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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Hierarchical Bayesian Inference of Normal Means #\n",
      "\n",
      "This notebook is based on Chapter 5.4, 5.5 and 5.6 of 'Bayesian Data Analysis' (Gelman et. al, 3rd Edition).\n",
      "\n",
      "Suppose we have $J$ observations $\\bar{y}_{\\cdot j} \\mid \\theta_j \\sim \\text{N}(\\theta_j, \\sigma_j^2)$, conditionally independent of each other given its parameters.  The variance parameter $\\sigma_j^2$ is assumed to be known, and the mean parameter $\\theta_j$'s are independently sampled from prior $\\text{N}(\\mu, \\tau^2)$.  Finally, we assign uniform hyperprior distribution for $\\mu$ given $\\tau$:\n",
      "$$\n",
      "p(\\mu,\\tau) = p(\\mu \\mid \\tau) p(\\tau) \\propto p(\\tau).\n",
      "$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# prepare inline pylab\n",
      "% pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Parallel Experiments in Eight Schools (BDA 5.5) ##\n",
      "\n",
      "Please refer to the corresponding chapter of the book for description of the data.  I typed the data myself:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# load hand-typed data\n",
      "from pandas import *\n",
      "import numpy as np\n",
      "school_data = DataFrame(data={'means':[28,8,-3,7,-1,1,18,12],'serrs':[15,10,16,11,9,11,10,18]},\n",
      "                        index=['A','B','C','D','E','F','G','H'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# the data looks like this\n",
      "school_data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>means</th>\n",
        "      <th>serrs</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>A</th>\n",
        "      <td> 28</td>\n",
        "      <td> 15</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>B</th>\n",
        "      <td>  8</td>\n",
        "      <td> 10</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>C</th>\n",
        "      <td> -3</td>\n",
        "      <td> 16</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>D</th>\n",
        "      <td>  7</td>\n",
        "      <td> 11</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>E</th>\n",
        "      <td> -1</td>\n",
        "      <td>  9</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>F</th>\n",
        "      <td>  1</td>\n",
        "      <td> 11</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>G</th>\n",
        "      <td> 18</td>\n",
        "      <td> 10</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>H</th>\n",
        "      <td> 12</td>\n",
        "      <td> 18</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "   means  serrs\n",
        "A     28     15\n",
        "B      8     10\n",
        "C     -3     16\n",
        "D      7     11\n",
        "E     -1      9\n",
        "F      1     11\n",
        "G     18     10\n",
        "H     12     18"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since mean parameters are conjugate to each other, only tricky part is the standard deviation parameter $\\tau$ for group means.  We marginalize out all other variables to make inference on $\\tau$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# define marginal log posterior function of tau\n",
      "def log_posterior_tau_helper(tau, means, serrs, log_prior=lambda tau: 0):\n",
      "    '''\n",
      "    computes log marginal hyperparameter density of tau\n",
      "    '''\n",
      "    ret = log_prior(tau)\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    # precision weighted average\n",
      "    mu_hat = np.sum((1.0/marginal_variances) * means) / \\\n",
      "            np.sum(1.0/marginal_variances)\n",
      "    ret += 0.5 * log(total_variance)\n",
      "    ret -= 0.5 * np.sum(np.log(marginal_variances))\n",
      "    ret -= 0.5 * np.sum(((means - mu_hat) ** 2)/marginal_variances)\n",
      "    return ret\n",
      "# vectorize the function for convenience\n",
      "log_posterior_tau = \\\n",
      "    np.vectorize(log_posterior_tau_helper, otypes=[np.float], excluded=[1,2,3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let us reproduce Figure 5.5, which draws marginal posterior density $p(\\tau \\mid y)$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab as pl\n",
      "# grid points to evaluate evaluate density function\n",
      "tau_min = 0; tau_max = 30; tau_grid_num = 1000\n",
      "tau_knots = np.linspace(tau_min, tau_max, tau_grid_num)\n",
      "lop_posterior_tau_densities = \\\n",
      "    log_posterior_tau(tau_knots, school_data.means, \n",
      "                      school_data.serrs, log_prior=lambda tau: 0)\n",
      "# when calculating densities, it is numerically more stable to \n",
      "# first compute in log space, subtract the maximum, and then exponentiate\n",
      "posterior_tau_densities = \\\n",
      "        np.exp(lop_posterior_tau_densities - np.max(lop_posterior_tau_densities))\n",
      "#np.exp(log_posterior_tau_densities - log_posterior_tau_densities.max())\n",
      "pl.plot(tau_knots, posterior_tau_densities, color='k', linestyle='-', linewidth=1)\n",
      "pl.axes().set_xlabel(r'$\\tau$')\n",
      "# the y-axis of unnormalized posterior means nothing, so rather hide the scale\n",
      "pl.axes().get_yaxis().set_visible(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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6DpFV4fiC7mv+/Pk4cuQIdu/eDXt7e9VxiHSpvuMLljLdV3l5OSIjI+Hu7o4NGzbwFRlE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\nCEuZiEhD/h+brcDWTAfcEgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f866e50>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This plot indicates that values of $\\tau$ near zero are most plausible, but large values such as 10 or 15 are still quite likely.\n",
      "\n",
      "Now, we study the change of $\\mathbb{E}[\\theta_j \\mid \\tau]$'s and $\\text{sd}[\\theta_j \\mid \\tau]$'s as a function of $\\tau$.  This can be done by marginalizing out $\\mu$ from the conditional distribution $\\theta_j \\mid \\mu,\\tau,y$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mean_posterior_given_tau(tau, means, serrs):\n",
      "    assert(len(means) == len(serrs))\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    # precision weighted average\n",
      "    mu_hat = np.sum((1.0/marginal_variances) * means) / \\\n",
      "            np.sum(1.0/marginal_variances)\n",
      "    if tau == 0:\n",
      "        return np.repeat(mu_hat, len(means))\n",
      "    return ((1.0/(serrs ** 2)) * means + 1.0/(tau ** 2) * mu_hat) / (1.0/(serrs ** 2) + 1.0/(tau ** 2))\n",
      "\n",
      "def sd_posterior_given_tau(tau, serrs):\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    individual_variances = (((serrs ** 2)/(serrs ** 2 + tau ** 2)) ** 2) * total_variance\n",
      "    if tau == 0:\n",
      "        return np.sqrt(individual_variances)\n",
      "    return np.sqrt(individual_variances + 1.0 / (1.0/(serrs ** 2) + 1.0/(tau ** 2)))\n",
      "\n",
      "mean_posterior_given_taus = \\\n",
      "    np.vectorize(mean_posterior_given_tau, otypes=[np.ndarray], excluded=[1,2])\n",
      "tau_conditional_means = \\\n",
      "        pandas.DataFrame.from_records(mean_posterior_given_taus(tau_knots, school_data.means, school_data.serrs),\n",
      "                                      index = tau_knots, columns=school_data.index)\n",
      "    \n",
      "sd_posterior_given_taus = \\\n",
      "    np.vectorize(sd_posterior_given_tau, otypes=[np.ndarray], excluded=[1])\n",
      "tau_conditional_sds = \\\n",
      "        pandas.DataFrame.from_records(sd_posterior_given_taus(tau_knots, school_data.serrs),\n",
      "                                      index = tau_knots, columns=school_data.index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# I was not able to put inline labels in Python. \n",
      "# this page contains an example code for it: http://stackoverflow.com/questions/16992038/inline-labels-in-matplotlib\n",
      "tau_conditional_means.plot(style=['-','--','-.',':','-','--','-.',':'])\n",
      "pl.legend(bbox_to_anchor=(1.05, 1), loc=2)\n",
      "pl.ylim(-5,30)\n",
      "pl.axes().set_xlabel(r'$\\tau$')\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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+8RBxCxB/4v7HjsH997vo1esb3nvvOjp3Hlktaq0dM49rmNk3aHz/CgvB4aix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\nIspJcYuIiHJS3CIiopx/AHOM7OgjEIlhAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f9d0dd0>"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "When $\\tau = 0$, all group means are treated to be the same, while as $\\tau \\rightarrow \\infty$ they converge to individual MLEs."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tau_conditional_sds.plot(style=['-','--','-.',':','-','--','-.',':'])\n",
      "pl.legend(bbox_to_anchor=(1.05, 1), loc=2)\n",
      "pl.ylim(0,20)\n",
      "pl.axes().set_xlabel(r'$\\tau$')\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DTEeRKKVUCvA34BngI6XUTVR092/Ki/REyRZto9m1CxYtgh49THxXX13tzcxM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\nfKN98YvxwzfmiOfomgnLFmq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LZszg5euuo2+H7qS9m8aB1w/gKnHR9ra2tJnUBr8oaTsT\nQpw8TdnG1lK4I7EN1FpnHeO9Zk9sLhdcedoebK1bsfbXMGbNysWn2wzCDr3Bd6vO4+VnvuDs087m\n5rCbCVoSRKtzWtH2trZEjIqQno1CiGYhia3xGtvGpoFvlFI/KaVucccFuUtqKtx9N4Rt/p4RvX9h\nyZKptI7uSMr+//LnjTFE7D2Vd9q/w33b7qPbKd0YtG0QvT7qVe/u+lav55f4vJuV47NybMI9Gtsr\n8nSt9UGlVDTwtVLqV6314VXhJk+eTEJCAgARERH069fv8OSllT+c7t7OyxvJ88/D+vXJjBkDt29M\n4MevRvPcRwFs/r0N9xc9wQtLY9nRbQfOCU6GPDQEZVPm87/W//s2bNjQJNfvKdsSn3dvWz0+K20n\nJyczZ84cgMO/L0XjuG0cm1JqGlCgtZ5VsX1SqyKLtu7m5/vfYdxPj9HzvCLefiKIpARFzv4cTjtj\nEM8GzCK6MJrYybHE3RxHQAfPmk1fCCFAqiLdocElNqVUEGDTWucrpYKBc4G/u+3K6unQITi74w7m\nFV7MwV4Xs+SLIp4O2kXRL63ZOvUQWV9m8d8xC4i7Kc5UM9rk50UIIaysMW1sbYAVSqkNwBrgc631\nEvdcVt3Ky2HXLpg2DQYOzGDoza/z8p0pPFL0Fh899iT3XZRP8dR9hA0JY8gfQ+j1YS8iz410a1Kr\nrEqwKonPu1k5PivHJtyjwSU2rfUuoJ8br+X4XC62fH2QyY/FkVmwnUcevZXX/r2GhR/HsGlBErc6\nrmXcheOIeyaOkFNDZNyZEEK0QF4xV2RKCjz5JPiuSqb79pkc/Nvt9O9+N3w1nIgvriBmTBLtr2tP\nxJkRUtUohPBq0sbWeB6b2HIyytj8qy9z58L8/5YT3DuVF8IP8fjSCbwc8jIB5wbQ+arORI6JxMev\nRc4MJoSwIElsjedRGaGkBH7824d8ePapJHbexbpVvRi78z98plfxfmYKp/YOZOWylZyZeiZD3h1C\n1EVRzZbUrF7PL/F5NyvHZ+XYhHs02+z+WkNmuotNGxVrPy/hw5U/c9FZr/P9T+/x8zpFn5gLCFg/\nnlMnDaLde/H4x/k316UKIYTwIk1aFfmPO6bhX3aAwNYRbMvvRBAHaJfREcfaEfzrwG4SXXn82RWF\nM9iX3SN/JrxnLondTqP/mGEEtJVxZkKIlkeqIhuvSRNbVKsbiQp7l3FntcJZfiO+difdnO2IUZeS\nE5tC37Pj6D6sI7YgW5NcgxBCeBtJbI3nsZ1HPF1ycvLh6XGsSOLzblaOz8qxgSQ2d/CoziNCCCFE\nY0mJTQghPIiU2BpPSmxCCCEsRRJbA1l9LI3E592sHJ+VYxPuIYlNCCGEpUgbmxBCeBBpY2s8KbEJ\nIYSwFElsDWT1en6Jz7tZOT4rxybcQxKbEEIIS5E2NiGE8CDSxtZ4UmITQghhKZLYGsjq9fwSn3ez\ncnxWjk24hyQ2IYQQliJtbEII4UGkja3xpMQmhBDCUiSxNZDV6/klPu9m5fisHJtwD0lsQgghLEXa\n2IQQwoNIG1vjSYlNCCGEpUhiayCr1/NLfN7NyvFZOTbhHpLYhBBCWIq0sQkhhAeRNrbGkxKbEEII\nS5HE1kBWr+eX+LybleOzcmzCPSSxCSGEsBRpYxNCCA8ibWyNJyU2IYQQliKJrYGsXs8v8Xk3K8dn\n5diEe0hiE0IIYSnSxiaEEB5E2tgaT0psQgghLEUSWwNZvZ5f4vNuVo7PyrEJ95DEJoQQwlKkjU0I\nITyItLE1npTYhBBCWIoktgayej2/xOfdrByflWMT7iGJTQghhKVIG5sQQngQaWNrPCmxCSGEsJQG\nJzal1Fil1K9KqR1KqT+786K8gdXr+SU+72bl+Kwcm3CPBiU2pZQNeAUYC/QEJiilerjzwjzdhg0b\nmvsSmpTE592sHJ+VYxPu0dAS22Dgd631bq11GfAf4BL3XZbny8nJae5LaFISn3ezcnxWjk24R0MT\nWzsgpdr2vop9QgghRLNqaGJr8d0dd+/e3dyX0KQkPu9m5fisHJtwjwZ191dKDQGma63HVmz/BXBp\nrWdUO6bFJz8hhGgI6e7fOA1NbHbgN2A0cABYC0zQWm9z7+UJIYQQJ8bekA9prZ1KqbuAxYANmC1J\nTQghhCdosplHhBBCiObQJDOPWH3wtlJqt1Jqk1LqZ6XU2ua+nsZSSr2llEpTSm2uti9SKfW1Umq7\nUmqJUiqiOa+xoWqJbbpSal/F/ftZKTW2Oa+xMZRS7ZVS3yqlflFKbVFK3VOx3yr3r7b4LHEPlVIB\nSqk1SqkNFfFNr9hvifvXXNxeYqsYvP0bcDawH/gRi7W/KaV2AQO01tnNfS3uoJQaDhQA87TWfSr2\nzQQytdYzK/44aaW1fqQ5r7MhaoltGpCvtX6+WS/ODZRSsUCs1nqDUioEWAeMA27AGvevtvjGY517\nGFL1ltcAAAMWSURBVKS1Lqrou7ASmAJcjgXuX3NpihJbSxm8bZleS1rrFcChI3ZfDMyteD0X88vE\n69QSG1jk/mmtU7XWGypeFwDbMGNKrXL/aosPrHMPiype+gG+mOFUlrh/zaUpEltLGLytgW+UUj8p\npW5p7otpIm201mkVr9OANs15MU3gbqXURqXUbKtU8yilEoD+wBoseP+qxbe6Ypcl7qFSykcptQFz\nn5Zorddiwft3MjVFYmsJvVFO11r3B84D7qyo7rKsivWHrHRf/wUkAv2Ag8Cs5r2cxquoppsPTNFa\n51d/zwr3ryK+TzDxFWChe6i1dmmt+wHxwGlKqd5HvO/19+9ka4rEth9oX227PabUZhla64MVzxnA\np5jqV6tJq2jfQCkVB6Q38/W4jdY6XVcA3sTL759SyheT1N7RWi+o2G2Z+1ctvncr47PaPQTQWucC\n3wJjsND9aw5Nkdh+AroopRKUUn7AVcDCJvieZqGUClJKhVa8DgbOBTbX/SmvtBCYVPF6ErCgjmO9\nSsUvikqX4sX3TymlgNnAVq31i9XessT9qy0+q9xDpVRUZTWqUioQOAfTjmiJ+9dcmmQcm1LqPOBF\nqgZvP+32L2kmSqlETCkNzAD397w9PqXUB8CZQBSmPv9vwGfAR0AHYDcwXmvtddOqHyO2acBITBWW\nBnYBt1Vrz/AqSqkzgO+ATVRVV/0FMxuQFe7fseKbCkzAAvdQKdUH0znEhilofKi1flIpFYkF7l9z\nkQHaQgghLKVJBmgLIYQQzUUSmxBCCEuRxCaEEMJSJLEJIYSwFElsQgghLEUSmxBCCEuRxCaEEMJS\nJLEJIYSwFElsQgghLMXe3BcgxMlSMR3aM0AnzIzwZcBErXVJs16YEMKtJLGJlqSd1voqpdRtWut/\nN/fFCCGahlRFihZDa72y4mVcnQcKIbyaJDbRoiilkoCi5r4OIUTTkcQmWpohmCVdhBAWJcvWCCGE\nsBQpsQkhhLAUSWxCCCEsRRKbEEIIS5HEJoQQwlIksQkhhLAUSWxCCCEsRRKbEEIIS5HEJoQQwlL+\nH/0TD9bUUNJFAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10f9d0390>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Naturally, larger $\\tau$ means higher uncertainty in estimates.  \n",
      "\n",
      "Now, let us sample parameters from the joint posterior distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# seed the RNG\n",
      "np.random.seed(13531)\n",
      "sample_num = 200\n",
      "# first sample tau's\n",
      "tau_probs = posterior_tau_densities / posterior_tau_densities.sum()\n",
      "samples_tau = np.random.choice(tau_knots, sample_num, p=tau_probs)\n",
      "# now sample mu conditioned on tau\n",
      "def sample_means_from_tau(tau, means, serrs, include_mu=False):\n",
      "    if isinf(tau):\n",
      "        if include_mu:\n",
      "            raise ValueError(\"mu is not well defined when tau is infinity\")\n",
      "        else:\n",
      "            return np.random.normal(loc=means, scale=serrs)\n",
      "\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    # precision weighted average\n",
      "    mu_hat = np.sum((1.0/marginal_variances) * means) / \\\n",
      "            np.sum(1.0/marginal_variances)\n",
      "    sample_mu = np.random.normal(loc=mu_hat, scale=np.sqrt(total_variance))\n",
      "    if tau == 0:\n",
      "        if include_mu:\n",
      "            return np.repeat(sample_mu, len(means) + 1)\n",
      "        else:\n",
      "            return np.repeat(sample_mu, len(means))\n",
      "        \n",
      "    conditional_means = \\\n",
      "        ((1.0/(serrs ** 2)) * means + 1.0/(tau ** 2) * sample_mu) /\\\n",
      "        (1.0/(serrs ** 2) + 1.0/(tau ** 2))\n",
      "    conditional_scales = np.sqrt(1.0 / (1.0/(serrs ** 2) + 1.0/(tau ** 2)))\n",
      "    if include_mu == True:\n",
      "        return np.concatenate(([sample_mu],\n",
      "                               np.random.normal(loc=conditional_means,\n",
      "                                                scale=conditional_scales)))\n",
      "    else:\n",
      "        return np.random.normal(loc=conditional_means,\n",
      "                                scale=conditional_scales)\n",
      "        \n",
      "sample_means_from_taus = \\\n",
      "        np.vectorize(sample_means_from_tau, otypes=[np.ndarray], excluded=[1,2,3])\n",
      "\n",
      "samples_df = DataFrame.from_records(sample_means_from_taus(samples_tau, school_data.means, school_data.serrs),\n",
      "                                    columns=school_data.index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now that we have posterior samples, we can reproduce Table 5.3. which shows quantiles of posterior samples:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_df.quantile([0.025,0.25,0.5,0.75,0.975]).transpose().apply(np.round)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>0.025</th>\n",
        "      <th>0.25</th>\n",
        "      <th>0.5</th>\n",
        "      <th>0.75</th>\n",
        "      <th>0.975</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>A</th>\n",
        "      <td> -4</td>\n",
        "      <td> 6</td>\n",
        "      <td> 10</td>\n",
        "      <td> 15</td>\n",
        "      <td> 27</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>B</th>\n",
        "      <td> -4</td>\n",
        "      <td> 3</td>\n",
        "      <td>  7</td>\n",
        "      <td> 12</td>\n",
        "      <td> 20</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>C</th>\n",
        "      <td>-12</td>\n",
        "      <td> 2</td>\n",
        "      <td>  7</td>\n",
        "      <td> 11</td>\n",
        "      <td> 19</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>D</th>\n",
        "      <td> -6</td>\n",
        "      <td> 5</td>\n",
        "      <td>  8</td>\n",
        "      <td> 12</td>\n",
        "      <td> 19</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>E</th>\n",
        "      <td>-10</td>\n",
        "      <td> 2</td>\n",
        "      <td>  6</td>\n",
        "      <td>  9</td>\n",
        "      <td> 17</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>F</th>\n",
        "      <td>-11</td>\n",
        "      <td> 3</td>\n",
        "      <td>  7</td>\n",
        "      <td> 10</td>\n",
        "      <td> 19</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>G</th>\n",
        "      <td> -0</td>\n",
        "      <td> 7</td>\n",
        "      <td> 10</td>\n",
        "      <td> 14</td>\n",
        "      <td> 29</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>H</th>\n",
        "      <td> -9</td>\n",
        "      <td> 4</td>\n",
        "      <td>  8</td>\n",
        "      <td> 13</td>\n",
        "      <td> 26</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "   0.025  0.250  0.500  0.750  0.975\n",
        "A     -4      6     10     15     27\n",
        "B     -4      3      7     12     20\n",
        "C    -12      2      7     11     19\n",
        "D     -6      5      8     12     19\n",
        "E    -10      2      6      9     17\n",
        "F    -11      3      7     10     19\n",
        "G     -0      7     10     14     29\n",
        "H     -9      4      8     13     26"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Lower and upper quantiles deviate a bit from the book, but this is probably due to small sample size (200).\n",
      "\n",
      "Figure 5.8 (a) reproduced below shows posterior samples for the effect in school A."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_df['A'].hist(bins=20)\n",
      "pl.axes().set_xlabel(r'Effect in School A')\n",
      "pl.xlim(-20,60)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "(-20, 60)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10fa4da50>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Figure 5.8 (b) reproduced below shows posterior samples of the largest effect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.hist(samples_df.max(axis=1), bins=20)\n",
      "pl.axes().set_xlabel(r'Largest Effect')\n",
      "pl.xlim(-20,60)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "(-20, 60)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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baN9Vth8qU59us/3N0v5y2zeVtrNsv61MjbvV9n49nv/0Bs1giXmAIMdc62vggqvbCw7K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\ncgQ5ACRHkANAcgQ5ACRHkANAcv8P64+kcljD6c8AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fd67f90>"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$\\text{Pr}(\\max\\{ \\theta_j \\} > 28.4 \\mid y)$ can be calculated as:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(samples_df.max(axis=1) > 28.4)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "0.055"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Since the probability is small, the accuracy with only 200 samples is quite poor.\n",
      "\n",
      "We can also compute $\\text{Pr}(\\theta_1 > \\theta_3 \\mid y)$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(samples_df['A'] > samples_df['C'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "0.61499999999999999"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model Checking (BDA 6.5) ##\n",
      "\n",
      "To check the model fit, we sample predictive data from posterior distribution and then measure its test statistics."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_df.head(20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>A</th>\n",
        "      <th>B</th>\n",
        "      <th>C</th>\n",
        "      <th>D</th>\n",
        "      <th>E</th>\n",
        "      <th>F</th>\n",
        "      <th>G</th>\n",
        "      <th>H</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0 </th>\n",
        "      <td>  7.716427</td>\n",
        "      <td>  9.991674</td>\n",
        "      <td>  0.866800</td>\n",
        "      <td> 14.593627</td>\n",
        "      <td> -3.965988</td>\n",
        "      <td> 20.090856</td>\n",
        "      <td> 12.917670</td>\n",
        "      <td>  1.829894</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1 </th>\n",
        "      <td>  0.502421</td>\n",
        "      <td>  0.895309</td>\n",
        "      <td>  6.927228</td>\n",
        "      <td>  7.559977</td>\n",
        "      <td>  6.383656</td>\n",
        "      <td>  5.732490</td>\n",
        "      <td>  1.512876</td>\n",
        "      <td> 11.911749</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2 </th>\n",
        "      <td>  8.107001</td>\n",
        "      <td>  8.818356</td>\n",
        "      <td>  9.584960</td>\n",
        "      <td> 11.167918</td>\n",
        "      <td>  9.818180</td>\n",
        "      <td>  9.268566</td>\n",
        "      <td> 13.150036</td>\n",
        "      <td> 11.544678</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td>  9.534934</td>\n",
        "      <td>  0.192279</td>\n",
        "      <td>  4.933994</td>\n",
        "      <td>  0.482355</td>\n",
        "      <td> -5.051685</td>\n",
        "      <td> 10.671843</td>\n",
        "      <td> 22.620177</td>\n",
        "      <td>  2.510405</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td> 18.022723</td>\n",
        "      <td>  6.934803</td>\n",
        "      <td>  8.512424</td>\n",
        "      <td> 10.223763</td>\n",
        "      <td> -0.429200</td>\n",
        "      <td> -6.964528</td>\n",
        "      <td>  9.610435</td>\n",
        "      <td>  6.192576</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td>  6.633026</td>\n",
        "      <td>  8.278496</td>\n",
        "      <td>  4.938248</td>\n",
        "      <td>  9.555146</td>\n",
        "      <td>  3.424603</td>\n",
        "      <td>  5.327314</td>\n",
        "      <td>  6.755715</td>\n",
        "      <td>  6.239499</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6 </th>\n",
        "      <td> 17.482265</td>\n",
        "      <td> 13.638312</td>\n",
        "      <td>  9.628664</td>\n",
        "      <td> 17.087535</td>\n",
        "      <td> -3.717156</td>\n",
        "      <td>  8.630172</td>\n",
        "      <td> 19.108511</td>\n",
        "      <td> -1.979328</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7 </th>\n",
        "      <td> 24.679603</td>\n",
        "      <td>  3.786353</td>\n",
        "      <td>-13.655367</td>\n",
        "      <td>  1.635514</td>\n",
        "      <td>-16.328680</td>\n",
        "      <td>-11.222549</td>\n",
        "      <td> 17.283001</td>\n",
        "      <td> -7.251771</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td>  5.607194</td>\n",
        "      <td>  7.493853</td>\n",
        "      <td>  6.257384</td>\n",
        "      <td>  7.402898</td>\n",
        "      <td>  4.467476</td>\n",
        "      <td>  6.417064</td>\n",
        "      <td>  6.110007</td>\n",
        "      <td>  7.335749</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td>  1.510968</td>\n",
        "      <td>  4.395459</td>\n",
        "      <td>  0.566861</td>\n",
        "      <td>  9.807944</td>\n",
        "      <td> 20.997995</td>\n",
        "      <td> -1.304262</td>\n",
        "      <td>  5.611880</td>\n",
        "      <td> 13.863666</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td> 12.992872</td>\n",
        "      <td> 12.435256</td>\n",
        "      <td> 13.049840</td>\n",
        "      <td> 12.809142</td>\n",
        "      <td> 12.259121</td>\n",
        "      <td> 13.060207</td>\n",
        "      <td> 13.397225</td>\n",
        "      <td> 12.888974</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td>  3.284644</td>\n",
        "      <td> 14.320452</td>\n",
        "      <td>  5.336783</td>\n",
        "      <td>  6.618106</td>\n",
        "      <td> -0.524970</td>\n",
        "      <td> -3.601224</td>\n",
        "      <td>  7.833326</td>\n",
        "      <td> -3.732031</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12</th>\n",
        "      <td>  7.377929</td>\n",
        "      <td>  6.828941</td>\n",
        "      <td>  7.854961</td>\n",
        "      <td>  9.082657</td>\n",
        "      <td>  7.013176</td>\n",
        "      <td>  7.083400</td>\n",
        "      <td> 10.005125</td>\n",
        "      <td>  8.248841</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13</th>\n",
        "      <td>  7.581249</td>\n",
        "      <td>  7.036055</td>\n",
        "      <td>  7.733224</td>\n",
        "      <td>  7.954896</td>\n",
        "      <td>  7.830516</td>\n",
        "      <td>  7.242541</td>\n",
        "      <td>  8.061920</td>\n",
        "      <td>  7.625156</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14</th>\n",
        "      <td> 13.330399</td>\n",
        "      <td> 15.175647</td>\n",
        "      <td> 17.757907</td>\n",
        "      <td> 16.201320</td>\n",
        "      <td> 19.855363</td>\n",
        "      <td> 19.631324</td>\n",
        "      <td> 20.120813</td>\n",
        "      <td> 19.342776</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>15</th>\n",
        "      <td>  0.630096</td>\n",
        "      <td>  7.182227</td>\n",
        "      <td>  3.427380</td>\n",
        "      <td> -0.388352</td>\n",
        "      <td>  8.674099</td>\n",
        "      <td>  3.847556</td>\n",
        "      <td>  8.419566</td>\n",
        "      <td> 19.522541</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>16</th>\n",
        "      <td> 19.841116</td>\n",
        "      <td>  9.744172</td>\n",
        "      <td> 16.355059</td>\n",
        "      <td> 10.245631</td>\n",
        "      <td>  8.982854</td>\n",
        "      <td> 10.994532</td>\n",
        "      <td> 18.775112</td>\n",
        "      <td> 16.951828</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>17</th>\n",
        "      <td>  5.840998</td>\n",
        "      <td>  4.386583</td>\n",
        "      <td>  7.317891</td>\n",
        "      <td>  6.027662</td>\n",
        "      <td>  4.462467</td>\n",
        "      <td>  2.977552</td>\n",
        "      <td>  4.499661</td>\n",
        "      <td>  5.723083</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>18</th>\n",
        "      <td>  6.137699</td>\n",
        "      <td>  7.815479</td>\n",
        "      <td>  6.554743</td>\n",
        "      <td>  7.187624</td>\n",
        "      <td>  8.016367</td>\n",
        "      <td>  7.061611</td>\n",
        "      <td>  5.763623</td>\n",
        "      <td>  5.859263</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>19</th>\n",
        "      <td>  8.870123</td>\n",
        "      <td> 10.109709</td>\n",
        "      <td> 12.002920</td>\n",
        "      <td>  8.231484</td>\n",
        "      <td>  6.697967</td>\n",
        "      <td> 11.152029</td>\n",
        "      <td>  7.715419</td>\n",
        "      <td>  8.036580</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "            A          B          C          D          E          F  \\\n",
        "0    7.716427   9.991674   0.866800  14.593627  -3.965988  20.090856   \n",
        "1    0.502421   0.895309   6.927228   7.559977   6.383656   5.732490   \n",
        "2    8.107001   8.818356   9.584960  11.167918   9.818180   9.268566   \n",
        "3    9.534934   0.192279   4.933994   0.482355  -5.051685  10.671843   \n",
        "4   18.022723   6.934803   8.512424  10.223763  -0.429200  -6.964528   \n",
        "5    6.633026   8.278496   4.938248   9.555146   3.424603   5.327314   \n",
        "6   17.482265  13.638312   9.628664  17.087535  -3.717156   8.630172   \n",
        "7   24.679603   3.786353 -13.655367   1.635514 -16.328680 -11.222549   \n",
        "8    5.607194   7.493853   6.257384   7.402898   4.467476   6.417064   \n",
        "9    1.510968   4.395459   0.566861   9.807944  20.997995  -1.304262   \n",
        "10  12.992872  12.435256  13.049840  12.809142  12.259121  13.060207   \n",
        "11   3.284644  14.320452   5.336783   6.618106  -0.524970  -3.601224   \n",
        "12   7.377929   6.828941   7.854961   9.082657   7.013176   7.083400   \n",
        "13   7.581249   7.036055   7.733224   7.954896   7.830516   7.242541   \n",
        "14  13.330399  15.175647  17.757907  16.201320  19.855363  19.631324   \n",
        "15   0.630096   7.182227   3.427380  -0.388352   8.674099   3.847556   \n",
        "16  19.841116   9.744172  16.355059  10.245631   8.982854  10.994532   \n",
        "17   5.840998   4.386583   7.317891   6.027662   4.462467   2.977552   \n",
        "18   6.137699   7.815479   6.554743   7.187624   8.016367   7.061611   \n",
        "19   8.870123  10.109709  12.002920   8.231484   6.697967  11.152029   \n",
        "\n",
        "            G          H  \n",
        "0   12.917670   1.829894  \n",
        "1    1.512876  11.911749  \n",
        "2   13.150036  11.544678  \n",
        "3   22.620177   2.510405  \n",
        "4    9.610435   6.192576  \n",
        "5    6.755715   6.239499  \n",
        "6   19.108511  -1.979328  \n",
        "7   17.283001  -7.251771  \n",
        "8    6.110007   7.335749  \n",
        "9    5.611880  13.863666  \n",
        "10  13.397225  12.888974  \n",
        "11   7.833326  -3.732031  \n",
        "12  10.005125   8.248841  \n",
        "13   8.061920   7.625156  \n",
        "14  20.120813  19.342776  \n",
        "15   8.419566  19.522541  \n",
        "16  18.775112  16.951828  \n",
        "17   4.499661   5.723083  \n",
        "18   5.763623   5.859263  \n",
        "19   7.715419   8.036580  "
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior_data_list = []\n",
      "for row_index, row in samples_df.iterrows():\n",
      "    posterior_data_list.append( np.random.normal(loc=row, scale=school_data.serrs) )\n",
      "posterior_data_df = DataFrame.from_records(posterior_data_list,\n",
      "                                           columns=school_data.index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.hist(posterior_data_df.max(axis=1), bins=20)\n",
      "pl.axes().set_xlabel(r'T(y) = max(y)')\n",
      "pl.axvline(school_data.means.max(), color='r', linestyle='dashed', linewidth=2)\n",
      "print \"p-value: %.2f\" % (np.sum(posterior_data_df.max(axis=1) > school_data.means.max())/float(len(posterior_data_df)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-value: 0.56\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10fdc53d0>"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.hist(posterior_data_df.min(axis=1), bins=20)\n",
      "pl.axes().set_xlabel(r'T(y) = min(y)')\n",
      "pl.axvline(school_data.means.min(), color='r', linestyle='dashed', linewidth=2)\n",
      "print \"p-value: %.2f\" % (np.sum(posterior_data_df.min(axis=1) > school_data.means.min())/float(len(posterior_data_df)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-value: 0.23\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10f984390>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.hist(posterior_data_df.mean(axis=1), bins=20)\n",
      "pl.axes().set_xlabel(r'T(y) = mean(y)')\n",
      "pl.axvline(school_data.means.mean(), color='r', linestyle='dashed', linewidth=2)\n",
      "print \"p-value: %.2f\" % (np.sum(posterior_data_df.mean(axis=1) > school_data.means.mean())/float(len(posterior_data_df)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-value: 0.51\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10f90ad10>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.hist(posterior_data_df.std(axis=1), bins=20)\n",
      "pl.axes().set_xlabel(r'T(y) = sd(y)')\n",
      "pl.axvline(school_data.means.std(), color='r', linestyle='dashed', linewidth=2)\n",
      "print \"p-value: %.2f\" % (np.sum(posterior_data_df.std(axis=1) > school_data.means.std())/float(len(posterior_data_df)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "p-value: 0.80\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10fd67110>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Surprisingly, these p-values are too close to what we have in the book, considering the small data size!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Model Comparison based on predictive performance (BDA 7.3) ##\n",
      "\n",
      "(Sorry for extreme low quality code with a lot of redundancies here; I quickly began tosmell something bad, but was too lazy to go back.)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from scipy.stats import *\n",
      "# computing AIC\n",
      "# first, compute MLE estimate\n",
      "marginal_variances = school_data.serrs ** 2\n",
      "total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "# precision weighted average\n",
      "mle_complete_pooling = np.sum((1.0/marginal_variances) * school_data.means) / np.sum(1.0/marginal_variances)\n",
      "mle_lpd_complete_pooling = norm.logpdf(school_data.means, loc=mle_complete_pooling, scale=school_data.serrs).sum()\n",
      "mle_lpd_no_pooling = norm.logpdf(school_data.means, loc=school_data.means, scale=school_data.serrs).sum()\n",
      "print \"AIC for complete pooling: %.1f\" % (-2 * mle_lpd_complete_pooling + 1 * 2)\n",
      "print \"AIC for no pooling: %.1f\" % (-2 * mle_lpd_no_pooling + 8 * 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "AIC for complete pooling: 61.3\n",
        "AIC for no pooling: 70.6\n"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# computing DIC\n",
      "# here we increase sample number to improve the precision\n",
      "sample_num = 2000\n",
      "# sample \n",
      "complete_pooling_samples_df = DataFrame.from_records(sample_means_from_taus(np.repeat(0,sample_num), school_data.means, school_data.serrs),\n",
      "                                                     columns=school_data.index)\n",
      "no_pooling_samples_df = DataFrame.from_records(sample_means_from_taus(np.repeat(float('inf'),sample_num), school_data.means, school_data.serrs),\n",
      "                                               columns=school_data.index)\n",
      "\n",
      "samples_tau = np.random.choice(tau_knots, sample_num, p=tau_probs)\n",
      "hierarchical_samples_df = DataFrame.from_records(sample_means_from_taus(samples_tau, school_data.means, school_data.serrs),\n",
      "                                                 columns=school_data.index)\n",
      "# first, compute expected mean from posterior distribution\n",
      "pmean_no_pooling = no_pooling_samples_df.mean()\n",
      "pmean_complete_pooling = complete_pooling_samples_df.mean()\n",
      "pmean_hierarchical = hierarchical_samples_df.mean()\n",
      "\n",
      "pmean_lpd_no_pooling = norm.logpdf(school_data.means, loc=pmean_no_pooling, scale=school_data.serrs).sum()\n",
      "pmean_lpd_complete_pooling = norm.logpdf(school_data.means, loc=pmean_complete_pooling, scale=school_data.serrs).sum()\n",
      "pmean_lpd_hierarchical = norm.logpdf(school_data.means, loc=pmean_hierarchical, scale=school_data.serrs).sum()\n",
      "\n",
      "print \"-2lpd with no pooling: %.1f\" % (-2 * pmean_lpd_no_pooling)\n",
      "print \"-2lpd with complete pooling: %.1f\" % (-2 * pmean_lpd_complete_pooling)\n",
      "print \"-2lpd with hierarchical pooling: %.1f\" % (-2 * pmean_lpd_hierarchical)\n",
      "\n",
      "pdic_no_pooling = 2 * (pmean_lpd_no_pooling - \\\n",
      "    no_pooling_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                      scale=school_data.serrs),\n",
      "                                axis=1).sum(axis=1).mean())\n",
      "pdic_complete_pooling = 2 * (pmean_lpd_complete_pooling - \\\n",
      "    complete_pooling_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                            scale=school_data.serrs), \n",
      "                                      axis=1).sum(axis=1).mean())\n",
      "pdic_hierarchical = 2 * (pmean_lpd_hierarchical - \\\n",
      "    hierarchical_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                        scale=school_data.serrs), axis=1).sum(axis=1).mean())\n",
      "print \"p_DIC for no pooling: %.1f\" % (pdic_no_pooling)\n",
      "print \"p_DIC for complete pooling: %.1f\" % (pdic_complete_pooling)\n",
      "print \"p_DIC for hierarchical pooling: %.1f\" % (pdic_hierarchical)\n",
      "\n",
      "print \"DIC for no pooling: %.1f\" % (-2 * pmean_lpd_no_pooling + 2 * pdic_no_pooling)\n",
      "print \"DIC for complete pooling: %.1f\" % (-2 * pmean_lpd_complete_pooling + 2 * pdic_complete_pooling)\n",
      "print \"DIC for hierarchical pooling: %.1f\" % (-2 * pmean_lpd_hierarchical + 2 * pdic_hierarchical)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-2lpd with no pooling: 54.6\n",
        "-2lpd with complete pooling: 59.3\n",
        "-2lpd with hierarchical pooling: 57.5\n",
        "p_DIC for no pooling: 8.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "p_DIC for complete pooling: 1.0\n",
        "p_DIC for hierarchical pooling: 2.8\n",
        "DIC for no pooling: 70.7\n",
        "DIC for complete pooling: 61.3\n",
        "DIC for hierarchical pooling: 63.0\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# WAIC computation\n",
      "# here I am not being careful in numerical precision; in principle I should've done these calculation in log space.\n",
      "lppd_no_pooling = np.log(no_pooling_samples_df.apply(lambda x: norm.pdf(school_data.means, loc=x, \n",
      "                                                     scale=school_data.serrs), axis=1).mean(axis=0)).sum()\n",
      "lppd_complete_pooling = np.log(complete_pooling_samples_df.apply(lambda x: norm.pdf(school_data.means, loc=x, \n",
      "                                                                 scale=school_data.serrs), axis=1).mean(axis=0)).sum()\n",
      "lppd_hierarchical = np.log(hierarchical_samples_df.apply(lambda x: norm.pdf(school_data.means, loc=x, \n",
      "                                                                            scale=school_data.serrs), axis=1).mean(axis=0)).sum()\n",
      "print \"-2lppd with no pooling: %.1f\" % (-2 * lppd_no_pooling)\n",
      "print \"-2lppd with complete pooling: %.1f\" % (-2 * lppd_complete_pooling)\n",
      "print \"-2lppd with hierarchical pooling: %.1f\" % (-2 * lppd_hierarchical)\n",
      "\n",
      "pwaic_1_no_pooling = 2 * (lppd_no_pooling - \n",
      "                          no_pooling_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                      scale=school_data.serrs), axis=1).mean(axis=0).sum())\n",
      "pwaic_1_complete_pooling = 2 * (lppd_complete_pooling - \n",
      "                                complete_pooling_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                                  scale=school_data.serrs), axis=1).mean(axis=0).sum())\n",
      "pwaic_1_hierarchical = 2 * (lppd_hierarchical - \n",
      "                            hierarchical_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                          scale=school_data.serrs), axis=1).mean(axis=0).sum())\n",
      "\n",
      "print \"p_WAIC1 with no pooling: %.1f\" % (pwaic_1_no_pooling)\n",
      "print \"p_WAIC1 with complete pooling: %.1f\" % (pwaic_1_complete_pooling)\n",
      "print \"p_WAIC1 with hierarchical pooling: %.1f\" % (pwaic_1_hierarchical)\n",
      "\n",
      "pwaic_2_no_pooling = no_pooling_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                 scale=school_data.serrs), axis=1).var(axis=0).sum()\n",
      "pwaic_2_complete_pooling = complete_pooling_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                 scale=school_data.serrs), axis=1).var(axis=0).sum()\n",
      "pwaic_2_hierarchical = hierarchical_samples_df.apply(lambda x: norm.logpdf(school_data.means, loc=x, \n",
      "                                                 scale=school_data.serrs), axis=1).var(axis=0).sum()\n",
      "\n",
      "print \"p_WAIC2 with no pooling: %.1f\" % (pwaic_2_no_pooling)\n",
      "print \"p_WAIC2 with complete pooling: %.1f\" % (pwaic_2_complete_pooling)\n",
      "print \"p_WAIC2 with hierarchical pooling: %.1f\" % (pwaic_2_hierarchical)\n",
      "\n",
      "print \"WAIC with no pooling: %.1f\" % (-2 * (lppd_no_pooling - pwaic_2_no_pooling))\n",
      "print \"WAIC with complete pooling: %.1f\" % (-2 * (lppd_complete_pooling - pwaic_2_complete_pooling))\n",
      "print \"WAIC with hierarchical pooling: %.1f\" % (-2 * (lppd_hierarchical - pwaic_2_hierarchical))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-2lppd with no pooling: 60.2\n",
        "-2lppd with complete pooling: 59.8\n",
        "-2lppd with hierarchical pooling: 59.2\n",
        "p_WAIC1 with no pooling: 2.5"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "p_WAIC1 with complete pooling: 0.6\n",
        "p_WAIC1 with hierarchical pooling: 1.0\n",
        "p_WAIC2 with no pooling: 4.0"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "p_WAIC2 with complete pooling: 0.6\n",
        "p_WAIC2 with hierarchical pooling: 1.3\n",
        "WAIC with no pooling: 68.2\n",
        "WAIC with complete pooling: 61.0\n",
        "WAIC with hierarchical pooling: 61.9\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "LOOC is omitted since I am too lazy."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Clinical Trials of Beta-blockers (BDA 5.6) ##\n",
      "\n",
      "Here, we perform a meta-analysis which estimates the effect of beta-blockers from 22 clinical trials.  Since a lot of plots are omitted in this chapter of the book, this notebook might be interesting for someone who wanted to take a deeper look on this analysis. \n",
      "\n",
      "The data can be retrieved from the BDA book website:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blocker_data = read_csv(\"http://www.stat.columbia.edu/~gelman/book/data/meta.asc\",\n",
      "                        index_col='study', skiprows=3, delim_whitespace=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blocker_data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>control.deaths</th>\n",
        "      <th>control.total</th>\n",
        "      <th>treated.deaths</th>\n",
        "      <th>treated.total</th>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>study</th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "      <th></th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1 </th>\n",
        "      <td>   3</td>\n",
        "      <td>   39</td>\n",
        "      <td>   3</td>\n",
        "      <td>   38</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2 </th>\n",
        "      <td>  14</td>\n",
        "      <td>  116</td>\n",
        "      <td>   7</td>\n",
        "      <td>  114</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td>  11</td>\n",
        "      <td>   93</td>\n",
        "      <td>   5</td>\n",
        "      <td>   69</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td> 127</td>\n",
        "      <td> 1520</td>\n",
        "      <td> 102</td>\n",
        "      <td> 1533</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td>  27</td>\n",
        "      <td>  365</td>\n",
        "      <td>  28</td>\n",
        "      <td>  355</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6 </th>\n",
        "      <td>   6</td>\n",
        "      <td>   52</td>\n",
        "      <td>   4</td>\n",
        "      <td>   59</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7 </th>\n",
        "      <td> 152</td>\n",
        "      <td>  939</td>\n",
        "      <td>  98</td>\n",
        "      <td>  945</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td>  48</td>\n",
        "      <td>  471</td>\n",
        "      <td>  60</td>\n",
        "      <td>  632</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td>  37</td>\n",
        "      <td>  282</td>\n",
        "      <td>  25</td>\n",
        "      <td>  278</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td> 188</td>\n",
        "      <td> 1921</td>\n",
        "      <td> 138</td>\n",
        "      <td> 1916</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td>  52</td>\n",
        "      <td>  583</td>\n",
        "      <td>  64</td>\n",
        "      <td>  873</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12</th>\n",
        "      <td>  47</td>\n",
        "      <td>  266</td>\n",
        "      <td>  45</td>\n",
        "      <td>  263</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13</th>\n",
        "      <td>  16</td>\n",
        "      <td>  293</td>\n",
        "      <td>   9</td>\n",
        "      <td>  291</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14</th>\n",
        "      <td>  45</td>\n",
        "      <td>  883</td>\n",
        "      <td>  57</td>\n",
        "      <td>  858</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>15</th>\n",
        "      <td>  31</td>\n",
        "      <td>  147</td>\n",
        "      <td>  25</td>\n",
        "      <td>  154</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>16</th>\n",
        "      <td>  38</td>\n",
        "      <td>  213</td>\n",
        "      <td>  33</td>\n",
        "      <td>  207</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>17</th>\n",
        "      <td>  12</td>\n",
        "      <td>  122</td>\n",
        "      <td>  28</td>\n",
        "      <td>  251</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>18</th>\n",
        "      <td>   6</td>\n",
        "      <td>  154</td>\n",
        "      <td>   8</td>\n",
        "      <td>  151</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>19</th>\n",
        "      <td>   3</td>\n",
        "      <td>  134</td>\n",
        "      <td>   6</td>\n",
        "      <td>  174</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>20</th>\n",
        "      <td>  40</td>\n",
        "      <td>  218</td>\n",
        "      <td>  32</td>\n",
        "      <td>  209</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>21</th>\n",
        "      <td>  43</td>\n",
        "      <td>  364</td>\n",
        "      <td>  27</td>\n",
        "      <td>  391</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>22</th>\n",
        "      <td>  39</td>\n",
        "      <td>  674</td>\n",
        "      <td>  22</td>\n",
        "      <td>  680</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "       control.deaths  control.total  treated.deaths  treated.total\n",
        "study                                                              \n",
        "1                   3             39               3             38\n",
        "2                  14            116               7            114\n",
        "3                  11             93               5             69\n",
        "4                 127           1520             102           1533\n",
        "5                  27            365              28            355\n",
        "6                   6             52               4             59\n",
        "7                 152            939              98            945\n",
        "8                  48            471              60            632\n",
        "9                  37            282              25            278\n",
        "10                188           1921             138           1916\n",
        "11                 52            583              64            873\n",
        "12                 47            266              45            263\n",
        "13                 16            293               9            291\n",
        "14                 45            883              57            858\n",
        "15                 31            147              25            154\n",
        "16                 38            213              33            207\n",
        "17                 12            122              28            251\n",
        "18                  6            154               8            151\n",
        "19                  3            134               6            174\n",
        "20                 40            218              32            209\n",
        "21                 43            364              27            391\n",
        "22                 39            674              22            680"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Our estimand in this analysis is log odds ratio; this is estimated by empirical logit which sampling variance is estimated by eq (5.24).  We regard these values as means and variances of hierarchical normal means model.  First, let us calculate these values:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "blocker_data['means'] = np.log(blocker_data['treated.deaths']\\\n",
      "                               /(blocker_data['treated.total']-blocker_data['treated.deaths'])) \\\n",
      "                        - np.log(blocker_data['control.deaths']\\\n",
      "                               /(blocker_data['control.total']-blocker_data['control.deaths']))\n",
      "blocker_data['serrs'] = np.sqrt(1.0/blocker_data['treated.deaths'] + \n",
      "                                1.0/(blocker_data['treated.total'] - 1.0/blocker_data['treated.deaths']) + \n",
      "                                1.0/blocker_data['control.deaths'] + \n",
      "                                1.0/(blocker_data['control.total'] - 1.0/blocker_data['control.deaths']))                                "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pylab as pl\n",
      "# grid points to evaluate evaluate density function\n",
      "tau_min = 0; tau_max = 0.6; tau_grid_num = 1000\n",
      "tau_knots = np.linspace(tau_min, tau_max, tau_grid_num)\n",
      "lop_posterior_tau_densities = \\\n",
      "    log_posterior_tau(tau_knots, blocker_data.means, \n",
      "                      blocker_data.serrs, log_prior=lambda tau: 0)\n",
      "# when calculating densities, it is numerically more stable to \n",
      "# first compute in log space, subtract the maximum, and then exponentiate\n",
      "posterior_tau_densities = \\\n",
      "        np.exp(lop_posterior_tau_densities - np.max(lop_posterior_tau_densities))\n",
      "#np.exp(log_posterior_tau_densities - log_posterior_tau_densities.max())\n",
      "pl.plot(tau_knots, posterior_tau_densities, color='k', linestyle='-', linewidth=1)\n",
      "pl.axes().set_xlabel(r'$\\tau$')\n",
      "# the y-axis of unnormalized posterior means nothing, so rather hide the scale\n",
      "pl.axes().get_yaxis().set_visible(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UVCHEpMo/36AoyndCiEFCiAwAhQDGVnWfxkST9QkhXAAkAHAAUCGEmI7Hf6EP\npAXXkCbrA/AXAK8AWFfZoZUpitJdVuaa0HB9IwBECCHKABQDGCktcA1ouDbV0nB9vwEwRQhRDqAI\nwChpgWtIw9p5RQjxPYAkPN74/lJRlJSX3Sdfbk5EpAJ8BSMRkQqwWBMRqQCLNRGRCrBYExGpAIs1\nEZEKsFgTEakAizURkQqwWBMRqQCLNRGRClT3Rk5EqiGEeBXA/+Dx+4H8hMfvQf6OoigPpQYj0gEW\nazIlroqijBRCTFL7e2cQPYtjEDIZiqKcqrzaVGoQIj1gsSaTIoRwx+N3aCMyKSzWZGr8APxbdggi\nXeNbpBIRqQA7ayIiFWCxJiJSARZrIiIVYLEmIlIBFmsiIhVgsSYiUgEWayIiFWCxJiJSgf8DzcTI\nE2mvRQUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ffb78d0>"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As mentioned in the book, the marginal posterior density function of $\\tau$ peaks at nonzero value, but still values around zero are quite plausible.\n",
      "\n",
      "The plot below shows mean effects conditioned on $\\tau$; combined with the information from plot above, this indicates that moderate amount of shrinkage in estimates are necessary."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mean_posterior_given_tau(tau, means, serrs):\n",
      "    assert(len(means) == len(serrs))\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    # precision weighted average\n",
      "    mu_hat = np.sum((1.0/marginal_variances) * means) / \\\n",
      "            np.sum(1.0/marginal_variances)\n",
      "    if tau == 0:\n",
      "        return np.repeat(mu_hat, len(means))\n",
      "    return ((1.0/(serrs ** 2)) * means + 1.0/(tau ** 2) * mu_hat) / (1.0/(serrs ** 2) + 1.0/(tau ** 2))\n",
      "\n",
      "def sd_posterior_given_tau(tau, serrs):\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    individual_variances = (((serrs ** 2)/(serrs ** 2 + tau ** 2)) ** 2) * total_variance\n",
      "    if tau == 0:\n",
      "        return np.sqrt(individual_variances)\n",
      "    return np.sqrt(individual_variances + 1.0 / (1.0/(serrs ** 2) + 1.0/(tau ** 2)))\n",
      "\n",
      "mean_posterior_given_taus = \\\n",
      "    np.vectorize(mean_posterior_given_tau, otypes=[np.ndarray], excluded=[1,2])\n",
      "tau_conditional_means = \\\n",
      "        pandas.DataFrame.from_records(mean_posterior_given_taus(tau_knots, blocker_data.means, blocker_data.serrs),\n",
      "                                      index=tau_knots, columns=blocker_data.index)\n",
      "    \n",
      "sd_posterior_given_taus = \\\n",
      "    np.vectorize(sd_posterior_given_tau, otypes=[np.ndarray], excluded=[1])\n",
      "tau_conditional_sds = \\\n",
      "        pandas.DataFrame.from_records(sd_posterior_given_taus(tau_knots, blocker_data.serrs),\n",
      "                                      index = tau_knots, columns=blocker_data.index)\n",
      "# I was not able to put inline labels in Python. \n",
      "# this page contains an example code for it: http://stackoverflow.com/questions/16992038/inline-labels-in-matplotlib\n",
      "tau_conditional_means.plot()\n",
      "pl.legend(bbox_to_anchor=(1.05, 1), loc=2)\n",
      "pl.ylim(-1,0.5)\n",
      "pl.axes().set_xlabel(r'$\\tau$')\n",
      "pl.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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bo5kMHY7DItMMBDAvgpcWFPQJYomuj+rvPnc6h33QJl2XJn0wjV1nn4eazU1ky1FyXujq\n6uLRRx/lkUceoaamhiuvvJJ3vetd3HzzzSxcuHCqiyeRvClCCE45ziDhGyiErhCsjERYHomwIm/L\nIxGWmSbzw2G0NxM/z4OuLryWduw97dj7e0gfypA+5mE3a6RPm+BDJNKOZbRgiSYi2cPMS/5WthzH\niOxWlUwJ7e3t/PrXv+aRRx7hxRdf5JprruGWW27hne98pzy1XjIt8YXgRDY7TPgO2zZHMhnCitIn\nfCuGCGGZYQStPyEgkYC2tsBOn4aOjkEm2jvInnBInzRId0SxE4Wkc5XY6iJyohgz3EmkoBur1Maq\ncoksVrBWhDAWFaKUlkBJvykVFXNaHA8dOsT69et573vfy7//+7+f072TKo6KotwI3AdowI+EEPeO\nkOZ+4O1AGrhdCLFrhDQz4kWMlekw7jFZDKxbR0cHv/jFL/iP//gPXnnlFa677jpuueUW3vGOdxCP\nx6e2oGNkNr87mHv1E0JwMpejzrY5mE5Tl05zKC+ARzMZinV9sPiFQqzIZlne00NRR8dg0Rvo9vpP\nn4ZQCMrL8YqrSJurSKtLSOcqSadKSXfGsNvD6DEFq1ojsjKCdWEB1oYSImuimNUmqj76Jehzfczx\n+uuvJ5PJUF1dzb/927+d072TNuaoKIoG/BPwR8AJYIeiKI8KIWoHpLkJWCGEWKkoyluA7wGXjee5\nkulFNpvl4Ycf5sEHH6SmpoYbbriBT3ziE/zyl7+Ue5VKpoyE61Jn2zzd0UFNfT11tk1dOk2dbWMq\nCqsVhVWOw6pEgq3t7axsbmbZsWNEW1sHi15PT9BKKy+HsrLB7sqViMsuJ6eXk+4pIn3aIn1CI30o\nS/pAGme/E4jfBRbWGouy1RbWBRaRlRH0+Ll//Qoh8G0fL+XhpTz8tD8Jn9zM4aGHHqK4uJi1a9dy\n+PDhCc17XC1HRVEuB/5WCHFjPvw5ACHE1wek+T7wrBDi5/nwAeAqIUTrkLxmxK8USYDneTzzzDM8\n+OCD/PrXv+aSSy7hgx/8IO95z3vkYnzJecPxfY5mMtSlUtR1dHCwqysQQc+jW1FYmUyyqqOD1S0t\nrGpoYNXBg6x6/XWKPQ/mzeu3ysrAragYLH7l5VBUBJqG7/pkjmZIH0gHVpvu86OCtcYiuiYaiN+q\nCGa1iV6s46d9vISHl/RwE26f30vmBS7l46UH+PPCN2LY9lFDKmpURYtqaFGNt9S+ZU62HHt6erjk\nkkt49tln+cEPfsCRI0cmtFt1vLNVFwBNA8LHgbeMIs1CoBXJjEIIwa5du/jJT37CQw89xPz58/ng\nBz/I1772Naqqqqa6eJLZiO8jTp3i5IkTHDx1ioM9PdTlchxUVeoiERrjcRZ0dLD62DFWnTzJpmSS\n9+dyrFIUFkSjqL2it24dXHttvxia5rBHeRkPr9sjeyJL8o0k9hM29qGTZBoayB7P4rQ5aDENvVhH\ni2mopoqiK0TWRhAZgdPm0H60nVMPncJLeagRFS2uoceD9Fp8gMW0PnHTYhrGPKM/HNUGid+gsKWh\naEO+y+fo5O4vfOELfPzjH2f+/PmTMsN9vOI42p8VQ0s+fX+OTBIzeVynvb2dBx98kH/5l3+hu7ub\nD3/4wzzzzDNccMEFQFC32SyOM/ndjYYpqZ8Q0NUFzc195jU3U9/VRa3rUqtp1MZi1JaXc2DxYgwh\nuKCzk9WZDKsUhbeaJqsNg2XxOOFVq/BvuBk3Z+B2u7jdLl63R3ve/8LOF7ikfD1et4fbbeN2H8bp\ncnBPuzjtDm63G3RPCoJvKgGqqQZCWKSjl+kUXFZAeGG4Txj7RK9X6OJD4qIjiNgsRJmgfWvFOf79\n7d69m6effppdu4LpK5PRwh2vOJ4AFg0ILyJoGZ4tzcJ83DBuv/12qqurASgqKmLTpk19/7S9mwfP\n1PDu3bunVXneLPz000/z2muv8dprr/Hkk09y8cUX86d/+qd8+tOfRlVVampqOHny5LQprwxPo7AQ\n1Pz613DqFNvmzYOmJmp+97sg7DjYbW08aNs0VlWhXHkltUuXsuP0aU5Eo8y/+hpW5wTW7n0s8CN8\nvuAaltab7Nv5El6PwhbrCtwOl5cbXqY50UNHrgS3u4Fd7i/RohqXlF+CXqiz298ddDkufwt2q01N\nbQ1+2mezuplcW45Xml5BNVS2XrCVoquLeN16HXOpyfW3Xo+52OS555/Dx+eKbVeMvv4p2HbB5H++\nNTU1bN++HaDv+3KqOFdRmyiee+45GhoaWLx4MQDJZBLP86itrWXnzp0T8ozxjjnqwEHgWqAZeBW4\nbYQJOXcLIW5SFOUy4D4hxLAJOdO9f3uucPToUbZv38727dupqKjgjjvu4NZbb5XHPUn66emBpqbA\nGhv7/XkTx49D2KRj6Qr2rV7PvsXL2F8xnwNlJdQVR2m1NBZ2q1S36iw5DouPCBYe8Fl4xCdmGegl\nOkZx3i0x0Iv1QX6jJLimF+tBy65QRzEUMvUZ0vvTpPanSO1Lkd4fLJQ3Sg2i66JYa4NJMdG1UazV\nFkapMdWf5IQwF2er2rZNIpEAglbjt771LRoaGvj+979PaWnpqPOZtDFHIYSrKMrdwJMESzn+WQhR\nqyjKn+WvPyCEeFxRlJsURTkMpICPjueZkonHdV0ee+wxvvvd77J7924+8IEP8Nhjj7Fx48apLprk\nfCMEnDoFDQ1QXw8NDYgj9fhHjkFjI0rLcfA8vKL5uNFKsqF5HC9YxJ7KTexfeh0HLy3iSKXJsSUa\n2TAsPa2yrMdgZdbgT9pMVneaLLcimCUGxmoD/fJ+0dPi2puOHfmOj33EJr0/TefTnYEY7kth19mE\nKkNYawPxK/6jYhZ+aiHWBRZ6gdwIbLYRiUSIRCJ94VgsRiQSOSdhfDPkJgDniZppOG7V3NzMD3/4\nQ374wx9SXV3NXXfdxS233EI4HD6nfKZj3SaSWVU/IeD0abyDR/D2HsGvPcJzr/6eq9I51JPH0LtO\n4KsRsqEqMlSRzlaQ8ebhFs4nsWABdevnc2RVjCMLBIfLPA7GHYQKaxSTtabF2sIo68rjrCuIMT8U\nGvNECT/nYx+ySe1P9bUG0/vT2IdtQgtCQesvL4TRdcEMUS068v6js+r9jcBcbDlOFHJvVUkfQgie\neeYZvve97/HMM8/w/ve/n8cff5wNGzZMddEk40QIgXPaIXe4A/e1g4jaw4j6etQTx9DaGtG7TxCy\nm/ExyIhKcpH5OAUL6YkU07byrXD5UtRVS2FJEY0VPnVFLrWhLLWuzeupFK25HBdYFuujUTbGYnwo\nGuXCaJSq8Yhg1iddl+7rBu0TwaM25hKzTwTL3lWG9blgjaAWOfMm3BLJRCFbjnOErq4utm/fzve/\n/30Mw+Cuu+7iQx/6kFyTOEPwbI9cc47siSzZ4xncw6fwa+tQ6o+iNh/F6GgklG4iQjMaKXLRRbjF\ni/HmLUYsrEZZvhT1gmVoG5YTWlGGXhz8Lm7KZnk9leL1ZJLXUyneSKU4ZNssCoe5MBplfTTK+liM\n9dEoyyORN98f9CzlTx9M93WD9gph5liGyNII1jprUGswsiqCZkoRHA2y5Th25N6qc5i6ujruv/9+\nHnzwQW688UY++clPcuWVV8qTL6YRXsYj25QlcyxDtjFLpjFDttHGO3ocrbEe7VQDYbsJyzyJpZwg\nnDsBqoJbXo1YuBRWrEBZtwJ9y2q0C1dDVRUMeb8djtMnfgOFMKppgQDmW4HrYzHWWhaRsxyRdNa6\npDzSB/pbgKl9KVL7U2SPZ4msiPR3g/aK4MoIamj0W6VJhiPFcezIbtVpwPkc9+jtOr3vvvt45ZVX\n+MQnPsG+ffuYP3/+pDxvto/pjKd+Qgicdqdf9I4Fbq8Qug2nMDrrKShuIR5pJkoTpfYx9K5GiBXg\nL1mGculK1LWrUFa+A5YvhxUroKSEkeTL9jxqB4hfrxAmPK+/JRiNcmtFBetjMUoNI6jfOU6+chMu\n6dr04DHBfWlyJ3NEVkX6WoGVt1dirbWILI+gGlMjgrP971MyOUhxnEVkMhkefPBB7rvvPnzf59Of\n/jQ///nPp8WBwbMZp8shczSDfdTudxv6hVAzXAoq2yiIn8QymihyGgkljqG3HkFxc7BpNcrq1bB6\nNay6PnBXrIBYjDPJiScER+1gLLC3W/SNVIpj2SwrI5E+Ibx7wQLWx2IsDofH1FvgdrvDJsWk9qdw\n2pxgv9B8C7Dq41VE10Yxl53bptlzAd/1ETmBnwtc4eT9A9zx+CWTg+xWnQW0tLTwve99jwceeICL\nLrqIT3/601x33XWy63SC8F0/6PYcKoBHM9hHbIQjMJeGiS9IE48dx9KOY2YaMDoa0I4fRmk+DosX\n58VvVeD22rx5w7pAB9J7gsQbvSKYF8LadJqKUGhwl2g0yirLIqSeuzg5nc6gbtBeEXQ73WBt4Lro\noDFBs9qcljvACE/gZ/w+82wv8Nv5uKyPyAbCMsyfE/jZwf6R4vxc/r6B/rPkhwA1rKKEFNRQ4CqG\ngmqcwR9SUYzR+5d9eZnsVh0jcsxxlrJv3z6+9a1v8atf/YrbbruNT33qU31buknODd/xg0XkdWns\nQzZ2nY192MY+apM9niVUGSKyLIK5NEysrJuodoxIph6j/RDq0YMo+/eDqsKaNYPFb9UqWLYsOMLo\nTUi4bp8IvjFACIG+STG9QrguGqVAP/eOH6fdGTYemN6Xxkt6fcI3cHKMudhEUcf+ves7ft/pEQNP\nkuhz016/cNlDBG2gqI0yjXAFqqkGFhnimipquN+UkDLIHeQPqSjhIf5QPs1A/wj3Doub5Ja0HHMc\nO1IcpwETOe7x4osvcu+997Jjxw7+/M//nLvuuouSkpIJyXsszJQxHeELssez2IfsQATr7D4xzDRm\nCC8IY60KTlSILA8TLWwnkqvnpR1PcY2bg/37A4tGYe3a4VZePqpyOL7PwXS6vyWYF8NTuRxrB7QC\ne23eGJZK5Npyw3aLSe1P4dv+oBagtc5iZ+dOrnn7NcEpEYl+cxMuXnKImA0ROC894OSI9PATJoQQ\n/ZtnW/2bZ/dupK1GVLSINrKY5d2+66NIo4SUYZ/VTPn7HCtSHMeOnJAzC/B9n8cee4xvfOMbtLa2\n8pnPfIaHH3540C4RkgA36QZHCe3PHymUF0L7sI1erAfn6+VFsOhtcSyrFTPRjHroQCB+L+6HHx0I\nzvBbuxY1HocbboA77ghahqP8ISKE4FgmM7hLNJXisG2zJBzuaw1+tLKS9dEoy85hqYTwBW6PS+ZI\nhsSuRN8uMZn6DNnjWYQjMMoN9EIdNRa0YqLroviOj5/06X6+m/bftuMlPGrtWqyYNXzz7CGnR6hW\nsBm3UWEME7k+vzVYCOVMVMlMRbYcpznZbJYHH3yQb37zm1iWxWc/+1n+5E/+BG2MU+1nE05XME42\ndNak0+b0z5i8wMJanW8NFibQ62vh9dcD27s3EMOyMrjwwsGtwAsugMLCUZel3XEGLZHodeO9SyXy\nQnhhNMoay8JExe1yh1v3cL/T6eCcdnBaHdxOFy/lIXIiOEFCCU6Q0AuCvUaNCoPw/DDGPAO9QB8u\ndiOENUsbV9fpTEQIcJx+y+UGu0P9rjvYPG943NlsMtPv2zc3W47btm3jlVdeQc8PLyxcuJDa2to3\nuWswslt1BtLT08MPfvAD7rvvPtatW8c999zDNddcMycn2QzsIkzvT5OqDVwv4WGt6Z8x2buptFnh\noxzY3y+CvZbLwfr1g+3CC89JBG3PY3863SeEr6dSvJFMkXI91igma5wwq5IGqzoMlrcoRFv94Fik\njuB4JKfdwW13cXvcPkHTiwLTCjTUsIpwBX7ax+12gx1vWnKgQmR5JKjjhijxzXGiG6KE5o19d5rJ\noFd0stkzWyZz9usDbSSxOpOAnYvfdUHXwTCC4WDDOLvfMIL0mha4o7XzkX7DhrkpjldffTUf/vCH\n+djHPjbmPGS36jRgtOMeJ0+e5B//8R/54Q9/yHXXXcdjjz3G5s2bJ7+A42CixnS8jBeI3+spknuT\nfa7IimCSyJpgrKz05lKstRbhKh3l6NF+8duebw0ePx5MhukVwOuvD9wFC846MxSCrlC32yXTmuPA\nqQSvd6XjbzUDAAAgAElEQVT4rz/UkFy7ngNmlpaIx+LTKssbFZYcFlyz3+fOEwoLfINQiYJe6mPk\nTS/RMapN4hfFA3+pgVEanCjhp3zSBwfvFpN8LoliKIHYD5wdui6KUW6ckwgKEYiQbQ+3dHpwePfu\nGhYv3jYsfug9ZxO13mu5XPCFHQ6f3UzzzdNEIsHvltEI2Nmu79hRw1VXbRsmdtPoN4VkjEymeEtx\nnCbU1dXxrW99i0ceeYQPfOAD7Nixg6VLl051sSYFIQSZYxlSr6dI7e0Xwkx9JthFZUOU6PooCz+9\nkOiGKOEFYZSenkD4du+Gh3fDnj1QWwsVFf0i+N73wle+EswQNYxBz3M7XXL702Sbs+Sac+Rac+RO\nBXYineWAkeVg3OFwmUf9MmhcBKUphZWdBvEOl5tOWnwmXMoFhTGseSGMCwOhM0oM1PDI42rCE2Qa\nMkFL90DQ/dsrhGpEJbo2SmiVhboyhnnNPLT5FulQiPYUHEtCKgXJOkjtgmQysFTqzO5AcctkAmGI\nREY2y+r3d3UF9/TGFxfD/Pkj3/dmghcKBeI4nWhoCP5MJLOPz3/+83zuc59j9erV/P3f/z1XXXXV\nhOUtu1WnmB07dnDvvffy/PPPc9ddd3H33XdTPspZjzMBL+2R3JskuSvZL4RvpNBiGrENsT4hjG2I\nYV1goRpK0PLbvXuwtbYGArhpU2AbNiDWrsX1rWDP0eYsuZZcv/gN8GdbsqimirMsRON6jYaVCkcW\n+hwq8aiL5lBVhXW6xYWxKBtL42wsirPWsoifYamE40AiAd3dwdGG3W0eyVqbTF0avz6F0pQmdDJN\npMMmEzZoj1q0hCyOq1GO+hZ12SittkEqFYhKLBZYNHp2983SDBQ805x+IiWZHObqbNVXX32VdevW\nEQqF+NnPfsbdd9/N7t27WbZs2ajzkGOO0wwhBE8//TRf//rXqaur46/+6q+44447iMViU120ceF0\nOiR3J0n+IUliV4LkriSZ+gzWGovY5lifGMbWx4KDZh0HDhwYLoShEGzahL9mA7n5a7ELVmN7C8ic\nCLZhyzYFO8/kmnMoYYXw/DChqlDgzg/BfIPGhXC4zKMulmO/muWNTIp2x2FtfnnE6lCUxV6USjuG\n2hWisxM6O6GjgxH9nZ3gdjoUdaepctKsCKWpVlMs9NIUOlm6rQg9xRbpcgu3ykIsjmIsixAr1yko\nCLoHCwoCi8f7BU0KmGS8TKU41ig1E/KsbWLbuPN4+9vfzjve8Q7uvvvuUd8jxxynATU1Nbz1rW/l\nl7/8JV//+texbZt77rmH2267jdAoFohPN7InsyT/ELQIn3nyGdYcX4PT5hDdGEwWKb62mEWfWUR0\nbTSYzt/d3d8t+u+7Ebt2Q20tfsVCclXrsAtWkwrfRmLj/yZ5Kkb2pSy8COFFYcKLw5iL0oQXhym6\npghzsUl4URhjfogmxWFHe4pXT6d4PZniYK6dFiVDcdakuDmKdTKK1lhC2ZEo0aMRmtoV9nYGdSgp\nCboQi4sH+IsEVXqWZSJNsZYmqqTZ1/4cWzrXQtYnst4iti44OslaU0V0TX7LtCnaN3QimO3rAGd7\n/aaSiRC16YoUx/NANpvlN7/5DZ/4xCcoLS3li1/8IjfffDPqGLb5Ot8IIcg2ZUnsTJD4Q9AaTP4h\niZ/ziW+JE9sco/CqQjZ8aAORFREUFTh+HLFrB97P/4D38h8Q+/eidLWRLVpJylhFT3YpXV0fx6lY\nTWhJcSB+ecGbt9ikqjJMjxmmNaXT2qrQ3CKo73Q46CQ51pyitauVrsYU9rw0IqmhHYsRPRWltLuE\nRdlFvFW1qCzRKC8PVmmUbYOS/zVYBMNq/kT5g/mxwAHrItWoGkz+WWNhXWphXzuPS99/UTD2KWdx\nSKYBvROuenqmuiRTQ3d3Ny+//DJXXXUVuq7z85//nBdeeIHvfOc7E/YM2a06ifT09PDAAw9w3333\nsXHjRj73uc/x1re+dVp/wTrtDj07ekjsSJB4NUHPjuC/L35xnPhFgRjGt8QJLwqD45F9/g3c/3kV\nsfMPaHWvEzq5D1/oJMUKUvoKclVr8VatR71wNSyIkiqI0Bk2aREmJ9tVWlrg5En63BPdDj0laWLr\nU4RWp/AWp0hXpFBUwfxslKVKlDXhKBsLo1xaHmVFpcGZ9kEQQpBrzgUCeDC/I87BYFOA7PEs5mIz\nWA/ZK4RrghahUWyMnKFEkkcIgS98XN/FEx6u7/aZ5w8JD7jueC4p26Un6dGTdOlJuiRSLomkRzLt\n9lnK9kjZLmnbJZ1xsbMedtYlnXXJZD2yOQ9F8wibPukn/mbOjTmePn2am266iQMHDqBpGmvWrOHv\n/u7vuPbaa88pHznmeJ5pbW3l/vvv54EHHuD666/ns5/9LBvP8Uig84GX8kjsCkQwsSNBz6s9OG1O\nIISXxCm4tIDYxTEUQyGzrxvnud15EdxL6OQ+IvZhXK2YTMlaMosupGfJJpoXXURTwRIasiYN7QZN\nTcH8mqam4Nfu/PlQWQnlCz1CK9J4i1Mky1OcjqVo0lP04LAu1r+H6IWj2ELNTbiDxG+gCGoxDWtV\nfiOA1ZE+v7nUlLu3nCeEEOS8XJ85vhO4noPjO2d0JzTNGa4PFLHRCF1fnHBRUVEVDRUdReio6CA0\nFF8HX0f4OsLTEJ6O7wbmuRqK0NEVHU3VMVQdXdMwNJ2Q3msaIUMnbOiYIR0zpAVuWMMK60RMjUhY\nI2RoaIrG//mj/zPnxHGikOJ4njh8+DDf/va3+dnPfsatt97KZz7zmb6ZU1M97uE7Pql9qUFCaB+2\nia6LEr80TmxDDL1Ux0/7ZN44jb9zF3rdXkIn9xPjEBG/EdtaTEfJehqLN7Infik12qXsO1VCQ0MN\nqrqNRYtg0SJYuLDfnb/Ix6u06ShKcVSk2JffOaZxyNFKvUK4xDRRRxBB381vDD5Q/PJ+t9sNtoRb\nbQXbwq0O/JGVEYyi8bcCp/rdnStCCDJuhoybwXZtbMfu82fcDFk3S9bL9rl7Xt7Dss3L+uJyXm7Q\n9ZyX679nSHjQtTPcm/NyGKpBSAsR0kIYWuA3VANDM87onjHNAH9vfmfKQ1cNDrxymBXrN5KzDXIZ\ng5xtkLUNsmmDdEonkzJIJ3XSKY10QieZ0EkldJIJjWSPTqJLJ9GtY+gaBVGdgphOQVyjqFDtm2TV\nawMnXo0UF48HM5Qnkrk6W3UimLQJOYqilAA/B5YADcD7hBBdQ9IsAv4NqAAE8AMhxP3jee50QgjB\niy++yD/8wz/w4osv8olPfILa2lrmzZs3pWWyD9t9IpjYkSC5J4m5xCS6MYq5wKTs3WV4SY/sGyfw\nfvE7Mg/sJ2bWE3PrKMu1ciq6mgPmJl4sfAdP9VxMy7z1VC2LUF0NS5cGJzB9LC+CDQ1ww00+9ZkM\n+1Mp9qfT7E+l+FUqRZ1tszAbZn0yEL/3V1Twd9EoKyMRjCFjrr7rk23IBKdhHLaD0zEOB5uDZxoy\nhOeHiawKhC+2MUb5e8uxVlvBWOA03v6sV6zSTpqUkyKVS5FyUkE4F7i9ItYrYAMFzXZsMt4IcWcR\nv5AWImJEMHWTiJ5382FTNwlpIcJamLAepqOlg7aKtr5w77V4OE6ZVhaE9fCw671xZ7veK4iqcm6t\ndCGCtZe9y2V6bWi4pwc6RogbmE5Vaygu3nZG4SougCUlUFB9ZoErKBjVwSqSWcS4Wo6KonwDOC2E\n+IaiKJ8FioUQnxuSphKoFELsVhQlBrwG/LEQonZIuhn1K8V1XR555BH+4R/+gc7OTv7iL/6Cj3zk\nI0Sj0fNelmxLtm98MPFqgsTOBKqlYq200Et0UIKxxNy+BiJdB4hYDZjeIQoyBzG8BG+wkV3hi2ip\n2kJy5WaM9RewZIXB0qVQXQ1LlgTr5gCyvs+hdJr96TS1eRHcn05z2LaZHwqxNhplrWWxxrJYH4ux\nxrKwBqxX8B2fzLHMIPHrtcyxDKF5ISIrIoPMWmVhLjfRzMld9+B4DolcgkQ2QSKXoCfbQyKbIJlL\nnlHY+vz5ayOlSztpDNUgGooSNaJEQ1Eswxrkj+iRQSI2VNAiemREsRspXVgPn7MYTRRCBBsSDBWr\ns4nXmeIMY7hQvVnLbGhcPD77RU22HMfOpHWrKopyALhKCNGaF8EaIcRZDxRUFOVXwHeEEE8PiZ8R\nL6K7u5sf/ehH3H///VRXV/NXf/VX53XmqdvtktjZ3yLsfqUbP+VjLjZRYxqZhE/uuE3YbkK3GtG9\nw1iZOipz+/EUjcNFW2hfvBnnws1ErthC1dalLF2uMnSJZdrzOJgXwV4BrM2fNF9tmqyxLNZaVp8Y\nrhoggn4u6AK1D9ukD6UHCWD2eDZoAQ4UwJWBay49dwF0PIfubDddmS56sj19gjZQ5BLZvNDlhscP\nFEHXd4mH48RD8UFuLBQLhGwEYYsa+fAA4RsaZxkWmjq9FzR6XrCxwZuJ2ptZIhH8kBqp5RWP94vW\naLofZ7uoTRRSHMfOZIpjpxCiOO9XgI7e8BnSVwPPAeuEEMkh16b1i9i/fz/f/e53+elPf8qNN97I\nX/7lX3LxxReP+v6xjFt5GY/UnhQ9r/YE9lIPueYc+jyDjKbj9njonWlEpBnXO4aaPUyVUssysZ+U\nVUpHXgStK7cw78bNRFdUDdtQstt1OZAXwIEtwZZcjpWRSNAKzAvg2t7uUEXB7XSxjwZHJD3738+y\nSd1E5kggiNmWLOYic5Dw9ZpZPXgiTMbN0JXp6rPuTPfgcPbs4ZyXozBcSKFZSGG4cLi4heIUhAtG\nFL2BbkG4AFM3R5z0M53HHB1n/ILW0VFDLreNWGxkUTsXi8eDDbGnE9P5/U0EUhzHzrjGHBVF+W+g\ncoRL/3tgQAghFEU54yeZ71J9BPh/hwrjdMVxHH71q1/x3e9+lwMHDnDnnXeyd+9eFi5cOOHP8l2f\ndG2axKsJul7qoud3PaSPZsjGwngoGMkcCgls7QRuUwNlxiFW6Aeo4hCpeDXuhi1Er9xMZOuHYdMm\nrJISejehc/1gPPBgezsHbZuD6XSfJT2PVZbFurwA3jl/Pmssi2pCOI1ZMvUZMkcz2PU9ZI6eYm99\nBvuoDQpElgWtPVd3CV0ZguvAXeCSLknT6DTSYXfQbrf3ue2vtdPxYn9cV6YLBYUis6jPCs3CwB/u\nDy8sWNh/PVw4KL1lWNN6acxICBHsg5pIjL+15jhv3sVYUADLlp1Z0PbsgRtvhBmw7FYiOW9MRLfq\nNiHESUVRqoBnR+pWVRTFAH4D/JcQ4r4z5CU+8pGPUF1dDUBRURGbNm3q+8VXU1MDcF7Cx48f52/+\n5m/4zW9+w7p16/jkJz9JSUkJhmFMSP5CCJ766VOkalOsbV5L1+97ePrQq3iqyhZlE2Enyyvq8+S8\nVi43VRaZdTRkdhH201y2dgvhSzfyUtyE5cvZ9pGPgGVRU1NDt+NQdumlHEyn+e9nnqEpm6X9wgup\nt22K3niDxeEwl191FastC3vnayxIqtyw6Aqy9VmeffZZcs05NtgbSB9Ns6NtB5TC+hXrSVemedl5\nma6CLmKbYjQWNlJ7qJbubDe5RTna0+349T6F4ULmb5hPSaQE/6hPPBxn/aXrKbVKObXvFAXhAq66\n6ipKrVIO7DxALBTj+muvP+/v99zfFzz5ZA3pNGzYsI1EAp5/vgbbhqVLg/CuXcH1srJtJJNw+HAQ\nDoeD662tQfpcLriuaTVYVpC+oAB8PwgvWxaEu7qC8KZNQbixMQi/7W1B+I03gvANN2xDUabX5yXD\nkxuuqalh+/btAFRXV/PlL39ZthzHyGR2q34DaBdC3KsoyueAohEm5CjAj/Pp/uIseU3pi8hkMvzq\nV79i+/btvPrqq9x666188pOf5MILLxx33tmWLF3PdXH68Q4af5emu9FFFz4FvoNNjoQ4gWU2UBU9\nzGL1ABU9tfilFWhbNqJftDHYaHvjRqiuJu37HLVtDtv2oFbggXQaVwhWWxarLYsLNJMLugyq21WK\nm12SR7tIHE2QbcziHffQTmo4MYfuim7aS9tpLm7mWPwYh6KHaCpqQq1UKYuVURGtoDxaToVVQZlV\nRqlVSmmklJJICaVW3o2UEjHOsBJ/Cuid6ZhIBCdW9LbQBtq5xCeTwfhX756o8fhwO5f4WGz6dT1K\nZi6yW3XsTKY4lgAPA4sZsJRDUZT5wA+FEO9QFOVK4HlgL8FSDoDPCyGeGJLXeX8RQgh27NjB9u3b\n+fnPf85FF13E7bffznve8x4iZ9p25U3yyxzLcOo37Rz+bYK2PVmcthwx1+Ewv6eaKjTjOKXxYyww\nj1CZrSOSOgUXXoi2eWMggBs30rNuHUd0ncN5Eey1I7bNacdhaSTCai/M6jaf+S0ZCo+nsJrSqMdz\nKM0K4dYwZrdJd0E3JwtPcrLgJInyBNl5Wfz5PtoijcjiCKWlpZRb5VREK/pFMFpBPBQ/p67K8Y7p\n9G6FNV4BG+jX9bEJWDQuiMYEVlwQiUIkJvjDazW89eq34QGeEP02IOwD/gBXDAn7MHLcme49j/kd\n/f3vWXzZZYj8/SKf97mEGcM95yuP0zt2UHLJJWfPQwgQPgNzEQgQeXdAGIZa/qnC74tT8ncofeXq\nvc6ANME1BYEQPkpfXiAG5p2/NvDqQPfFrbdKcRwjchOAAQgh2L17N//xH//Bww8/jKIofOQjH+FP\n//RPWbx48ejz8QSdOxLs+/dOTryYJlWfIZzMUS6SCFrw1BMURo4xz6pnnn+InT2NbFu5GnXDhYh1\n6+hYv54jK1ZwuKSEw9lsn/gdtm3SWYc1XbC0zaGyNUNxi038RJZYi0es1aDwdCG6q9Ne1E5PWQ+Z\neRm8+R76Qh1riUXR8iIqlldQWVTJvOg8isyiCRmXE0LgCkHG9+mxBR0Jn46kzws1NSxYcyVdKUG3\n7dNj+6QygmRGkMoG/nROYOcEaUeQyfnYriDrCjKuIOcJ1JBPKCIwIgLDFOimQDd99LBACwtUQ6CG\nBIrhoxgCRRcomoCBpggU1UNVXAReYCIwhIeP3+cXwgV8hMjHBVKHio+OQMfHUAS64pPedZCSzSvQ\nFYGh+OgEpuWv68JHU4KwJnxU8mF6zUNBoOGjKj5a/otRRaDiow4IK/ioCoPiB6btT5dPO+A6A9Io\ng/w+CuTTB1/Q/ff67HutgwsvKkLp+4LuzwN8FBGkg4Hu8Gu99/UKiDJAQPq/+Af7EQPTMTj9ECEa\net/gawwKB0kD/+5dHps2K2e4b+h3jpK3AX5FGRD/ZnH99ymD0p05P2XE/AAlf22kcuWfpaDw1svr\n5qw4PvTQQ3z5y1+mqamJyspKtm/fzpVXXjnq++e8OHqex86dO3n00Ud5+OGH8X2f973vfbz3ve9l\n8+bNbyocXbU2r/+kk6bnUiQOZdA7c1Q4rZRTT05pxQw1U2I2Ua42EE81wpIl9Fy8hfrNm2lYtYr6\n+fOpi5ocspMc787inPQpOyVY1JZl3kmbkpNZCltditpUSjqjFKbiJAuS2GU2ToWDWqViLDKILY1R\nsqKEytWVVC2uQtdCpH2ftOed1bV9n56cR5ft05Xx6Mn6JHIeCccn5XqkPZ+M7+P4OXyRQ5AFJYui\nZFHVHIqWQ9ey6FoOQzjorkfIczF8j5DvEBYeIeFi4hJWXMKKQ1hxMVUHQ/UIKS4h1cPQvMBVPQwl\nCBuKi6566IqHKlxUPFTcwISHkvcreb8iAgMPRTggPBAuCAdwARUUDdBQFA0UDYW8q6gD/AMMFUXR\nUPPh4F51gL83Xh1039jTqfk0va4yIKyM8poyJJ+JvTZSutFfG/Llf8Ywo0hzLmHGnMdMm9Q1kLna\nrfrf//3f3HnnnTz88MNceumltLS0IIRg/vz5o85jTopje3s7Tz31FI8//jhPPPEE8+bN4x3veAfv\ne9/72LJly7B/Bt/3OfGKzcFf9tDyUorUoQxmRzsL3AbKaMSnBUs/QbHeSAGNnC4r4MTFWzi2ZgV1\ni6qoKy6m1Y2TTppoHQZF7QrlbTYlbRlKWj3K23UqOqNYdohUSZpceRZvnsCv0hELwigLY4hFRWQX\nFdJVotAlPE7bDl22TSrXQ8bpIecn8f0eBCmEYqMrGSzfIeI7mF6OsO8Q8nKE/BwhL4fhZzH8HCE/\nS0jJYqpZTC2LqWUIa1nCegZDy2CoWTQ1F3wOIowQIQQhFEIoaghVCaNpYQwtjK6HMIwwmhZCVcMo\nSghVDaEoYVR1YFyva6AoBoqiD3AH+4M0w+PPPb2e/5KWSOYOc1Uct27dyp133slHP/rRMecxJ8Sx\npaWFF154geeff57nn3+ehoYGtm3bxk033cTb3/52lixZgu8Lml61OfRogpOvpEkf7CLefoyy7DEq\nRSMRWsiaHSTLUiRKc5wsK+ZY1UrayhbSbZSTcQvQUlGiPWFKTzsUt7uUtiuUdOnEUjrJwgypeT3Y\nlQky5TZ2mYNd5pEqE9S1HKTosgocK4muprFIE/WzWL5NxLeJCBsTmwhpTCVNRE0T0dP4QiXjRsl6\nMXKeheNFcX0LQQRfMRFq3jQTNBNFM8EwUXUT1QijGCZqyAQ9jFDDeJi4iomvmriE8RQTjxCuEkIo\n2rDxqF7/2Tj28sssueyyMb+788VI/wEjtRiGxhx7+WWqh9RvrHmNFDeReY2Y/5vkdeT3v2f55ZeP\nPv8h+Y21XKMp20TkVffSS6zauvXc8j+Pn/85xw3J7/aqqjknjp7nYVkWX/nKV/jRj35EJpPhj//4\nj/nmN7+J2bud1yiYVYcdZ7NZ6uvr2bdvH7t372bXrl3s3r0b27bZsvZy1pRcxJ0L/z/mGSVoOzpw\nft/MC1/7vzxv9SAiLnbEwDYtHD2Kc5HFyXCEQ7pOSFlKRCymwMkQc9NYIsN8NUOZliLr78IJp3DK\nU3hxGz+aQYnk0MI5dCOD0NM4qk1cyRISJmFhkRERwliEhUWYCIW5DBXR+aSUCGnFpJNiTqkWOTWK\no1g4ShRXsXC1KJ5mIbQonhJFVQ10RRlkxpCwrihoioKqKPR1lPX6B8bR61dQ/aHpQMUbFKcNyONs\n3U5hVR20Rdx0ZKR/8pH+7YfGCfKf4YD6nymvofGjyn+M5Tpj3BjK0O26tDnOm+Y10r1jLddo752I\nvE5kMuRSqZHznwaf/2jzGind9JSuyae1tRXHcfjFL37Biy++iK7rvPvd7+arX/0qX/3qVyfkGdOq\n5fjHV/4/6JqPqvoYmkBTPTRNENZcwrogFvEotHwipiCkg66Brvnomo+meaiah6p7wX2qi646GHoG\nLWQjIjbCSkPERolkUEJZfNfAyZnkciY51ySTi5BxomQ8i7QbIeOFyTomTtbEyYXwsiZeLoybDeJy\nuQhONoKTd13HRBEaCAXhB917muKjqT6aKtAVEbiqQFNB1QSqqqBpAlVTUXUFTQNVU9EMBVVXCYUh\nFNYwTI1wWCMU1giHFUIhjVBIJRzWg/iQlvcbhEI6pmkQDoeJRCJEIhEsyyAU6hvHl0gks4Sp7Fat\nqZmYx27bdm461NnZSWlpKT/+8Y/58Ic/DMB//ud/8tWvfpU//OEPo85nxrQcH3/lToTQEEJHoIHQ\nEGgIoYEwEJhAlOD3UhpFSaMqNqpqo6kZND2NYSQJGSlCoTThUJaQ4WCYDuGIIGLpRC2VUMhF6Z2n\npviB4aPk/coQC64NnFEo0LAJKTZRRSFkKoRNFVNRMNDQfdB9BdUDxdUQjobvq/i+gucEE+ZcX8EX\n4PkKvi/wPRH4867rB9ccXyPn6+R8A0cYOITIEcYRIXIicB1h4HghHB8cT8FxVVzPx/Fcck4W1xVk\nsxE8TycUyhAOZwmHcoEbdjFNl7DpY5oupikwTR/ThEhEIRJRiUQ0LMvAsgwikRDRaIhIxCQWM7Es\njUiEYWZZ/X6584pEMjs5V1GbKIqLiydlp7KBTCtxzOYGHwjs+z49PT20t7fT1nacpsZGmo4coeHA\nEU4caeFkwylOn+yhJDaPkoIqwqEyBMXkvAISWYvurhA92QJOOzHSXgEZUYzHPKAcjW5MtY2YcZqC\nSAfF8S7KShOULeyibFkn4SVtOFVtJENpXC+F56URfgZEBoUcqsih4KAqLoriIxQfXwNNA0uHqAYx\nXSGqQ1QT7N4N6zboOITwlQiKGsPQi4maVRRFqymNLSUcKscwytD1UgyjLO8v7O/S9DzIZgPLZII9\nyFKpvPUM8KeCxX55v0glEXaCnJ0knc2QSmdJ2VnsnEcq62G7gpQWxTYKSetxbC2KLaLY2QjpnEmm\nJ0ynH6bFN7DdEBnHCCwbIpeL0t5eRzj8VnI5i2zWIpMxyWZNstkQ2ayOYfiYpodpCiIRkRdOFcvS\n8uKqjCiqZxPc8ynGs31vTlk/yUzkox/9KN/5zne48cYb0XWdb3/727zzne/8/9m78/i4qvv+/68z\n+6JlNFq8yLa8yBs2YFzZEBbbQIkNgaT+haRN+6PBfNuGpklLl0eTX4mpEwP9uun3UR6p+80jTVIg\ndb7tt6TQEBfihkVgsxnjBcv7gmXLlrWvo1nuvXN+f4w0lkYjWRot1kifJ4/zmHvvXN17jwbrPefc\ne88dte1PqHBMZbPZCAQCBAIBFixYwC1pLvowDIPTp09z9OhRjhw5wscff0zVhx/SEe6gYlUFD6xe\nzerVq7ntthspLCwkFg5z+fhRjn94lhOHGzh7ppPqixYXG+0cOe2j6fBSQlYpijloCvFyiaC9hpnu\nesoDbayYGWX1IsXixTamleeipk+DadOgpASrIEC70UltRy0XOy9S21HLyc466kN1HA4d4N36OF3R\nBkyzFW214VCX8do+JscRJ98J+Q4IuGwUuBR5TshzaFw2TUy70bY8HM4icrxlBPzz8Xtm4/bPwFUw\nA5drOi5XOU5nYdqrNXsuWPd0l2DqCqkPz2tru1KS801XlrW0QKgZ3dqE1dnEG22N3FagsKbnYZXk\nYKiVg7EAACAASURBVBb7sIIezAIXRp6dLo+bToeTTpuNzriNLgO6YtAVtQhH7JhmIaZZhGEEMYwC\nDCNAS0sedXW5GEYOsZifSMRHNOpNhm4k4iISsREOJ74jhMOJEokkHnU0mmF74kTiAbUD/Zy0jIUY\nf5s3b6axsZFFixbh8Xj4zd/8TR5//PGr/+AQTahzjqN5LHV1dXz44Yfs3buXDz74gPfee4+ysjLW\nrVvH2rVrWbNmDSUlJWl/Nh6PU1dXx8mT1RzYW8uRjxo4dTJK9UU7dS0FRM25KBaicFPoqKbMfpal\n8ROsNo6yoqCRpTNaKSj1JUOTadP6l6KixF/xbp3RTs62nOVU8ynOtpzlXNs5atpqqO+8SDhWD1Yb\nLtVFvsOkwAWFLihy2yh22ylyKwLOOG5bHFPlYHMU4XROx++dTcC/kBzffNzuWbjds3G7Z+Fw5KSt\n94iEw9DcPPTS1ARNTcQxMecEMWcVYM7MxZzmwyjyYAadmPl2zByN6TUx3AamowuDdgyjCcNoRCkb\nTmdhr5Z2YlrraZjmNAyjGNMswjQLMYwCTDOfaNRPJKL6BGpqGc57YxHGvYvbfaW4XH2n5fyxgKl7\nK8domBK3clyNaZrs37+ft956i8rKSt555x1mzpzJ3Xffzfr161m3bh05qQ81HEBHRwenTp1i//5P\n+PDDFqqqopw756S+Pg+lFhOPL8LjjDI3eJkbS+q5LVjLTY4TXBc7QH7zOairS4RDfn7/0EwXpsXF\nib+UQFzHaexq5EzzGY42HOVY4zHOtpzlQvsFGkOX0WYTXluYYo+DIhcEXSbT3DZmeB2UeBQFThNw\nYNqC2J3TcbtnkecvpzB3KTneeXg8iQC128fpoc1dXdDQAI2NiderTbe1QUEBuriI+Iwgxqw8jJk+\njGI3RqETM19h5MYxfCaGO4JhC2GYTZhmE4bRRDwe7g7T3iXRle1yFeN0FuN0lvSaLsZuH3goQa0T\nvdzDDdWhvtfTix6NQix2ZdowEqGcLjSvNp3Jz7hcieJ0Ximp8+mWS6t67Ek4Zk7CMQ3Lsjh48CCv\nvfYav/zlL9m3bx+rV69m/fr1bNiwgeuvv37Yo2bE43HOnz/Pxx8fZs+e8+zdG+LECQf19cXY7Qbx\n+G/j90cpL4+wepWH22+Em2bUsdh7HntTfSI0e5f6+iuvdjsEg+lLYWGfeSM/l1pnlHP2ds5GLnO8\n+QQnG09ytvUsNe0XsMxW5uR4mel1UOiKE3AY5DmiTPfYmO6xU+AyMbWLmCoAx3Rc7jnk+hdSlLuM\n6QU3ketbiN3uS9Z7XM/pmGbii8VgAVpff+V319ICgUDyi0d8RhHGrHyMGT7MYjdG0I6RD4bfwnCH\nicVbMIwGDKOBWKwew2jg4EEbN988IxmWA4Woy1XSHaa+q9djhLS+Epa9QzOT6ePHK5k5c92A6/QO\n5NQSiw2+zGYbXpiOZLnDkfhn4nD0LadOVbJ8+bp+y3tKup8ZbHnqe3b7tW3FSzhmTsJxCDo6Onjz\nzTfZtWsXu3btoquri09/+tN85jOfYf369eTl5WW87Vgsxk9/+lPcbi+7d1/oDk03hrEMu70C0yxk\n7txOKiocrFmTx8qViuXLE11twJVzgk1NA3dRDrQ8Hk+0UHtKXh5WXi6dbkWLO069I0qtClFNK2es\nBs5aTZi5PnJL8sktdOHP03h9MXIdYfLsIQocUaZ5IBp30BH3EyPI8SNeblh9Pbn+hRTmLWNG4CZm\n5s3F7XCPzoczEpZ1JTDTfelIXeZ292m965Ji3oh2cOunFhErcWEEEy3TmC+GYe/AMBqTIdpTwNYr\nREtSAvVKiF5pmfqv6fBlY/XlRuvEr3+wIB2t5aZ5pVhW3/mLFyspLFyX9r2BfmYo7/Ust6wrYTnU\nQO2ZH6hc7f3e633/+xKOmZJwzMDp06f55S9/ySuvvMKePXtYvXo1999/P/fffz/l5eUj3r7Wmtra\nWvbv38+771axe3c7VVVOQqGFuN03E4mUMW1aFytX2li7NpfVqxUrV4J/uL2dqRfaDPTaPa1bW4m2\nNGK2NkF7O46OEM5wDMOh6HRqom4HMZ8LY7qb2Ew7sRk2YiVxokEDIxBF5xvY8yxiEQi12wiHPRhG\nHhZFOOyl+DwLyM9fQGFwNiWFcygpLsOTE0iE0rU+iaZ14vcxlBCtr0+ccOwJ0u5XXVKMNaMAY7oH\no8hOLKAwci0Md4SY2dgnRGOxBgyjHiAlNEuS04nXEvq2TCfO48HElS8BwwlUw0hMD1R61h1K+aM/\nknDMlITjCHV2dvL666+zc+dOdu7cSX5+Pg888AD3338/t956K85eF9aMVGNjIwcOHGDv3oO89VY9\n+/dDZ+ci3O41dHXNo7Q0wqc+5WTNGi+rVsENNyS6mcZU9zOlYm3NXLh0nOqLR6m5fJLLl0/R2FBN\nc+MFfNE481wlzLYHmaFyKfTZcfnCxL3tRLytRHM6iBVEMYoMtF3jqlO4ajWei5BTA/5L4KxT2Fod\naIcL7XGD14fN68Phy8Hlz8Pu8yfOvSZuwux7MmwsitM5eJ9ZONy3C3egIK2rg9ZWKChIe27Zmh5I\ntEoL7Rj5mpg/hqFbkuF5pWWamLbZXH0CdPAwLcJmG+v/QcS1JN2qmZNwHEXxeJwDBw7wi1/8gp07\nd3L27FnWr1/PAw88wIYNGwgG+90oAYys66rnytv33vuIN95o5OOPXSh1M3b7LYTDMygvD3PHHR5u\nvdXFqlWweHHib/p4qaysZPnq5RxvPM6JxhOcaDrB8cbjHGs8Rk17DeXBcq4rvo5lxctYVryMJcFZ\nzPQqjGg14fBpWjuP0hE6iRE5B/FmYlYOXVEvrSEbzW0WDU0RLtd1YrY5KCTIdHsexSqXoN1PwOYj\nT3nJU25ycePHiU87cZhWov9tJCUaBa2ptNlY53L17yfrOdE1lGK3d4/+0N2ESN1PJNL36hynM9FN\nkJNzpeTloXNzied5sfIdWH4blk9h2qNYhDB1Z6LEO7B0O6buwIx3oBwe7K58HK4Adlc+dmcBDncB\ndlcBDlcB751sYd3KVTg9RTjcBSh795cCm+1K/13PdO/XnqLU4K9XW6enjOH/n5P5PkcJx8xJOI6h\nS5cu8corr7Bz507efPNNbrzxRu6//34eeOABlixZkjyXNJr/QLXWnD59mr1797Jnz0HefruDU6cC\n+Hxr0frXiMUCLFsWY906H7fcYuPmm2HWrLH7+zNY3cJGmBNNJzhSf4QjDUc42nCUIw1H0obmdcXX\nMT8wB8u4SDh8lkjkDOFwokQiZwmHz6KVh7h9Gl0U0Gb6aYg5uBiGs50RPulopa6znvpQPT6njxJ/\nCdNypiVe/VdeU5flufMGPucXj1P5xhusu+22K8GWepLramU46/ecRBvoKc89Azx0dV0pWve998Pj\nSV5mql1OtFMRd4K2xYljos0I2owQt2JgRnmrtYs7vHG0ZUDcxBZ3oHBgi9tROlFscRtK21BxhdI2\niIPSgFaoeDxxDOleB3uv57XHUII2gyCujERY5/dnts3BClx9nUzWHeb66ic/kXDMkITjOAmHw1RW\nVrJz505+8Ytf4HQ6uffee7nvvvtYt24dPt/YXcUYi8X4+OOP2bt3L2+/fYR33olSXz+HnJy7iURu\nwOVysGoVrFnj4eabFatWJS7ivFZSQ7MnOHtCsycslxUvY1nJMsqD5diVnVjscndYXgnOnnnLCuP1\nzsfjWYDNWUpUFdIRz6PRcHE5rKnraqQ+VE9dqI66zrrktGEZfYK00FtIka8oWXrPF/oKKfQW4rSP\nXlf6iHV29u/GHaiLNxRK3BqU7rahkhLi04owi93EChRGjknMaurTpXvlKt7EtGWFum+HGVo3r92e\n2/+LiNZXylDCdCRBnMlrupJ63IOV4aybwfpq0yYJxwxJOF4DWmuqqqp49dVXeeWVV/joo4+4/fbb\nuffee7n33ntZuHDhmB9Da2srH374Ie+//wFvvfUJH36osKxfw+NZQ0dHOdOmmdx2m4vbbnOyejXc\neGOiwXEthY0wxxuPJ1uYRxqOcKT+CJc6LrG4aDHXl1yfKNMSrzNzZyb/2Jpme5+w7N3qjEZrcbtL\n8XoX4PHMx+tdkCzaMYOmSBf1oUSrs6mricauxmRpCvedbw43k+PKSYZlMki9KfPdwRr0BinwFuBx\nDP1ROmMmGu1/nnSgIG1u7nMbTLr7ceMlQYxCB7GAxlBtfcIz3TnTeNxIXsU7tDAd+9tisp10q2ZO\nwnEC2LlzJ9FoNBmWfr8/2apcu3YtXu/YX4Gotaa6urp7xKAPqays59ixHPz+O1HqZjo6ZrJoUYy1\naz3ccouN1ath4cKr38g9Hud0QrEQRxqOcLjuMFX1VRyuP8zh+sMYlsH1065nefHyZGAuL1lOvie/\nz8/H4zEikeoBWp1nsdtzk2Hp8SzoE57vvHOUO++888q2dJy2SNugAdoz3xBqoCXSQku4BbvNToGn\ngAJvQd/X7umgN5j+/TEO1gE/v8Fug0l39a7H0z9Ie08XF2MV5WLkk7joqPvq3YHCNBarQynHMMK0\nGJut/7c7OeeY8XYn7N/knJycPj0Q4XCYr371q3zve98b1nYkHCeA3v9AtdZ8/PHHvPLKK7z66qsc\nPHgw2aq85557WLx48bjd92YYBocPH+aDDz5gz54D7NnTxeXLc8jL+3VisRWYZg4rV8a54w43t9yi\nWL0apk8fuG7jrT5Uz+G6RFD2vB5tOEqhr7BfK3Nx0WJc9v5XbmqticVq07Y6w+Ez7N8f4lOfWpQ2\nPN3uOdhsVx+iWGtNl9GVDMrer83h5ivL0ryfLlgDngB57jzy3fmJV0/+VefT1R1G6fPTOnFF7mBB\n2nuwho6OxNW7xcWJUlR0Zbq76KJCrCI/RkARyzUxdMtVWqYN2Gy+fmH60Udh1qxZ1S9ME1fyTujh\npYdkKoZjb6FQiOnTp/Pqq69y++23D+tnJRwnuNbWVn71q1/x6quv8vrrr2OaJnfffXeyjPWjWdId\nz4cffsgHH3zA228f54MP4sTjFfh86+joWEpuruJTn7Jz662J7tiKisTFlBNFXMc523L2SmjWJ1qb\n51rPUR4sT7Yue4KzLL9s0C8jptnW7/xmz3Qsdhm3e3afluaV8Jw/KsPwpQvWtkgbbdE22qPttEW6\nX6MprynL7cp+1RDNc+eR68olx5UzaPE4PCP7AmcY/Uc6SjfiUU9pakpcvZsmRHuW6eIizCIPRoEi\nlmMmBmkwGwcMU9Nsxm7PH3LL1OkMkm5g/2ttqofj888/z9atWzl9+vSwf3ZMwlEpFQT+L1AGnAO+\nqLVuHWBdO7APqNFap32mSLZ8EGNNa82ZM2d47bXXeP3113nzzTcpKipKBuWdd95JQUHBuB9TT3ds\n4vxlDUeO+MnJuQuH41O0tpYxZ47J7be7k92xy5f3GVd9QoiYEY41HOvTyjxcf5iOaEefsOx5DXrT\n35bTWzweJRI5lzY8I5FPsNvzBwjOBTidxePWQ6C1JmJGBg7UXvOhWIhOo5POWCcd0Q46Y539ihk3\nrxqgPSU1bP0uPz6nL23xOrzYbWnuQ+ppmV4tRHsv0zptiFJUBIWF6MICjEInRgBiORaGL4qh2gYM\nU8tq7zUG79XDtM/j5sbQVA/Hu+66i3Xr1vHEE08M+2fHKhz/FmjUWv+tUuobQIHW+psDrPtnwK8B\nuVrrzw6wTlZ8EJnKtOsqHo9z6NAhXn/9dV577TXeffddysvLuf3227njjju44447mJ7azzkOenfH\nvvjiLzh92ktt7WwCgU9jmivp7Czi+ustbr/dxc03J7pj58279oPgpNMcbu7XNVtVX0WuO5frS64n\nvzaf++65j+Uly7mu+Dq8zqGdH9Y6TjR6Ke2VteHwGbQ28Xjm4fHM7S69p+fidI7P5cSZ/L9pWAYh\nI5QMy4FCtE8xEut1GV2DFpfdNXB4Or1X5h3p10kWy4Y3FOXI7o+4be4cPK2deJrb8bZ04Glux93Y\niqOpJfmEGJqaEifYCwvTlnhhAKPYhRG0EcuPY+SYGN4oMXsHhtnQL0zj8UifYQR7BmVIfWZrz+D3\nTmdhRgM2TOVwrK6uZsGCBZw5c4aysrJh//xYheNxYK3Wuk4pNR2o1FovSbPeLOA54Cngz6Zqy3G0\nzsvFYjE++ugjdu/eze7du3nnnXcoLCzsE5bl5eXj1iKBK3Xr3R27Z8/HvP++iWX9Grm5dxEKLQM8\nrF6tuP32RHfsqlWJL/ETkdaa6rZqquqreHnXy4RKQ1TVV3Gy6SSz82b3uQhoeclyyoPlOIZ5/sow\nWohEzhGJfNL9eq7PvFKOPmGZGp4OR+bj/fY2kS5Y0VoTtaJXDdChlJARImJGaDjSgHOBk4gZ6VPC\nRhi7zY7H4blSbG48OPBgxxO34TEVHlPjiWk8URNPxMQTNvCEYnhCETwdYTxdMTxOHx5PDh5fLh5/\nPp6cAI68POxBD7aAG5Vnx5arsPlAeQxsrhioDlS8BawW4t1PjrHZvCmB2TtI0weq3e65ZuE4Wn9n\nMv3b/+STTyZ72DIxVuHYorUu6J5WQHPPfMp6LwBPA3nAX0zVcBwr8XicI0eOsGfPnmRgGobBrbfe\nyuruBz1XVFSMaOD0TPXujv3ggw/YvfssVVVePJ41OJ23096+kGAwzi232LjjDg833ww33ZR8OteE\nZFgGJ5tOJq+Y7Xmt7ahN3mrS00W7vGQ5s/JmZfQHRGuNaTYnAzMc7h+gNpvnKuE5gU4ET0Baa8y4\n2S80h12MLsKdrURCbUTCHUQinUSiIWKxMFEjQtSKErNiROMxYtokikVMxYnaIeqAmB1sGtzajkvZ\ncCk7Lpsdpz1RXA4bTrsNux2cdo3dFsehDBwY2Imy6w/1lG05Llq0iL/6q7/i4YcfzujnMw5HpdSv\ngHR9do8Dz/cOQ6VUs9a6z0kapdT9wL1a6z9SSq0D/lzCcWz1BNL777/P3r172bt3LwcPHqSsrCwZ\nlqtXr+aGG24Y1TFhh8qyrO5nYe7no48OsGdPA4cPe7HZbsHhuI1QqIw5c7q49VYH69b5uPlmxdKl\n4zscXiY6Y50cbTiaCMu6w1Q1JF4jZqRPWPa0NIdyPnMwWmsMo7Ffa7N3sdv9uN1l3c/onIPHM6f7\ngdeJaZdr+oS8wGTKCIehpQXd1ITZ3EisqZ5oSwOxlkaibU3E2pqJtjUT7Wwl1tFGtKuNWKiDaCRE\nzO8mmucnkufjf/z8/JQMx3fffZdPf/rT1NXV4R/2ExkSxrJbdZ3W+rJSagbwZmq3qlLqaeAhwAQ8\nJFqP/6G1/t0029Nf/vKXmTt3LgCBQIAVK1Yku3sqKysBsnb+mWeeuWb1MQyD5557jmPHjtHW1sbe\nvXs5deoU8+bNY82aNaxYsYJ4PM78+fO59957h739nulMj09rzb/+679y6tQpQiGLt99u59ChBixr\nEU7n72EYRZSU/JJFi+w8+OB9rFxpo6WlEq93fH5/I6nfslXLqKqv4qVXX+Js61mapzVTVV+F64KL\neQXzWLt2LctLlhM9HaUsUMaGX98wKsf/5ptvYpot3HzzbKLR87z55hsYRj033qiJRs/z3nunMc0O\nbrllFocP5yXPia1dewcez2z27q3D5Srh7rvvH/Pf71jPj/T/z4k2X/nGGzz3ox9BNMrcwkK+/cMf\nTslwfPTRRwmHwzz//PMZb2MsL8hp0lpvU0p9EwgMdEFO9/prmcLdqpUT6LwOJJ5feejQIQ4ePJh8\nPXLkCLNmzWLFihXJcuONNzJz5sxBuwbHom5aay5evMj+/ft5770jvP12G8ePe2hrm4fbvZpodD5F\nRSGWLTO4/fYcbr3Vz4oViXvNR9to109rzfm28326ZXvOZ87Km9Wva3Zh4cJhn88cing8SjRaw2uv\n/YJVq4JEIueJRi8QjZ7vnj4PqD6tzsRrTwu0FLe7dMKPYjPR/u2Ntql8Qc5IjeWtHP8OzKHXrRxK\nqZnAD7XWn0lZfy2JbtUpebVqNjBNkxMnTvQJzEOHDhGJRLjuuuv6lKVLlzJnzhxstvHtlmtvb6eq\nqooDB6p4++16DhyA6uoAcBNa34DLpSkv76CiwslddwW56SYHCxcmHowx0RmWwanmU31GAaqqr+Ji\nx0UWFy5OXgTUc9VsWaAM2xh2iybOe7YRjSZCsycwI5EL3csuEotdwmbz4HKVJsPS7S7tNT8Lt7sU\np7NIunDHiIRj5mQQADEijY2NHDt2jGPHjnH06NFkaW1tZcmSJVx33XUsWbKE8vLyZBnPC4B6zrMe\nOvQxu3ef4/33I5w44aW5uQyH40YsazrFxS2Ul0epqPCwZk2Qm25yMmfO1YfGmwhCsRBHG44mbzU5\n2niUow1HaQ43s6RoCdcVX8d1RdclXouvY37B/PT3Co6BnguHotGLyRKLXSQaremzzLI6cLlmDBCg\nV+bt9gkw/myWkXDMnITjBDAZu3ba2to4fvw4L774IgBnzpzh9OnTnD59Gp/PR3l5OQsXLuwTmgsW\nLKCgoGBcbjUJh8McPXqUAwdO8u67LRw8aHLunJ+2ttnYbDcAeUyb1sjChTEqKjysW1dERYWHkpK+\n92NO1M+uPdrOsYZjHG1IhGVPaF7uvMyiwkX9QrM8WJ72aSLjUT/LihCLXUoJ0NRAvYTdnoPLNQOX\nazpud+I1Md97evqwbrCfqJ/faJFwzJyE4wQwmf+BptZNa83ly5eTQZlatNaUlZUly5w5c/rMT58+\nfUy7a6PRKKdOnWLv3tPs2dPCoUMW587l0NJSilLX43AoSkoamT8/yvLlTgKBo/ze732WsjKVNS3N\nnieb9A7NC20XWBBckHwcWE+5dPgSn77709f6sNE6jmE0Eotd7i61xGKXiUZr+8zHYrVobfQJy9TX\nnmB1Oqfx9tt7Ju2/PZBwHAkJRzGhtLa2Ul1d3aecP38+Od3a2sqsWbMoKyujtLSUmTNn9iszZszA\nPcrP1zJNkzNnzvLOO2d5771Wqqosqqu9NDUVYRgLgCB5eXWUlraxaJFm5Uofd9xRzKpVAfz+CTj0\nT4qwEeZk08l+oflJyyfMDcxNhuWSoiUsLlzM4qLF5LnH//7YobCsUDJE04Vnz6thNOJwFHQH5/Re\nI9Wkf53oFxelI+GYOQlHkVXC4TAXLlzg/PnzXLx4kUuXLvUpFy9e5PLly+Tl5fULz5KSkn4lGAxi\nH+GNku3t7Rw8eIbdu+vZv7+LEycUly7l0dY2g3h8Li5XC0VFDcyeHWbxYsUNN/j51KeKqagoxuWa\n2M3NmBXjVNOp5DM0TzSd4HjjcU42nSTfnc/iosUsKVzC4qLFLC5czJKiJczJnzNu5zVHQmuLWKyh\nOyjre42b2v/1yiOyBg7P3q8T5akeEo6Zk3CcAKZSt+p4iMfjNDY29gvN+vp6GhoaqK+vT5bW1laC\nwWCfwCwuLk5OFxUVEQwG+xSfz5c8pzVY/RJdyI3s3n2Bd99tpqrKoLraRX19Hp2d04nHi3E6LxMI\nNDBjRoj58zXLl3tYtSrArbeWUlR07VtmA9UvruPUtNdwojERlieaTiSDs7GrkYXBhX0Cc6K2Nof6\n/6fWGsvqvGqI9rxeeapHT1gOPMxbzxBwYzEYuYRj5gb73V37rz1CZMBmsyXDbcWKFYOua5omTU1N\nfQKzJ0D37dtHU1MTzc3NtLS00NzcTHNzM6ZpJoPSZrMxb968fgEaDAYJBALk5+ezbFket966hLy8\nPHJycpLnTJubQ+zZE2PfvjiHDyvOnrXxzjtutm3LwTDc2GznyMm5THFxO7Nnx1iwwMayZX5Wrgyy\nfHkpweD4XLyUjk3ZmJM/hzn5c7hnwT193uuMdXKy6WQyOHee3Mn/avpfWd3aVErhcOTicCQefH01\nWlsYRnOv0GzCMBoxzSai0Qt0dh5ILkuUJuLxLhyO4FVDtO+yfLkN5hqQlqMQaUQikT5h2bv0Xt7S\n0kJ7ezttbW3J166uLnJycsjPzycvL6/fa8+015tPa2s+Fy64uXTJx+XLOTQ359LWFiQcnkY8bqHU\nefz+eoLBdmbMiDF/vmLJEg833VTA0qUzmDVrFh7PxLn9oae1ebzxOCcar7Q0TzSdoCHUwNzAXBYW\nLmRhMFHKg+UsLFzI7LzZEzo4R0s8HusOzCuhaZpNyfDsHaQ905YVwukMdodqEKezMDntcASZN+8J\naTlmSLpVhRhHlmXR0dHRLzQHew2FQoRCITo7OwmFQnR0dBIKOQmFinA4FmK3lwNzicfLiMdnY1lz\nSIzK+Ak22wXc7sv4/c3k57dTUhJjxgyTsjIXM2eWMHPmTKZNm4bP58Pr9aYtIz0nOxRdRhdnW85y\nqukUp5pPcbr5NKeaT3Gq6RRN4SbmBeYlwjK4kIWFC5PTs/Nnj+lgBxNdIlCbMc3mNK9NLFjw9JQM\nx3PnzvHVr36V999/H7fbzYMPPsgzzzwzrP+XJRwnADnnmL2uZf201oTD4WRo9g7Py5djnD2rOXXK\noLpaUV/vorU1h1CogEikGMsqQKkG4AJan8dmq8Vuv4TdfhGlLqH1eSzrIoYRweFw4PF48Pl8g4ao\n2+3G7XbjcrmS06MxbyqTi6GLnOs8x5mWM30CtCncxPyC+VeCs1eLszS39Kotzsn+/+dUPed43333\nMW3aNH7wgx/Q0tLCPffcw+///u/z9a9/fcjbkHOOQmQppVQysIYrFoPa2lIuXCjlzJmVHD/eyenT\nEaqr41y+7KCpyU8s5sXpfBm7fS7R6AW6umrwetvIze0AIni9EXy+GMEg+P1XQtLj8eByuTAMg2g0\nSkdHB01NTUSj0T4lFosNOp+6zDAMXC5XsjidTgqdhbTZ2thn28cH6gOM7v8iOoKJidftxefxkePJ\nIdebS74vn3xfPgX+AvweP3V1dbz88ss4nc6Mit1ux+Fw9HtNt+xq69rt9nEfcnGyOnfuHH/8BcnL\nzgAAIABJREFUx3+My+Vi2rRpbNiwgSNHjoza9qXlKMQUFo3CpUtQUwO1tXD+vMnZs2Gqq2NcuqSp\nr7fT0uIhFnPidrficDSgdS2GUU0sdg6fr53CwiglJXFmzbJTWuqipCRIYWEhRUVFfUphYeFV702N\nx+PJwI3FYhiGMWjpDHdS01JDTWsNF1svUttWy+X2y9S111HfXo8TJ4XuQgrcBRQ4C8h35pPrzCXX\nnovH5sEyravuw7IsLMvCNM1+r+mWXW3dxIU/Vw/SoYbur371qynZcvynf/on3n33Xb7//e/T3NzM\nhg0bePLJJ/nc5z435G1It6oQYkQiEbh8ORGgly4lXi9ejHPuXIQLF0wuXVI0NjoJhZy43RE8nnbs\n9maUasCyaonFaujqOofL1UogEKOoKE5JCUyf7qW4+Ep49g7SgoICCgoK8Pv9GT8wuqGrgbMtZ9OW\nulAds/NmM79gPvMC85hfMJ/5BfOZG5hLWaCMYl/xqF8prLUmHo8POUiH8rp+/fopGY7Hjh3joYce\n4tChQ1iWxcMPP8w///M/D2sbEo4TwGQ+7zGZ6wZSv+GwLGhuhvr6/uXyZU1trcmlSxYNDdDU5MAw\nFH5/Fx5PB05nCzZbI/H4ZQyjlmi0lq6uC1hWPXl5MQoK4gSDmsLC3GRwXq3k5uby1ltvpa1f1IxS\n3VbdLzTPtZ6juq2asBGmLFBGWX53CZQlgrN7ekbOjAlxhe21POc4Wt8dhvunPx6PM2/ePB599FH+\n4i/+go6ODh555BEWL17Mtm3bhrwdOecohBgXdjsUFyfKsmWp7yrA2V0SwmFoaMilvj6X+vqZySBt\naoLGxp7XOPX1cZqbobrahssVx++P4PV24XJ14nC0YbM1EY83YlkfE43WEg7XEAqdJxq9hM/XSUlJ\nDgUFgT630qROr8xbyZ35d5I3M7Hc7rHTTjuNViM1oRqqW6t5+cTLVLdVc671HM3hZkpzS5MtzdQQ\nnZU3C5fdNY6//fF3rdozzc3NXLhwga997Ws4nU6CwSAPP/wwmzdvHlY4DkZajkKIrKE1tLcnQvNq\nJRGumqYmTSSiyMmx8PkMfL4IbncYlyuE3d6JzdYOtBCPN2OajRhGPZHIZSKRWkKhi3R0XMDjoV+Y\n+nP9OLwO4s44MUeMsArTSSdtuo1mq5nWeCuBvAAzC2cyu3g2c4rmMLdkLgumLWBOYA6z82dT4i8Z\n8W0qU/Vq1QULFvCVr3yFP//zP6ejo4NNmzbh9/vZsWPHkLch3apCiCnNNKG19UppaRl8uu8yjc0G\neXlxcnJM/P4YHk8UlyuMw9GFzdaJzdaJUh1o3UY83oplNRONNhEK19IZvkQoXEs41EA0EsaIGNic\nNrRLo50ap9eJ1+fF5/eRl5tHIC9AMD9ISUEJ04PTmVYwjZycHPx+f7L4fL7k9KJFi6ZkOB46dIjH\nHnuMQ4cOYbfbufvuu/mHf/gHiouLh7wNCccJYDKft5rMdQOpX7Ybaf20TlyQlBqe7e3pS0dH+uWh\nEPj9kJenycnR+P0mHk8MnB1YthZMmojGGwjH6wmb9XQZdXTF6jHMFjw2E4/NwEUMp47i0BEwDMyo\nSc25mikZjqNBzjkKIUSGlAKvN1FmzMh8O/E4dHZCe7vqLq7ukkN7+4w+wdrWlgjTjg5o77BobjNo\na7fo7IS2kI1olwtlt1CuEBActbqKK6TlKIQQWUbrxD2qHR1QUjI1zzmOBulWFUKISWqqXpAzGgb7\n3ck4RuOksrLyWh/CmJnMdQOpX7ab7PUTYyPjcFRKBZVSv1JKnVRK/bdSKjDAegGl1M+UUseUUkeV\nUrdkfrhCCCHE2Mu4W1Up9bdAo9b6b5VS3wAKtNbfTLPe88BbWut/Vko5AL/Wui3NepO+CS+EEKNN\nulUzNybnHJVSx4G1Wus6pdR0oFJrvSRlnXzggNZ6/hC2N+k/CCGEGG0Sjpkbq3OO07TWdd3TdcC0\nNOvMAxqUUs8qpfYrpX6olBr+s3cmgcl83mMy1w2kftlustdPjI1Bw7H7nOLhNOWzvdfr/nqR7iuG\nA1gJ/G+t9UogBPTrehVCCCEmkpF2q67TWl9WSs0A3kzTrTodeE9rPa97/nbgm1rr+9NsT3/5y19m\n7ty5AAQCAVasWJEc2aLn25/My7zMy/xUnq+srOS5554DYO7cuXz729+ekt2qx44d44/+6I/Yv38/\nxcXFfPe73+U3fuM3hrWNsTrn+LdAk9Z6m1Lqm0BggAty3gZ+T2t9Uim1BfBqrb+RZr0J/UEIIcRE\nNBXPOZqmyXXXXcdXv/pV/uRP/oTKykoeeOABDhw4wMKFC4e8nbE65/g/gXuUUieBu7rnUUrNVEr9\nV6/1vg78VCl1CLgBeHoE+8xaPd/8JqPJXDeQ+mW7yV6/qej48ePU1tby2GOPoZTizjvv5LbbbuNf\n/uVfRm0fGY+tqrVuBn49zfJLwGd6zR8CVmW6HyGEEOJq4vE4VVVVo7Y9GT5OCCGy2FTsVjUMgyVL\nlvDoo4/y2GOP8eabb/LAAw9w11138eqrrw55OzK2qhBCTFLXMhzVt0dnt/qvh/+3//Dhw3z961+n\nqqqKVatWUVRUhMfj4Yc//OGQtyHhOAFUTuJn5k3muoHUL9tN9vpNxZZjOrfeeiubNm3i93//94f8\nMzLwuBBCiEnl8OHDRCIRurq6+Lu/+zvq6up4+OGHR2370nIUQogsNlVbjn/5l3/Jj370IwzDYM2a\nNfzDP/wD8+dfdaTSPqRbVQghJqmpGo6jQbpVJ4DJfK/VZK4bSP2y3WSvnxgbEo5CCCFECulWFUKI\nLCbdqpmTblUhhBBiGCQcx8lkPu8xmesGUr9sN9nrJ8aGhKMQQgiRQs45CiFEFpNzjpmTc45CCCHE\nMEg4jpPJfN5jMtcNpH7ZbrLXT4wNCUchhBBZZfv27VRUVODxeNi0aVOf915//XWWLFmC3+/nrrvu\n4vz58xntQ845CiFEFpuK5xxfeuklbDYbu3btIhwO8+yzzwLQ2NhIeXk5P/7xj3nggQf41re+xe7d\nu3nvvffSbmew351j7A5fCCGEGH0bN24EYN++fdTU1CSXv/jiiyxfvpzPf/7zAGzZsoWioiJOnjzJ\nokWLhrUP6VYdJ5P5vMdkrhtI/bLdZK/fVJbasj1y5Ag33nhjct7n81FeXk5VVdWwty3hKIQQIisp\n1bdHNBQKkZeX12dZXl4enZ2dw962dKuOk8n8JPLJXDeQ+mW7yV6/a0qN0qnODM9tprYcc3JyaG9v\n77Osra2N3NzcYW8745ajUiqolPqVUuqkUuq/lVKBAdb7U6VUlVLqsFLq/yil3JnuUwghxASi9eiU\nDKW2HJctW8ahQ4eS86FQiDNnzrBs2bJhb3sk3arfBH6ltV4EvN4934dSqhT4OvBrWuvrATvwWyPY\nZ9aazOc9JnPdQOqX7SZ7/aYiy7KIRCKYpollWUSjUSzLYuPGjVRVVfHiiy8SiUT49re/zYoVK4Z9\nMQ6MLBw/CzzfPf088BsDrOcAfEopB+ADLo5gn0IIIaa4rVu34vP52LZtGzt27MDr9fLUU09RVFTE\nf/zHf/D4448TDAbZt28f//Zv/5bRPjK+z1Ep1aK1LuieVkBzz3zKen8CPAmEgV1a64cG2N6EvadG\nCCEmqql4n+Noyfg+R6XUr4Dpad56vPeM1lorpfr9FpVSBSRamHOBNuAFpdTvaK1/OsRjF0IIIcbd\noOGotb5noPeUUnVKqela68tKqRlAfZrVfh34RGvd1P0zLwK3AmnD8eGHH2bu3LkABAIBVqxYkbzS\nrOe8QbbOP/PMM5OqPr3ne5/TmQjHI/WT+k3m+lVWVvLcc88BJP9eitE3km7VvwWatNbblFLfBAJa\n62+mrLMa+GdgFRABngP2aq3/Mc32JnUTvrKyMvk/+mQzmesGUr9sN9nrJ92qmRvsdzeScAwC/w7M\nAc4BX9RatyqlZgI/1Fp/pnu9LcBvAiawH/g9rbWRZnuT/oMQQojRJuGYuTEJx9E2FT4IIYQYbRKO\nmZOHHU8Avc97TDaTuW4g9ct2k71+YmxIOAohhBAppFtVCCGymHSrZk66VYUQQohhkHAcJ5P5vMdk\nrhtI/bLdZK/fVLR9+3YqKirweDxs2rQpudwwDB588EHmzZuHzWbjrbfeyngfEo5CCCGySmlpKZs3\nb+aRRx7p996aNWvYsWMH06dP7/fUjuGQc45CCJHFpvI5x82bN1NTU8Ozzz7b773Zs2fz05/+lDVr\n1gz483LOUQghxKQzluEt4ThOJvN5j8lcN5D6ZbvJXr+pbCTdplcz6MDjQgghxEDUKH3x0BmOfTuW\nLUcJx3EymQc+nsx1A6lftpvs9buWMg210TKWLUfpVhVCCJFVLMsiEolgmiaWZRGNRrEsC4BoNEok\nEuk3PVwSjuNkMp/3mMx1A6lftpvs9ZuKtm7dis/nY9u2bezYsQOv18tTTz0FwOLFi/H5fFy6dIn1\n69fj9/s5f/78sPch3apCCCGyypYtW9iyZUva986dOzcq+5D7HIUQIotN5fscR0rucxRCCCGGQcJx\nnEzm8x6TuW4g9ct2k71+YmxIOAohhBAp5JyjEEJkMTnnmDk55yiEEEIMQ8bhqJT6glLqiFLKUkqt\nHGS9DUqp40qpU0qpb2S6v2w3mc97TOa6gdQv2032+omxMZKW42FgI/D2QCsopezAdmADcB3wJaXU\n0hHsM2sdPHjwWh/CmJnMdQOpX7ab7PUTYyPjQQC01sfhqmPbrQZOa63Pda/7b8DngGOZ7jdbtba2\nXutDGDOTuW4g9ct2k71+YmyM9TnHUuBCr/ma7mVCCCFERrZv305FRQUej4dNmzYll7///vvcc889\nFBYWUlJSwhe/+EUuX76c0T4GDUel1K+UUofTlAeGuP3JfanTMIzWkEYT0WSuG0j9st1kr99UVFpa\nyubNm3nkkUf6LG9tbeXRRx+lurqa6upqcnNz+4TncIz4Vg6l1JvAn2ut96d57xZgi9Z6Q/f8/wfE\ntdbb0qwrQSqEEBmYqrdybN68mZqaGp599tm07+/fv59169bR3t6e9v3BbuUYrYHHB/pg9gELlVJz\ngUvAbwJfSrfiWHy4QgghJq+rhffbb7/N8uXLM9r2SG7l2KiUugDcAvyXUurV7uUzlVL/BaC1NoGv\nAbuAo8D/1VpPuYtxhBBCjL7BLgj9+OOP2bp1K9/97ncz2vZIrlZ9CXgpzfJLwGd6zb8KvJrpfoQQ\nQkxMlapyVLazTq/L6OcGajmePn2a++67j+9973vcdtttmR2U1npcC4l7Ho8Dp4BvDLDO97rfPwTc\nNN7HOFZ1A5YA7wEREudpr/kxj3L9fqf7M/sYeAe44Vof8yjX73Pd9TsAfAjcdq2PeTTr12u9VYAJ\n/D/X+phH+fNbB7R1f34HgG9d62Mezc+uu34HgCqgchT2qSe6b33rW/rhhx/us+zcuXN67ty5+gc/\n+MFVf767junrP9AbY1EAO3AamAs4gYPA0pR17gNe6Z6+GXh/PI9xjOtWDFQAT2ZbOA6xfp8C8run\nN2TLZzeM+vl7TV8PHLvWxz2a9eu13hvATuDz1/q4R/nzWwe8fK2PdYzqFgCOALO654tGYb96ojJN\nU4fDYf3Nb35TP/TQQzoSiWjTNHVNTY2eP3++/ru/+7shbWewcBzvsVWTgwJorQ2gZ1CA3j4LPE/i\nqD8AAkqpaeN7mBm5at201g1a632AcS0OcISGUr/3tNZt3bMfALPG+RhHYij1C/WazQHi43h8IzWU\nf3sAXwd+BjSM58GNgqHWLxsv/BtK3X4b+A+tdQ2A1rpxnI9xXG3duhWfz8e2bdvYsWMHXq+XJ598\nkh//+Md88sknbNmyhdzcXHJzc8nLy8toH+MdjkMZFCDdOtnwR3ayD3gw3Pr9D+CVMT2i0TWk+iml\nfkMpdYxEy+qR1PcnsKvWTylVSuKP7ve7F03s6/j7Gsrnp4FblVKHlFKvKKWuG7ejG5mh1G0hEFRK\nvamU2qeUemjcju4a2LJlC/F4vE/567/+a5544gni8TgdHR3JMtBtHFczWrdyDNV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CAAAF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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fd67110>"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let us sample from the joint posterior distribution."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# seed the RNG\n",
      "np.random.seed(1353135)\n",
      "sample_num = 5000\n",
      "# first sample tau's\n",
      "tau_probs = posterior_tau_densities / posterior_tau_densities.sum()\n",
      "samples_tau = np.random.choice(tau_knots, sample_num, p=tau_probs)\n",
      "# now sample mu conditioned on tau\n",
      "samples_df = DataFrame.from_records(sample_means_from_taus(samples_tau, blocker_data.means, \n",
      "                                                           blocker_data.serrs, include_mu=True),\n",
      "                                    columns=np.concatenate((['mu'],blocker_data.index)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_columns_df = samples_df.drop('mu', 1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Posterior quantiles in Table 5.4 can now be reproduced."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_columns_df.quantile([0.025,0.25,0.5,0.75,0.975]).transpose().apply(lambda x:np.round(x,decimals=2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>0.025</th>\n",
        "      <th>0.25</th>\n",
        "      <th>0.5</th>\n",
        "      <th>0.75</th>\n",
        "      <th>0.975</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td>-0.58</td>\n",
        "      <td>-0.32</td>\n",
        "      <td>-0.25</td>\n",
        "      <td>-0.15</td>\n",
        "      <td> 0.12</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td>-0.64</td>\n",
        "      <td>-0.37</td>\n",
        "      <td>-0.28</td>\n",
        "      <td>-0.20</td>\n",
        "      <td>-0.01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td>-0.60</td>\n",
        "      <td>-0.35</td>\n",
        "      <td>-0.27</td>\n",
        "      <td>-0.19</td>\n",
        "      <td> 0.03</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td>-0.44</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.25</td>\n",
        "      <td>-0.19</td>\n",
        "      <td>-0.06</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5</th>\n",
        "      <td>-0.43</td>\n",
        "      <td>-0.28</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.10</td>\n",
        "      <td> 0.14</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
        "      <td>-0.61</td>\n",
        "      <td>-0.34</td>\n",
        "      <td>-0.26</td>\n",
        "      <td>-0.18</td>\n",
        "      <td> 0.05</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
        "      <td>-0.61</td>\n",
        "      <td>-0.43</td>\n",
        "      <td>-0.35</td>\n",
        "      <td>-0.28</td>\n",
        "      <td>-0.17</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8</th>\n",
        "      <td>-0.41</td>\n",
        "      <td>-0.28</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.13</td>\n",
        "      <td> 0.10</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9</th>\n",
        "      <td>-0.59</td>\n",
        "      <td>-0.36</td>\n",
        "      <td>-0.28</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.03</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td>-0.48</td>\n",
        "      <td>-0.35</td>\n",
        "      <td>-0.29</td>\n",
        "      <td>-0.24</td>\n",
        "      <td>-0.13</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td>-0.47</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.25</td>\n",
        "      <td>-0.17</td>\n",
        "      <td> 0.01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12</th>\n",
        "      <td>-0.43</td>\n",
        "      <td>-0.29</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.12</td>\n",
        "      <td> 0.10</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13</th>\n",
        "      <td>-0.63</td>\n",
        "      <td>-0.36</td>\n",
        "      <td>-0.28</td>\n",
        "      <td>-0.20</td>\n",
        "      <td> 0.01</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14</th>\n",
        "      <td>-0.34</td>\n",
        "      <td>-0.22</td>\n",
        "      <td>-0.13</td>\n",
        "      <td> 0.01</td>\n",
        "      <td> 0.29</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>15</th>\n",
        "      <td>-0.55</td>\n",
        "      <td>-0.34</td>\n",
        "      <td>-0.26</td>\n",
        "      <td>-0.19</td>\n",
        "      <td> 0.03</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>16</th>\n",
        "      <td>-0.47</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.23</td>\n",
        "      <td>-0.15</td>\n",
        "      <td> 0.07</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>17</th>\n",
        "      <td>-0.47</td>\n",
        "      <td>-0.29</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.11</td>\n",
        "      <td> 0.16</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>18</th>\n",
        "      <td>-0.49</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.23</td>\n",
        "      <td>-0.13</td>\n",
        "      <td> 0.17</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>19</th>\n",
        "      <td>-0.52</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.23</td>\n",
        "      <td>-0.14</td>\n",
        "      <td> 0.17</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>20</th>\n",
        "      <td>-0.50</td>\n",
        "      <td>-0.32</td>\n",
        "      <td>-0.25</td>\n",
        "      <td>-0.17</td>\n",
        "      <td> 0.04</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>21</th>\n",
        "      <td>-0.65</td>\n",
        "      <td>-0.40</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.24</td>\n",
        "      <td>-0.09</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>22</th>\n",
        "      <td>-0.65</td>\n",
        "      <td>-0.40</td>\n",
        "      <td>-0.30</td>\n",
        "      <td>-0.23</td>\n",
        "      <td>-0.07</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "    0.025  0.250  0.500  0.750  0.975\n",
        "1   -0.58  -0.32  -0.25  -0.15   0.12\n",
        "2   -0.64  -0.37  -0.28  -0.20  -0.01\n",
        "3   -0.60  -0.35  -0.27  -0.19   0.03\n",
        "4   -0.44  -0.31  -0.25  -0.19  -0.06\n",
        "5   -0.43  -0.28  -0.21  -0.10   0.14\n",
        "6   -0.61  -0.34  -0.26  -0.18   0.05\n",
        "7   -0.61  -0.43  -0.35  -0.28  -0.17\n",
        "8   -0.41  -0.28  -0.21  -0.13   0.10\n",
        "9   -0.59  -0.36  -0.28  -0.21  -0.03\n",
        "10  -0.48  -0.35  -0.29  -0.24  -0.13\n",
        "11  -0.47  -0.31  -0.25  -0.17   0.01\n",
        "12  -0.43  -0.29  -0.21  -0.12   0.10\n",
        "13  -0.63  -0.36  -0.28  -0.20   0.01\n",
        "14  -0.34  -0.22  -0.13   0.01   0.29\n",
        "15  -0.55  -0.34  -0.26  -0.19   0.03\n",
        "16  -0.47  -0.31  -0.23  -0.15   0.07\n",
        "17  -0.47  -0.29  -0.21  -0.11   0.16\n",
        "18  -0.49  -0.31  -0.23  -0.13   0.17\n",
        "19  -0.52  -0.31  -0.23  -0.14   0.17\n",
        "20  -0.50  -0.32  -0.25  -0.17   0.04\n",
        "21  -0.65  -0.40  -0.31  -0.24  -0.09\n",
        "22  -0.65  -0.40  -0.30  -0.23  -0.07"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let us sample predicted effects."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_predicted_effect = np.zeros(len(samples_tau))\n",
      "samples_predicted_effect[samples_tau > 0] = np.random.normal(loc=samples_df['mu'][samples_tau > 0],scale=samples_tau[samples_tau > 0])\n",
      "samples_predicted_effect[samples_tau == 0] = samples_df['mu'][samples_tau == 0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now Table 5.5 can be reproduced."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "DataFrame({'mean':samples_df['mu'], \n",
      "           'standard deviation':samples_tau, \n",
      "           'predicted_effect':samples_predicted_effect}).quantile([0.025,0.25,0.5,0.75,0.975]).transpose().apply(lambda x:np.round(x,decimals=2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>0.025</th>\n",
        "      <th>0.25</th>\n",
        "      <th>0.5</th>\n",
        "      <th>0.75</th>\n",
        "      <th>0.975</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>mean</th>\n",
        "      <td>-0.37</td>\n",
        "      <td>-0.29</td>\n",
        "      <td>-0.25</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.11</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>predicted_effect</th>\n",
        "      <td>-0.60</td>\n",
        "      <td>-0.33</td>\n",
        "      <td>-0.25</td>\n",
        "      <td>-0.16</td>\n",
        "      <td> 0.14</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>standard deviation</th>\n",
        "      <td> 0.01</td>\n",
        "      <td> 0.07</td>\n",
        "      <td> 0.13</td>\n",
        "      <td> 0.18</td>\n",
        "      <td> 0.31</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "                    0.025  0.250  0.500  0.750  0.975\n",
        "mean                -0.37  -0.29  -0.25  -0.21  -0.11\n",
        "predicted_effect    -0.60  -0.33  -0.25  -0.16   0.14\n",
        "standard deviation   0.01   0.07   0.13   0.18   0.31"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Histograms of estimates, not shown in the book, are presented below."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_columns_df.hist(figsize=(12,12),sharex=True, bins=20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x10faf2bd0>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x10ffec850>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x110f20390>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x110042d50>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x10ff78710>],\n",
        "       [<matplotlib.axes._subplots.AxesSubplot object at 0x10fed8c90>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x110064bd0>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x10ffc5950>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x110f84e50>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x110fc1fd0>],\n",
        "       [<matplotlib.axes._subplots.AxesSubplot object at 0x111a5e390>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x1118e3690>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111966810>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111add710>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111b5e890>],\n",
        "       [<matplotlib.axes._subplots.AxesSubplot object at 0x111bade10>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x10b740f90>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x10b7c3c10>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111e26750>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111eab7d0>],\n",
        "       [<matplotlib.axes._subplots.AxesSubplot object at 0x111f10050>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111f931d0>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x111f4a4d0>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x11207b910>,\n",
        "        <matplotlib.axes._subplots.AxesSubplot object at 0x1120fea50>]], dtype=object)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aFXiGZMX7PcBPSVa6X8T8Fe/XSvoEiUXDV7xPJmeTdFJ7hOPOlFhnMekU0FlM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\ny9zICv0dIuklH6Pu1znnfIhrrvmHjD1NtEsLyXN4vZPux4z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ew9a6AcgxlUFM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\nSiPYAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fc38390>"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def mean_posterior_of_mean_given_tau(tau, means, serrs):\n",
      "    assert(len(means) == len(serrs))\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    # precision weighted average\n",
      "    mu_hat = np.sum((1.0/marginal_variances) * means) / \\\n",
      "            np.sum(1.0/marginal_variances)\n",
      "    return mu_hat\n",
      "\n",
      "def sd_posterior_of_mean_given_tau(tau, means, serrs):\n",
      "    assert(len(means) == len(serrs))\n",
      "    marginal_variances = serrs ** 2 + tau ** 2\n",
      "    total_variance = 1.0/np.sum(1.0/marginal_variances)\n",
      "    return np.sqrt(total_variance)\n",
      "\n",
      "mean_posterior_of_mean_given_taus = \\\n",
      "    np.vectorize(mean_posterior_of_mean_given_tau, otypes=[np.ndarray], excluded=[1,2])\n",
      "sd_posterior_of_mean_given_taus = \\\n",
      "    np.vectorize(sd_posterior_of_mean_given_tau, otypes=[np.ndarray], excluded=[1,2])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Recall this was the posterior density of $\\tau$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(tau_knots, posterior_tau_densities, color='k', linestyle='-', linewidth=1)\n",
      "pl.axes().set_xlabel(r'$\\tau$')\n",
      "# the y-axis of unnormalized posterior means nothing, so rather hide the scale\n",
      "pl.axes().get_yaxis().set_visible(False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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UVCHEpMo/36AoyndCiEFCiAwAhQDGVnWfxkST9QkhXAAkAHAAUCGEmI7Hf6EP\npAXXkCbrA/AXAK8AWFfZoZUpitJdVuaa0HB9IwBECCHKABQDGCktcA1ouDbV0nB9vwEwRQhRDqAI\nwChpgWtIw9p5RQjxPYAkPN74/lJRlJSX3Sdfbk5EpAJ8BSMRkQqwWBMRqQCLNRGRCrBYExGpAIs1\nEZEKsFgTEakAizURkQqwWBMRqQCLNRGRClT3Rk5EqiGEeBXA/+Dx+4H8hMfvQf6OoigPpQYj0gEW\nazIlroqijBRCTFL7e2cQPYtjEDIZiqKcqrzaVGoQIj1gsSaTIoRwx+N3aCMyKSzWZGr8APxbdggi\nXeNbpBIRqQA7ayIiFWCxJiJSARZrIiIVYLEmIlIBFmsiIhVgsSYiUgEWayIiFWCxJiJSgf8DzcTI\nE2mvRQUAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fd95a90>"
       ]
      }
     ],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compared to the posterior quantile values of data, the conditional $\\mu \\mid \\tau$ changes very little within most plausible region of $\\tau$."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(tau_knots, mean_posterior_of_mean_given_taus(tau_knots, blocker_data.means, blocker_data.serrs))\n",
      "#pl.ylim((-0.6,0.1))\n",
      "pl.axes().set_xlabel(r'$E[\\mu \\mid \\tau,y]$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 37,
       "text": [
        "<matplotlib.text.Text at 0x112456dd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ZWU4WZmZWlpOFmZmV1epkIamPpCmS5kuaLKlXiTIDJT0kabakWZLOKbp+tqS5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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11247fc90>"
       ]
      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "However, the standard deviation changes greatly."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pl.plot(tau_knots, sd_posterior_of_mean_given_taus(tau_knots, blocker_data.means, blocker_data.serrs))\n",
      "pl.axes().set_xlabel(r'sd$[\\mu \\mid \\tau,y]$')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 38,
       "text": [
        "<matplotlib.text.Text at 0x112512f50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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8hpUz6bRvT6A3YWj93sAsM3vN3Vc0dnJrJf0aoEvSdhfCb6zmzumc2FcI0mlf\nIUurfYmbt/cDZe7+fivFlq0WfXfu/jczO9TM/sndN+U9uuyl077jgEkh37M/MMjMat19auuEmJWU\n7XP3j5JeP2Nm9xTZ97cWeM/dtwHbzOxloBfQaNJvrZsR7YBVhJsRXyD1jdx+FMiNwHTbl3RuOYV3\nIzed7+9gwg2nflHHm4e2Hcanw5t7A2ujjjuX7Wtw/kPAd6KOO8ff3wFJ318fYHXUcee4fUcAzxNu\n+u4NLAR6NHXNVqn0PbcPebU56bTPzA4EKgnTUdSb2VjCF7MlssDTlE77gPHAl4F7ExVjrbv3iSrm\ndKXZtnOA75lZLbANODeygFsozfYVrDTbNwy4zMzqgI+B8yILuIXSzJ1LzexZYAFhkMH97r6kqWvq\n4SwRkRjRcokiIjGipC8iEiNK+iIiMaKkLyISI0r6IiIxoqQvIhIjSvoiIjGipC8iEiNK+hJ7ZnaD\nmR2Xx+sPNbPv5+v6Ii2hpC+xZGblSSuYrXX3N/L1We7+F4p/JlYpEEr6EldOBonYzM7PQywirUZJ\nX4qOme1jZk+bWZWZLTSz4Yn9/2Fmy8zsb8D/I7N54/fMabAirUxJX4pRGVDj7se4+9HAjESf/bmE\necYHA8fTSKWfmOn1gsTrnydWlWp4ziFm9lhilaKnzOwJM2ufOHZU4h5Bv8T2pLy1UiQDSvpSjBYA\n3zKzX5rZN9x9M9AfeMLdt3tYVGMqjVf63wReT7zu5e6NLeTT2d3PJUxhO8Tdv+Pu2xPH9iWsg2xm\n1o0wTbhIm6GkL0XHwzJxxxIWk/hPM7uRUNUnJ3mj8T79I919mZntBexo4vqvJF7+SyPHXgN6u/ss\nwmJAr2bcEJE8UNKXomNm/wJsd/dHgFsJq129DJxlZu3N7EvAGY28b2/gS4nNvkCVmZ3SxGccSliQ\nY/f2IUmHd+8/ASV9aWNaa41ckdZ0NPBrM6sndLX8wN3nmdljwHzgXWBOI+/rC+xnZqcDHYF9gO2N\nnAehip8DkOj3nwl0Sxxbk7h5PMDdL89Rm0RyQklfio67Pwc818j+XwC/aOatJwGj3f2lND7j0aTX\nNWZ2KYCZXQJUEBa0ntKyyEXyT907Ip86DJiV4pzaJvbvk/jzTcLN3CHAjTmKSyRntEauxJ6Z3QA8\nk81TuWbWPmkET8NjQ4Evu/vvM72+SK4o6YuIxIi6d0REYkRJX0QkRpT0RURiRElfRCRGlPRFRGJE\nSV9EJEagGuBtAAAAEUlEQVSU9EVEYkRJX0QkRv4PZxQjtrRWKVgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11331e6d0>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The book comments the value of $\\text{sd}(\\mu \\mid \\tau,y)$ at $\\tau=0.13$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sd_posterior_of_mean_given_tau(0.13, blocker_data.means, blocker_data.serrs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "0.061826519379229505"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On the other hand, $\\text{sd}(\\mu \\mid y)$, marginalized over $\\tau$, can be computed from posterior samples as follows:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "samples_df['mu'].std()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 40,
       "text": [
        "0.064647961365995488"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Well this is a bit different from the value in the book, 0.071.  I wonder why...?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 40
    }
   ],
   "metadata": {}
  }
 ]
}