observe, trying varying this (keep it less than 100 ;)\n",
      "N = 100\n",
      "\n",
      "# the true parameters, but of course we do not see these values...\n",
      "lambda_1_true = 1\n",
      "lambda_2_true = 3\n",
      "\n",
      "#...we see the data generated, dependent on the above two values.\n",
      "data = np.concatenate([\n",
      "    stats.poisson.rvs(lambda_1_true, size=(N, 1)),\n",
      "    stats.poisson.rvs(lambda_2_true, size=(N, 1))\n",
      "], axis=1)\n",
      "print (\"observed (2-dimensional,sample size = %d):\" % N, data)\n",
      "\n",
      "# plotting details.\n",
      "x = y = np.linspace(.01, 5, 100)\n",
      "likelihood_x = np.array([stats.poisson.pmf(data[:, 0], _x)\n",
      "                        for _x in x]).prod(axis=1)\n",
      "likelihood_y = np.array([stats.poisson.pmf(data[:, 1], _y)\n",
      "                        for _y in y]).prod(axis=1)\n",
      "L = np.dot(likelihood_x[:, None], likelihood_y[None, :])\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "observed (2-dimensional,sample size = 100): [[0 1]\n",
        " [2 4]\n",
        " [1 3]\n",
        " [0 1]\n",
        " [1 1]\n",
        " [0 3]\n",
        " [0 1]\n",
        " [0 2]\n",
        " [3 5]\n",
        " [0 4]\n",
        " [1 3]\n",
        " [1 2]\n",
        " [0 5]\n",
        " [3 1]\n",
        " [0 3]\n",
        " [2 3]\n",
        " [1 1]\n",
        " [0 1]\n",
        " [0 0]\n",
        " [2 2]\n",
        " [1 2]\n",
        " [0 1]\n",
        " [0 0]\n",
        " [1 1]\n",
        " [1 1]\n",
        " [3 2]\n",
        " [1 3]\n",
        " [0 4]\n",
        " [1 3]\n",
        " [1 3]\n",
        " [1 3]\n",
        " [0 3]\n",
        " [3 3]\n",
        " [1 1]\n",
        " [1 2]\n",
        " [1 2]\n",
        " [1 7]\n",
        " [2 2]\n",
        " [0 5]\n",
        " [1 3]\n",
        " [1 3]\n",
        " [3 3]\n",
        " [0 3]\n",
        " [1 1]\n",
        " [1 4]\n",
        " [0 4]\n",
        " [5 3]\n",
        " [1 3]\n",
        " [0 2]\n",
        " [3 3]\n",
        " [3 3]\n",
        " [2 2]\n",
        " [1 1]\n",
        " [1 3]\n",
        " [1 1]\n",
        " [2 0]\n",
        " [2 3]\n",
        " [0 3]\n",
        " [1 3]\n",
        " [2 1]\n",
        " [1 3]\n",
        " [0 6]\n",
        " [1 1]\n",
        " [0 2]\n",
        " [1 2]\n",
        " [0 2]\n",
        " [2 4]\n",
        " [0 1]\n",
        " [0 5]\n",
        " [1 4]\n",
        " [1 4]\n",
        " [0 1]\n",
        " [3 0]\n",
        " [1 5]\n",
        " [1 4]\n",
        " [0 1]\n",
        " [1 4]\n",
        " [2 6]\n",
        " [0 4]\n",
        " [0 2]\n",
        " [0 3]\n",
        " [1 4]\n",
        " [1 2]\n",
        " [0 4]\n",
        " [0 4]\n",
        " [0 2]\n",
        " [1 1]\n",
        " [2 5]\n",
        " [2 2]\n",
        " [0 2]\n",
        " [1 0]\n",
        " [2 3]\n",
        " [1 4]\n",
        " [0 1]\n",
        " [0 1]\n",
        " [0 3]\n",
        " [1 5]\n",
        " [0 4]\n",
        " [3 2]\n",
        " [1 1]]\n"
       ]
      }
     ],
     "prompt_number": 53
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figsize(12.5, 12)\n",
      "# matplotlib heavy lifting below, beware!\n",
      "plt.subplot(221)\n",
      "uni_x = stats.uniform.pdf(x, loc=0, scale=5)\n",
      "uni_y = stats.uniform.pdf(x, loc=0, scale=5)\n",
      "M = np.dot(uni_x[:, None], uni_y[None, :])\n",
      "im = plt.imshow(M, interpolation='none', origin='lower',\n",
      "                cmap=jet, vmax=1, vmin=-.15, extent=(0, 5, 0, 5))\n",
      "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n",
      "plt.xlim(0, 5)\n",
      "plt.ylim(0, 5)\n",
      "plt.title(\"Landscape formed by Uniform priors on $p_1, p_2$.\")\n",
      "\n",
      "plt.subplot(223)\n",
      "plt.contour(x, y, M * L)\n",
      "im = plt.imshow(M * L, interpolation='none', origin='lower',\n",
      "                cmap=jet, extent=(0, 5, 0, 5))\n",
      "plt.title(\"Landscape warped by %d data observation;\\n Uniform priors on $p_1, p_2$.\" % N)\n",
      "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n",
      "plt.xlim(0, 5)\n",
      "plt.ylim(0, 5)\n",
      "\n",
      "plt.subplot(222)\n",
      "exp_x = stats.expon.pdf(x, loc=0, scale=3)\n",
      "exp_y = stats.expon.pdf(x, loc=0, scale=10)\n",
      "M = np.dot(exp_x[:, None], exp_y[None, :])\n",
      "\n",
      "plt.contour(x, y, M)\n",
      "im = plt.imshow(M, interpolation='none', origin='lower',\n",
      "                cmap=jet, extent=(0, 5, 0, 5))\n",
      "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n",
      "plt.xlim(0, 5)\n",
      "plt.ylim(0, 5)\n",
      "plt.title(\"Landscape formed by Exponential priors on $p_1, p_2$.\")\n",
      "\n",
      "plt.subplot(224)\n",
      "# This is the likelihood times prior, that results in the posterior.\n",
      "plt.contour(x, y, M * L)\n",
      "im = plt.imshow(M * L, interpolation='none', origin='lower',\n",
      "                cmap=jet, extent=(0, 5, 0, 5))\n",
      "\n",
      "plt.scatter(lambda_2_true, lambda_1_true, c=\"k\", s=50, edgecolor=\"none\")\n",
      "plt.title(\"Landscape warped by %d data observation;\\n Exponential priors on \\\n",
      "$p_1, p_2$.\" % N)\n",
      "plt.xlim(0, 5)\n",
      "plt.ylim(0, 5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 54,
       "text": [
        "(0, 5)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NMKdMhCElo5zczjWg++MolaKhoUGSNDAwoHg8rsmTJ3s6KQBAMFjvxzg3KRd8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\n4cKF7Nixo+W2Z8+eNsdR9e3bl8mTJ3PnnXcyceJE0tLSmDZ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dJ7L5sfT0dB599FH++te/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       "text": [
        "<matplotlib.figure.Figure at 0x7f764c1a6b50>"
       ]
      }
     ],
     "prompt_number": 54
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "?dot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    }
   ],
   "metadata": {}
  }
 ]
}