SimpleLinearRegression.ipynb

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  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Simple Linear Regression"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This notebook presents PyMC implementations of the Bayesian simple linear regression models described in [Kruschke](http://amzn.com/0123814855), Ch. 16. We'll start with a no-frills linear regression of a single metric response on a single metric predictor, then modify that for robustness, and finally add hierarchy to deal with repeated measures among multiple subjects. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Set up the environment for successive computational cells. \n",
      "# This stuff will not be repeated below, be sure to run this cell first.\n",
      "\n",
      "import pymc as mc\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "from IPython.display import Image\n",
      "\n",
      "class Struct:\n",
      "    # convenience 'bag of attributes' class\n",
      "    def __init__(self, **entries): self.__dict__.update(entries)\n",
      "\n",
      "def show_graph(model):\n",
      "    \"\"\"display a graphical representation of the model\"\"\"\n",
      "    graph = mc.graph.graph(model)\n",
      "    Image(graph.create_png())\n",
      "\n",
      "def posterior_hist(trace, label=\"\", HDI=.95, alpha=1.0):   \n",
      "    \"\"\"Render a histogram of the posterior sampling distribution of a model variable.\"\"\"\n",
      "    t = sorted(trace)\n",
      "    h = hist(t, normed=True, alpha=alpha, label=\"%s:%.2f\" % (label, mean(t)))\n",
      "    ymax = max(h[0])\n",
      "    axvline(mean(t), c='red', linestyle='-.')\n",
      "    hdidx = int(len(t)*(1 - HDI)/2.) \n",
      "    annotate(\"\", xy=(t[hdidx],0), xytext=(t[-hdidx],0),\n",
      "             arrowprops=dict(arrowstyle=\"|-|\", connectionstyle=\"arc3\", color='k',lw=2))\n",
      "    \n",
      "def ci_patch(x, ci, **kwds):\n",
      "    \"\"\"create a bounding polygon for the confidence intervals vs x\"\"\"\n",
      "    x, ci = zip(*sorted(zip(x,ci))) # sort x and ci by x\n",
      "    cit = zip(*ci) \n",
      "    diff = np.array(cit[1]) - np.array(cit[0])\n",
      "    print \"CI: min=%f, max=%f\" % (min(diff), max(diff))\n",
      "    return Polygon(zip(x,cit[0]) + zip(x, cit[1])[::-1], **kwds)\n",
      "\n",
      "def plot_regression(x, y, mu, tau,  y_sim=None, titlestr=\"\", HDI=.95, color='b'):\n",
      "    \"\"\"plot the regression results. X and Y are vectors of floats, \n",
      "       mu is a list of regression mean stochastics for y[i] on x[i],\n",
      "       tau is the precision stochastic\n",
      "       y_sim is a list of unobserved posterior Y stochastics, used for confidence intervals\"\"\"\n",
      "    ax = gca()\n",
      "    ax.scatter(x,y,color=color)\n",
      "    if hasattr(x,'name'):\n",
      "        xlabel(x.name)\n",
      "    if hasattr(y,'name'):\n",
      "        ylabel(y.name)\n",
      "    if titlestr:\n",
      "        title(titlestr)\n",
      "    if hasattr(mu[0], 'trace'):\n",
      "        # use the trace summary statistics for mean and slope\n",
      "        means = [mui.stats()['mean'] for mui in mu]\n",
      "        #slope = mu[0].parents['y'][1].stats()['mean']\n",
      "    else:\n",
      "        # use the current values for mean and slope\n",
      "        means = [mui.value for mui in mu]\n",
      "        #slope = mu[0].parents['y'][1].value\n",
      "    sx, smeans = zip(*sorted(zip(x, means))) # sort x,mean pairs by x and return as lists\n",
      "    ax.plot(sx, smeans, color=color)\n",
      "    legend()\n",
      "    # 95% HDI ci for the mean\n",
      "    if hasattr(mu[0], 'trace'):\n",
      "        ci_mu = [tuple(mui.stats()['95% HPD interval']) for mui in mu]\n",
      "        ax.add_patch(ci_patch(x, ci_mu, color=color, alpha=.2))\n",
      "        draw_if_interactive()\n",
      "    if y_sim is not None and hasattr(y_sim[0], 'trace'):\n",
      "        # 95% HDI for the predicted y's\n",
      "        ci_y = [tuple(y_i.stats()['95% HPD interval']) for y_i in y_sim]\n",
      "        ax.add_patch(ci_patch(x, ci_y, color='k', alpha=.2))\n",
      "        draw_if_interactive()\n",
      "    elif tau is not None:\n",
      "        # 95% ci for predicted y's assuming normal centered at current mu\n",
      "        ci_y = [(mui.value - 1.96/sqrt(tau.value), mui.value + 1.96/sqrt(tau.value)) for mui in mu] \n",
      "        ax.add_patch(ci_patch(x, ci_y, color='r', alpha=.2))\n",
      "        draw_if_interactive()    \n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 225
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The first data set is height and weight pairs randomly generated using Kruschke's HtWtDataGenerator.R and saved as htwt.csv for loading here:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Note: when reading, do not let column 0 be used as the index. \n",
      "# It starts at 1, and you will later be in a world of pain\n",
      "# wondering whether you are referring to the item at position\n",
      "# 1 or the item named 1 (which is in position 0). \n",
      "htwt = pd.read_csv(\"data/htwt.csv\", index_col=None)\n",
      "htwt.describe()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "scatter(htwt.height, htwt.weight);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We will fit a simple generalized linear model for weight (y) predicted by height (x):\n",
      "\n",
      "$y_i \\sim N(\\mu_i, \\tau)$\n",
      "\n",
      "$\\mu_i = \\beta_0 + \\beta_1x_i$\n",
      "\n",
      "$\\tau = 1/\\sigma^2$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "\n",
      "def make_normal_model(x, y):\n",
      "    \"\"\"\n",
      "    return a dict of model variables for the model constructor\n",
      "    \"\"\"\n",
      "    # priors for the regression coefficients and variance/precision.\n",
      "    # initialize beta to suit the data, or the MAP initializer may not converge.\n",
      "    beta = mc.Container((mc.Normal(\"beta_0\", mu=mean(y), tau=1e-12, value=mean(y)), # population intercept\n",
      "                         mc.Normal(\"beta_1\", mu=0, tau=1e-12, value=0))) # population slope\n",
      "    tau = mc.Gamma(\"tau\", alpha=.001, beta=.001, value=.001)   # population precision\n",
      "\n",
      "    # The distribution of each y_i has mean that is a deterministic function of the x_i\n",
      "    mu = mc.Container([mc.LinearCombination(\"mu_%d\" % i, (1, x[i]), beta)\n",
      "                       for i in x.index])\n",
      "\n",
      "    # likelihood for the data\n",
      "    y_obs = mc.Container([mc.Normal(\"y_%d\" % i, mu=mu[i], tau=tau, value=y[i], observed=True) \n",
      "                          for i in y.index])\n",
      "    \n",
      "    # posterior predictions, for generating confidence intervals\n",
      "    y_sim = mc.Container([mc.Normal(\"y_%d\" % i, mu=mu[i], tau=tau) for i in y.index])\n",
      "    \n",
      "    return mc.Model(input=locals())\n",
      "\n",
      "M = make_normal_model(htwt.height, htwt.weight)\n",
      "print M.beta[0].value, M.beta[1].value\n",
      "figure()\n",
      "plot_regression(htwt.height, htwt.weight, M.mu, M.tau, titlestr=\"pre MAP estimate\")\n",
      "show()\n",
      "mc.MAP(M).fit()\n",
      "plot_regression(htwt.height, htwt.weight, M.mu, M.tau, titlestr=\"initial MAP estimate\")\n",
      "show()\n",
      "S = mc.MCMC(input=M, db='ram')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "164.996666667 0.0\n",
        "CI: min=123.961284, max=123.961284"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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LIosCkbG0esUwevRoAECPHj3g6+srtnM2krxmzZqFp556CiqVCl26dGl1OqQ5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\nIiItLAxERKSFhYGIiLT8f4sIVmaLuwLhAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1117d3c10>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=110.890607, max=110.890607\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iJ5/8/HwsXrwYCadP49y5c9i8eTOioqLq3ZZjtCXGyIWHh8cdAy6cnZ1lP66u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\nRKTl/wMzwKHtpoL/zAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1158bb650>"
       ]
      }
     ],
     "prompt_number": 87
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S.sample(10000, burn=1000, thin=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 165 of 10000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 339 of 10000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 5%                  ] 525 of 10000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 705 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 880 of 10000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 1061 of 10000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 1240 of 10000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            14%                  ] 1410 of 10000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 1574 of 10000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           17%                  ] 1746 of 10000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          19%                  ] 1915 of 10000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 2098 of 10000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         22%                  ] 2261 of 10000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        24%                  ] 2435 of 10000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        26%                  ] 2610 of 10000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       27%                  ] 2792 of 10000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      29%                  ] 2973 of 10000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      31%                  ] 3152 of 10000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     33%                  ] 3319 of 10000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    34%                  ] 3489 of 10000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    36%                  ] 3653 of 10000 complete in 10.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   38%                  ] 3831 of 10000 complete in 11.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  39%                  ] 3998 of 10000 complete in 11.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  41%                  ] 4163 of 10000 complete in 12.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 43%                  ] 4332 of 10000 complete in 12.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------45%                  ] 4505 of 10000 complete in 13.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------46%                  ] 4689 of 10000 complete in 13.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 4861 of 10000 complete in 14.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------50%                  ] 5026 of 10000 complete in 14.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 5196 of 10000 complete in 15.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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      },
      {
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       "text": [
        "\r",
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      }
     ],
     "prompt_number": 88
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "On to the results:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_regression(htwt.height, htwt.weight, M.mu, M.tau, M.y_sim, titlestr=\"MC posterior estimate\")\n",
      "figure()\n",
      "posterior_hist(M.beta[0].trace(), \"beta0\")\n",
      "legend()\n",
      "show()\n",
      "posterior_hist(M.beta[1].trace(), \"beta1\")\n",
      "legend()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=27.815104, max=46.740338\n",
        "CI: min=145.090182, max=157.002683\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ioiIYDAbU1tbSVXiYe/fdd1FcXIza2lqUlZVh1apV3drejh07uAcE6fV6HD16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\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d077150>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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smLJ+Ji/DEU2sEw/UI488grlz52LNmjX4+OOP09bPZMuEY5OIicfMarFm8u9b\nLGQdw+3btyMnJwerV69OSnttbW1YvHgxZs8eW4stGcdPWnKYPXs2fvGLX0RdPxnLcMgiivX8+fO4\n4447AAA3b96MlP/whz/Eiy++qHRM0ciEYxMr0TGzWqyZ/PtmRoVjuGnTJmzatCkpbX3wwQeYM2cO\niouLI2XJOH6Gy2fIcPToUfT09CA3NxfFxcWR8TQrLsPx/vvv4/LlywCAZcuWRdZRyuSYJrJKHBNZ\n8ZhN9Ttnld+3qWKz0jEMBAJ44403cPfddwMABgcHsW3btqQcP+WSAxERyafkJDgiIpKLyYGIiHSY\nHIiISIfJgYiIdJgciIhIh8mBiIh0mByIiEiHyYGIiHT+DxBW57TqbNOCAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d077350>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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VNWrcXnWmcCRlcqfceDJbIBBAVlaWpeceWks/Gkl9NURiJjNY7MlRrHyAyOCtefiovTv0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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c2f46d0>"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The blue area is the 95% confidence interval around the estimated mean for each y. The gray area is the 95% HDI of predicted y's drawn as samples from distributions of $\\mu$ and $\\tau$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Centered Data"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Although the point results above look reasonable, there is a lot of variation in the shapes of the posteriors over repreated runs. And occasionally the MAP estimate blows up and the sampling run never recovers. This is because credible values of $\\beta_0$ and $\\beta_1$ are highly negatively correlated (a higher y-intercept implies a lower slope so the line will go through the center of the data mass). The MCMC can have trouble traversing the sample space because it cannot change $\\beta_0$ and $\\beta_1$ independently without falling out of the credible region.\n",
      "\n",
      "The standard cure for this is to first center the data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "h = pd.Series(htwt.height - htwt.height.mean(), name=\"height - %d\" % int(htwt.height.mean()))\n",
      "w = pd.Series(htwt.weight - htwt.weight.mean(), name=\"weight - %d\" % int(htwt.weight.mean()))\n",
      "M = make_normal_model(h,w)\n",
      "mc.MAP(M).fit()\n",
      "plot_regression(h, w, M.mu, M.tau, titlestr=\"initial MAP estimate\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=116.726690, max=116.726690\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nGenp6QgJCQHHcVi6bBkyMjIAAJcuXoRMJsNbb71l4gjbpzG/RmXl5djw5ZeQ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\nCEIFgxBCiCD/Dz/aYvxF8sPHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fbb36d0>"
       ]
      }
     ],
     "prompt_number": 96
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S_c = mc.MCMC(input=M, db='ram')\n",
      "S_c.sample(10000, burn=1000, thin=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 180 of 10000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 354 of 10000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 5%                  ] 525 of 10000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 688 of 10000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 838 of 10000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---              10%                  ] 1013 of 10000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 1184 of 10000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            13%                  ] 1372 of 10000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 1563 of 10000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           17%                  ] 1739 of 10000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          19%                  ] 1919 of 10000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         21%                  ] 2113 of 10000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         22%                  ] 2294 of 10000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
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        "\r",
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        "\r",
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      },
      {
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       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 10000 of 10000 complete in 28.3 sec"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_regression(h, w, M.mu, M.tau, M.y_sim, titlestr=\"MC posterior estimate\")\n",
      "show()\n",
      "posterior_hist(M.beta[0].trace(), \"beta0\")\n",
      "legend()\n",
      "show()\n",
      "posterior_hist(M.beta[1].trace(), \"beta1\")\n",
      "legend()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=0.432128, max=59.366041\n",
        "CI: min=140.785092, max=158.883314\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Pf/5zt8ffsGEDbrzxRrt9cAYSDBEg9adT8s+1OHOzdwX33HMP9uzZg8OHD8NgMCA2Nhbj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\nkSwMDCIikoWBQUREsjAwiIhIlv8ARZFN+OgtW3UAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10dd8c250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c385550>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c389410>"
       ]
      }
     ],
     "prompt_number": 98
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The $\\beta_1$ estimate is nearly the same as before. But this yields much tidier-looking $\\beta$ posteriors, with a much tighter interval for $\\beta_0$ around 0."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Robust Regression"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The normal likelihood used for $\\mu_i$ is sensitive to outliers. The example in section 16.2 demonstrates this with data for 25 brands of cigarettes ([McIntyre1994](data/McIntyre1994data.csv)), attempting to predict tar content from weight:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cig = pd.read_csv(\"data/McIntyre1994data.csv\")\n",
      "print cig\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "               Brand   Tar   Nic      Wt    CO\n",
        "0             Alpine  14.1  0.86  0.9853  13.6\n",
        "1    BensonAndHedges  16.0  1.06  1.0938  16.6\n",
        "2         BullDurham  29.8  2.03  1.1650  23.5\n",
        "3        CamelLights   8.0  0.67  0.9280  10.2\n",
        "4            Carlton   4.1  0.40  0.9462   5.4\n",
        "5       Chesterfield  15.0  1.04  0.8885  15.0\n",
        "6       GoldenLights   8.8  0.76  1.0267   9.0\n",
        "7               Kent  12.4  0.95  0.9225  12.3\n",
        "8               Kool  16.6  1.12  0.9372  16.3\n",
        "9              LandM  14.9  1.02  0.8858  15.4\n",
        "10        LarkLights  13.7  1.01  0.9643  13.0\n",
        "11          Marlboro  15.1  0.90  0.9316  14.4\n",
        "12             Merit   7.8  0.57  0.9705  10.0\n",
        "13       MultiFilter  11.4  0.78  1.1240  10.2\n",
        "14     NewportLights   9.0  0.74  0.8517   9.5\n",
        "15               Now   1.0  0.13  0.7851   1.5\n",
        "16           OldGold  17.0  1.26  0.9186  18.5\n",
        "17     PallMallLight  12.8  1.08  1.0395  12.6\n",
        "18           Raleigh  15.8  0.96  0.9573  17.5\n",
        "19        SalemUltra   4.5  0.42  0.9106   4.9\n",
        "20          Tareyton  14.5  1.01  1.0070  15.9\n",
        "21              True   7.3  0.61  0.9806   8.5\n",
        "22  ViceroyRichLight   8.6  0.69  0.9693  10.6\n",
        "23     VirginiaSlims  15.2  1.02  0.9496  13.9\n",
        "24     WinstonLights  12.0  0.82  1.1184  14.9\n"
       ]
      }
     ],
     "prompt_number": 55
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#w = pd.Series(cig.Wt - cig.Wt.mean(), name=\"Weight - %d\" % cig.Wt.mean())\n",
      "#t = pd.Series(cig.Tar - cig.Tar.mean(), name=\"Tar - %d\" % cig.Tar.mean())\n",
      "w = cig.Wt\n",
      "t = cig.Tar\n",
      "figure()\n",
      "M = make_normal_model(w, t)\n",
      "mc.MAP(M).fit()\n",
      "plot_regression(w, t, M.mu, M.tau, titlestr=\"initial MAP estimate\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=54.381268, max=54.381268\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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nFR8bkernn3/GqlWrcD03F85aLfo+8ADefuutetXP3pDVuzEGV1dXABDPJpJ6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\newAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ba43710>"
       ]
      }
     ],
     "prompt_number": 102
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = mc.MCMC(input=M, db='ram')\n",
      "S.sample(50000, burn=1000, thin=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 205 of 50000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 389 of 50000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 566 of 50000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 759 of 50000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 948 of 50000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  2%                  ] 1151 of 50000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 2%                  ] 1333 of 50000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1518 of 50000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1696 of 50000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1882 of 50000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2065 of 50000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2255 of 50000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2445 of 50000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 2640 of 50000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 2833 of 50000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3023 of 50000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3218 of 50000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3412 of 50000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 3600 of 50000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 3786 of 50000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               7%                  ] 3969 of 50000 complete in 10.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 4148 of 50000 complete in 11.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 4347 of 50000 complete in 11.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4553 of 50000 complete in 12.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4750 of 50000 complete in 12.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4953 of 50000 complete in 13.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---              10%                  ] 5146 of 50000 complete in 13.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 5348 of 50000 complete in 14.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5535 of 50000 complete in 14.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5732 of 50000 complete in 15.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5925 of 50000 complete in 15.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 6108 of 50000 complete in 16.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 6294 of 50000 complete in 16.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 6487 of 50000 complete in 17.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            13%                  ] 6685 of 50000 complete in 17.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
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     ],
     "prompt_number": 105
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_regression(w, t, M.mu, M.tau, M.y_sim, titlestr=\"Normal regression with outlier\")\n",
      "show()\n",
      "posterior_hist(M.beta[0].trace(), \"beta0\")\n",
      "legend()\n",
      "show()\n",
      "posterior_hist(M.beta[1].trace(), \"beta1\")\n",
      "legend()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=4.116669, max=9.185046\n",
        "CI: min=20.270202, max=22.487224\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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oaWF8XEWDgcYYKJRe8Hg8qKiogFKpRFZWVp8zffyho6MDNTU10Gq1YBhGrEPk\njdVqxaFDh6BSqaDX65GcnIzY2FjREJSVlfWrgxqE4YHNBjQ3y9DRwRsHlWpoxQ0CgcYYAiAafeeR\noKsmQghqa2tx4MABdHR0oLm5GUVFRXA6nX5dz2w2dzuW4ziUlZX1OhIQYBgGGo0Ghw8fhs1mQ3l5\nOX799VccPHgQJSUl6OjoiFjgWAp+856Qoq5QaXK7gbo6Pm5gNMpgtwNKJW8U+qOs7HhINEkBOmKg\nhBSTyQSj0QhCiJgAJpfLQQjBwYMHkZWVhbS0tF7PdzqdOHr0KHQ6HaZOnSrur6ioGNCIwzsJze12\n09HAMITjAJOJdxUJhkAu5/9ReGiMgRISnE4nysvL+53q6XQ6odfrkZub283Pz7IsDh48CIVCAZfL\nhczMTGRkZKC9vR0lJSX9jhYoFG/sdqChgZ9iKpOFN4gcbTEG6kqiBBWO41BRUYHCwkK43e4+jQLA\n9+AdDgcOHjzYrfzEsWPHxFGBSqXCqVOn4HA4cPz4cWoUKH7Dcfw00/Jy2bCaWTQYqGEIgGjw50eS\n06dP48CBA/jvf/8rBoT9QS6XQ6lU4tixYzhx4gQIITh58iTsdruP/1+tVmP//v0D0jac/OaDRYq6\nBqrJYgFKS2Xo6GCCHkimMYYBUFJSgrKyMnAch7PPPhuZmZloaGjAzp07IZfLMW/ePKSnp4fq9pQw\nYrVaUV5eDpfLJc7tHwgajQZtbW04cOAAWJbtVpSOYRjo9fpgSKYMYQgBrFbg9GnebRSt9YoiSchi\nDD/++CPmzp0LAPjmm2+waNEifPXVV1i6dCkAYNOmTVi2bFmP59IYQ3QgTD9taWmhrh1KRCGEHx20\ntPDGgOOkZRCiLcYQshGDYBS88a4+SWeDSB+Hw4HW1laYzWY4HA7k5uZCp9OBEIK6ujrU1NRAoVBQ\no0CJCELNopYWGWy2TmOgVEZaWfQT8hjD9u3bMXPmTADwWchEGYWfnpT8+QLB1GSz2cT6P8Jc/9ra\nWjidTjAMg0OHDuHUqVMoLCxEXV0d1Gp1j26joeSjDiVS1ARIU5egieOA9nYGFRUyHD0qQ1UVH1BW\nKsM/QqAxhgGya9cu5OTkIDk5GQB8io31F5jcvXs3zj33XPFvABHf9tYmBT2D2SaEoKCgAC0tLfjx\nxx/hcrkwadIkqFQqFBcXAwAKCgoAdP4oCwoK0NjYiJKSkl5fBwCj0djn65HYNhqNktLjjVT0SPXz\nKywswpGvDgx5AAAgAElEQVQj1YiNPQs2G1BeboRCwSE3dwKAzgY63NsC/hzf2KgWXUmh/n0Hg5DF\nGH766SeMGDECeXl54r4vv/wSy5cvByEEW7duxZIlS3o8l8YYgg/Hcejo6EBTUxNsNhvsdjs4joNa\nre5WRoJCiTRCElpbGwObjc87iEIngwiNMYCftrhnzx7k5eWhtLQUHR0duO666zBr1ixs3LgRhBDM\nnz8/FLem/IbH40F7eztaW1thsVjgcDgA8FM+GYYJeBlKCiXUeBevs9n4TGSFQlpB5OFCSAxDSkoK\nHnjggW77MzIysHLlylDcMix4u7ekgqDJ5XLBZDKhra0NVqsVTqcTMplMNAD9JZoFk6KiItENIBWo\nJv8Jty7v4nVAz/GCsrLjomtGKkhRU7Cg+X9Rit1uR2trK6qqqqDVauF0OqFQKKBSqSCTyehMIYqk\n8XiApiZ+SUy3m84mkhq0VlIUwHEcLBYLmpubYbVaYbfbwbIslEpln+sIUChSQnAVNTfzriKheN1w\ngMYYKINGcAuZTCZYrVY4HA4wDCOOBmgOCCWa6MlVNFzXOYgW6HSUAAhFHkPX9YN//fVXHDhwAJWV\nlbDZbGAYBlqtFhqNpsfZQ1Kecy4lqCb/CYYujweor+++zsFA3UVSzBnwV5PNJkd1dXRZQjpiCDMe\nj0d0C3lPGxVqDCmVyqhM/qNQenMVDRd3kYDFokB5eTzKy+NQXh6H06e1OO+8Vlx3XaSV+Q+NMYQY\nh8MhuoVsNpuYRSxMG6VQop2eXEXDCbNZhePH434zBPFoa1Nj/HgzcnLMmDDBjNGjO5CREUNjDMMV\njuNgtVrR0tICi8UCu90Oj8cDhUIBpVJJZwtRhgzDeVZRS4taNALl5XGwWJTIzuaNwJw5pcjMtET9\nKIkahgDomsfgdrvFJDIhSAxADBKHwy0kxbnwVJN/SFET0LuuSLqKIpUzQAjQ1KRBeXn8b6OCeLjd\nMuTkmBEXdxw336xGRoYVQ614ADUMAeB0OlFbW4v29nbRLSSXyyOSREahhIvhNKuIEKC+XuczImAY\nICfHhJwcMy655BRSU+1gGN5YZWYOzQQ3GmPoBZZlYbFY0NLSQnMHKMOOnlxFQzEkxnFAbW0Mjh+P\nh9HIxwk0GvY31xBvDJKTHYN+7zSPIUrpLXdACBLT3IHQ0dbWhq+//hoajQaXXnopHXlFiOEwq4hl\ngVOnDOKI4MSJWBgMbuTkmFBQ0IwrrjiBxERnpGVGnGFtGFpaWtDQ0ACbzQaPxwO5XA6VSiXmDnRF\nij7haNfU3NyMe++9F9XV1QCA77//Hi+99FLQi/xF+3MKJV1dRRUV0qsBNNAYg9vNoKrKILqFKipi\nkZjoQE6OGbNmNeLaa8sQF+cOq6ZoYFgbhtOnT8PtdtPcgQjy/vvvi0YBAEpLS7Fz504sWrSo33Nd\nLhdqampgMBgwYsSIUMoccgzVWUUulwwnT8aKOQSVlbFITbUhO9uMuXPrcOONx6DXeyItU/IMa8MQ\nKFLo3XUl2jV5L94k4PH0/8NtbW3FAw88gNraWmg0GixatAh/+tOfgqIpXIRbk9vNr34mrHHQm6tI\nir3g3jQ5HDJUVMSJM4aqq/UYOdKKnBwT5s+vQXa2GVpt9+9YKDUNBahhoESUVatWoaioCA0NDQCA\ncePG+RU8e+WVV8SVxux2O77++mssXrwYaWlpIdUbTbjdQEcHg/Z2BnY7vy2XR/esIptN/luQmHcN\n1dfHYNSoDkyYYMbixVUYN84MjYaLtMyohxqGAJCKT9ibaNeUmZmJf/7zn/jkk0+gVqtx7bXXIiYm\npt/z7Ha7z7bNZoPJZOrVMET7c/IHj4cfEbS3M3A4AJer0xAEEkSWku+8o0MJozEOv/xC0NIyBqdP\nazF2bAdycsxYsaICWVkdUKkiYwik9JyCTb+GQViOk0IJFRkZGbj77rsDOufMM8/EkSNHxKTCjIwM\njBkzJhTyJI3LBbS08MbA6ew0BDJZ9I0KqqpOYePG7bBY8qFQnA2GmSGWl4iPP4GLLjJi9OgOKBSS\nm2E/5OjXMHCcrzXetm0bLrnkkpAJkjJS63ECw1fT1VdfDUIIDhw4ALVajTVr1vRZbsRbEyEEH3zw\nAQ4fPgydToe77roLSUlJIdfcl6ZAcDqB5mbeGLjdnSOCYBmCcPaC+fIS8Sgt1ePXX8eDZZcAOACG\n2Yfp0/dh3bpZXiMdex9XCj9DdbQA+GEYVCoVTp8+jZSUFAB89i+FEmkYhsGqVauwatWqgM99//33\n8fHHH4vf5YaGBrz++uuSnplms/EjA4uFgccTnTkGhACnT2thNMZ1Ky+RnFwJhnkWwFEABIQA7e15\nkMtnRVr2sKRfw2C1WvHSSy+JmcilpaVYtmyZXxfnOA6EEMij6dvbB8PBTx0MpK7p8OHDPh2c+vp6\n1NXVhd0V1d9zslqBlhYZLBY+fqBWh8cYBMt3Hkh5iY4OC/btq4PJ1Okm0uv1QdcUTKSoKVj0axi0\nWi2efvppcXvTpk1+Xfjbb79FRUUFli1bhoyMDADAli1bxOmJ48ePx5QpUwaimULxG5vNhu+//x41\nNTXIy8uDRqPpllmt1WoRGxsbIYWdcFynMbDZ+CxdlQpQKPh/Uqe38hI5OWbk57fi978/2Wt5CYNB\nj0suuQTbt38Ht9uD5OSkAY0GKcGh31pJFovFx3JXVFRg3Dj/an4cPXoU8fHxomHYvn07FixY0O95\n4aqVdOzYMeoaC4Dm5mZUVVVh1KhRomsxXDgcDrzwwguora1FbGws1q5di8TExD7PsVqtuOeee8Rp\nrbm5uXjhhRdgNpuxbt061NfXIyYmBkuWLMH1118fjrfRDbcbaGvrnFIK8CODaKCv8hI5Ofx6BIGW\nl/B4WDgcDsTExAyp2kxDrlaSt1EA4LdR6AmWZfHFF1+AEIKxY8dGvFAepX/cbjfeeOMNFBcXo66u\nDg6HA8nJybjxxhuxcOHCsOl47rnn8MMPP4jb69atwxtvvNHnOR999JFoFACgrKwMmzZtwqpVq/DG\nG2+gpqYGcXFxSE5ODpXsbhDCxwtaWxlYrQxcrs4RgdQNQijLSwgoFHLo9f1PV6aEloAHqAcOHMC0\nadMGdDPvhmTbtm0DukYkkbrvPBQ89dRT2LVrl8++5uZmfPzxx70ahlBoqqmp6abBbrf3OROpp9Gg\nML1VrVZj/PjxQdXYGywLmEwMzGZ+VMBxvIuovFyaPmrBdy6Ulzh+PA5GY2d5iZyc8JeXkKI/X4qa\ngkW/huHw4cMoLS2FyWRCbGwsKisrB2wYvOlvBoj3oji7d+8GgKBvC1MUhcXPhcast20Bf48fCtsV\nFRXoCYvFAkIIGIbpdr7QSw+mnq7TpmUymRgr6O38yy+/HHv37kVdXR0APpnu97//fVien8slw8iR\nU2G1MjhyxAiZjCA/PwdKZfdF5IVtuVyO/ft/BcCgoGAq8vLyfF4XGqFQbY8ZMxEnTsRi+/YJ+Pjj\nXLS0jEBGhhVJSScxcWIpbrlFD62WFY/X60Orx3u7uro65O8/0G0Bf45vbFSLrqRQtWfei4gNln5j\nDJ988gmuvPJKbNmyBUuWLMGnn36KK664wq+Ld40xVFVViTM/tm7diksvvbTH82iMQTqsXr0aJ06c\n8NnHMAzmzJmDJ554Imw6Tp06hccffxxtbW3Q6/W45ZZbMHv27H7Pq6urw4cffggAuOGGG0IWG3E6\n+axji4UfFbBsZ6KZP+zfvx8fffQxLJYOyGRynHHGFPz5z7eE1M/Ol5fg3ULHj/PlJUaP5stLZGeb\naXmJIDLkYgzCOgTCbCJ/53rv2LEDFRUV0Gg0yMrKwty5c1FVVYV9+/YBkGZiFqU7f/zjH/Haa6+h\npaUFSqUSGRkZmDp1Km6++eaw6hg9ejTWr18Pk8kEg8Hg9/cwIyMDa9euDboejuPdQyZTpyGw2zvQ\n0tKI5ORkxMfHB3S9Xbt+hMXS8du1WRiNRrS1tfYbYA8EobyE4BrqLC9hwmWXVWDs2HYolTSrmOKH\nYXC5XAD4nASWZeHvgm/z58/vtm/u3LkBypMWwzHGMHv2bEyaNAm1tbXIyMjwq8ELlSaZTDbghjIY\nmjwePmjc3s5XJxWCxkolcOxYMT7++CO0trYhLi4WS5YsxZw5fY9o+vZRM7/9Gzhms+q3RDJ+1hBf\nXqIdOTkmrFzZe3kJKfrOqabw0q9hOO+88wDw/quNGzciPT091JooEiMuLg5xcXGRlhEWOI4DwzBg\nfvPhsCxffsJs5gvTCcaga/mJLVu2oKWlBQBgMpnw3Xff9WsYvDn//PPR0NCAjo52yOUK5OTkICEh\nISDtfHmJOHHheqtV+dsSlWbMmVOKzExLVGVKUyJHr4bh+++/B9A5PTUlJQXXXntteFRJFKmNFgCq\nyV/600QIwbPPPofDh8tAiAGzZl2IhQuX+Uwn7asWUdc1JDweDziOQCbrvdfv3ds866wzkZCQgAMH\n9iM1NQ1z5szpM77QV3mJnBwTzj+/FhkZVr9jHL3pkgrRpokQvlMhfC0G8jlEkl4NQ2NjIy6++OJu\nJZArKyuRlZUVal0USsjxeAC7nY8VbNmyE99/3wiPJw6AB9u370JOzmTk5GT7da3Ro0ejoaEBhPDB\n2vT0tD6NQk+MHZuFsWOzenwtkPISlNAhNPgsy/8N8I2+UKpE6ETI5QQaDaBWEyiVQFJSdMVuejUM\nWq22R39uUVHRsDUMwzHGMBCkpMnp5Be4P3iwFDk5E+HxdPbkCOF/1EolUFVVDY/HIZ5nt9tRWXnS\nb8Nw/fXXw2DQo66uHklJSbjyyv5n7vXlo+Y4oK6OLy8hLFPpb3mJwSJF33k4NAnfDaHBZxjfxl6h\nAGQyArUa0GgIjh07jGnTzvDLPRdtBrtXw1BSUtJt7jjAT/H0t4gehRJOWJbPKjaZGDgcfFYxy/I/\naJdLLg7reypEN2HCBBw6VCROttDr9Zgwwf+GSC6X4fLLLx+U9upqg2gEjMY4sbxEQUEzrrjiRMDl\nJSi+uFy8wfVu8Dv/72zwlUr/6lOpVNyQjdn0+tYnTZrUowHYvHlzSAVJGan0gr0ZDpoI6ezFeftu\nXS5+cRqbjf/f5eocATAM/78wq7W/3ua5556L06dPo6SkBDIZg9/97nchrbbq8TCQy6fj22/jcPx4\nvE95iZkzT+Oaa44PurxETxDSf+9VaqMFYOCaWJavRxUTA4wezUGn441BMHrwUvztBYteDUNFRQV2\n7dqFrKwsnx9IT9NQKZRg4Xbjt9wAvsfvdne6fQQYht+Wyzv9u4NdsYxhgMsuW4HLLlsx+DfRA0J5\nCWFEUFlpQGqqPWzlJTiOw4YN76OiogIKhRy/+91cXHjhBSG7XyghhO/5cxzf8AOd3wmgs+GXy4G4\nOIKUFBIV1WmlRK+P69prrwXDMDAYDD77/VmPd6giJd+5QDRrYlnA4QAsFt71Y7fDZxYQELz1B8Lt\nN3c45DhxIlYMFtfU6JGRYUVOjgnz59cgO9uMU6eOhU3TN998gwMH9ouJqtu2fYO8vDyMHJnR7dhI\nxBi6xn0Eg88w/N/l5aWYNCkPDENE9w8/IiTid0ToIITLny/F316w6NUwhLusMmXowrJ8EFgwAE5n\n50iAYTp9vTIZ8NNP21FcXAy5XI7LLrsMmZmZkZbvF3x5ic4cAu/yEosXV0W8vERtbZ1oFAC+1tWp\nU6d6NAyhxOPpnMIpNO4qFe/bj4nh/fw9JbVbLDaMHk3Lc4QLOsAKACn2DqSkSRgBZGSciaoqX1eQ\nd8AP6Dm4t2vXLmzd+jWcTn520Ftv/Qf337+2W+n3gRDsHrDFohCnjZaXe5eXMPtdXiKcvfIxY0aj\nuPiwmG9hMMT2OjV2sLoI6ZzhIxh+pZKfuqnRQDQAgYwEpfQ9F5CipmBBDQMlYDye7iMAoSfoPQIA\nAlt97MiREtEoAEBT02lUVlZi8uTJIXgXgWE2q8Ric53lJfjFaPoqLyEVLr54IZqbm2E0noBcLsf5\n55+HtLS0QV2T43jDD3R+7ioV796JiQF0OgKVKjLJXTt27MC+ffswYcIEXHbZZWImO8U/qGEIACn6\nFEOhSZjJIfj93W5G7Pl37Qn2ZAAG6qPuOjLQarWIjw+sLERvBKqptVUtGoHy8jhYLMEvLxFOXz7D\nwO/KBV11efv/5fLO2V5qNYFe3znFM5RtbyDf8w0bNuCzzz6DzWbDrl27YDQa8cADD0RUU7RBDcMw\nxOPhG36nky8G5/F0b/gB34Ae0H0KaLC58sorUV9fj8bGBigUSsycOQOZmSNDczMvCAGamjSiETh+\nPHjlJaIJ4fN3u2XweLr7/zWa6Fh7eu/evbDZbAD4FQgPH+ZdaIpoEC8R6JMKACn2DnrSxM/x53v8\nDkdnj18YCQh5i6Fq+AfaC9ZqNbjvvvvQ1NQEjUaD+PjgFe7z1tRfeYmFC8NTXiIS+QK9+f9VKgKd\njvf/T548DjKZtAK9g/3tsSyL2tpaGAyGoJUyl2J7ECyoYYgiOK7zR+12842+0wlwnG+PX8julMn4\nH77QwDEM3wOUMnK5DGlpqUG9Zm/lJbKzQ19eIlwIhl/AO8ej8x8/tVOnA7RaEtBCQtHEpZdeig0b\nNsBkMkGn02HWrFlYs2YN6uvrodFosGTJElx//fWRlilpqGEIgFD4FL0zeQW/Pl/KgRGNgPc/IZFH\n+NEbjZ3+YJlMGg1/pGvtCOUlhAVpjMY4qNVWTJpkk1R5iYE8J0I6R31Cb1+jIUhK4nv7XUeBA0GK\nvvNANC1duhQ5OTk4cOAAcnNzsWXLFnG5WavVii1btmDRokVITk4Om6ZogxqGEOHd2DudfGPP9+iZ\nbo1916JdXVP2hYSfUPn2ox2Ph0FlpUF0C/VUXqKhoUSSpR76wjvoywd7+YBvbCzv76ffh96ZOHEi\nJk6cCAD4+OOPfV6zWq0wmUyDNgxDGWoYAuCMMwrEBl6o0yP07oVGvmuFRkCoyujbixP8u4ONh0mx\nsQu1poGUl4iLk/ZzEtyAQgdArebdPQYDbwTC6fKRYi94MJrOOOMMlJSUiOu7p6enY9SoURHVJHWG\nvWHozW9PCOMzS4dlO333gG/avjfBaOwpvjgcMlRUdOYQ9FReQqtl+7+QRBDiAYLrT6Ph5/wbDPy8\n/2iOdUiR6667DhzH4fDhw9BoNFizZg3UanWkZUmakDZhHMeBEAK5RGvTVlYyaGqSdfPbd5Ur7Iu0\n77wnhqIm7/IS5eV8eYlRozrLS4wfb4ZaHdismUg9JyEeIIwENBp+0Ra9nuDo0SJMniy9XqcUfeeD\n0cQwDG644YbgCoI0n1OwCJlh+Pbbb1FRUYFly5YhI4Ovx9LQ0ICdO3dCLpdj3rx5EV8/muOYQVXk\npASHjg6luESl0ehdXsKEyy6rQFZW/+UlpIC3EVCp+HhAcjKg15MeJwXQkQFFqjCEkJD94o4ePYr4\n+HjRMHz11VdYunQpAGDTpk29Lvizc+dOnHXWWaGSJfL112WwWiM/O2W4YTarfnMLeZeXaEdOjgkT\nJpglX15CwOnkG3dhCUeDobMMBIXijcFgwPjx40N+n8LCQlx44YWDvk5YveE6nU78W0V/PcOGruUl\nrFa+vEROTvDKS4QDYXKBQsEv/JKRwSEmhvb8KUOPsBoG78GJMgrn2g1Ff36wIQTYt68BHk9Bj+Ul\nLrigFunp4S8vMdDnJExA0On4RV8SEoI3IpCqj1qKuqim8BJWw+BdD76/aoe7d+/GueeeK/4NIOjb\nwAgAfKMBdE4f7G1bwN/jh8M2IcD//d9p1NSko719AsrL4+ByOTBmTBOmTWvHwoWnYDIdAsNEVm91\ndbVfx7tcwPHjRigUHCZPnoD4eIKamiJYLATZ2XwjUFRUBKBzuuJAtwWCdb1gbQvJYFLRU1RUBKPR\nKCk93vhzvE6nE11JoWrPhO1gENYYw5dffonly5eDEIKtW7diyZIlPZ5HYwzSpWt5CT6rmBVHBDk5\n5qgqLyFMHVWp+FFBbCw/Y4hOOaYEExpj+I0dO3agoqICGo0GWVlZmDt3LmbNmoWNGzeCEELXjo4S\nWBY4dcogGgGjMQ4Ggxs5OSZJlZfoD+9aQt5lo1NSAIOBREWMg0IJFyEzDD01/BkZGVi5cmWobhly\npObPNxpP4KOPNkKj0eCMM6bioosWDPqabjeDqqq+y0vExbn7vIYUnpNQSVYYCTQ0FGPWrEmSKhwn\nVR+1FHVRTeGFDpijFJPJjPfeexctLS0AgJqaGuh02oD9jN3LS8QiNdWG7Ozey0tIFSFQrNEAiYkE\niYlErCfU2urGUE12tVqteP3119HW1oYpU6Zg5cqVdMUyyqCghiEAIt0L9qa8vFw0CgDgcDhw5MiR\nfg1D1/IS1dV6jBwZ3PIS4XxOgotIpwNGjOBnDfUUHxhIz+7777/H3r17MXLkSFx//fVBz+APRm+T\nEIK//e1vOHLkCAC+F2u1WrF69eqI6go2VFN4oYYhShkxIhkajQYOR+cayXFx8d2O66+8xLhxZmg0\n0lqUpTe8q40KLqKUFL7aaLDdQ5988gk++OADWK1WyGQylJeX48knn5RcT7y1tRU1NTXittPpxOHD\nhyOoiDIUoIYhAKTgOxfIysrC7Nlz8Msvv4BhgPT0DKxYsQIWiwLl5fE9lJcwY8WKCmRldUClCq0h\nCMZzEmIEcnlnuWm1ms8s1ukCjxME6g/+8ccfYbVaAfA1v8rLy9HR0YHY2NjAbhxETT2h1Wq7JYsO\ndglLKfrOqabwQg1DFHPllVdg5MgCuFxnoK5uJJ55xre8xNVXGzFmTHSUlwD4kYDLxRuC+HjeLaRU\nsqiqqgKgxIgRmWHrsXe9D8MwkiwGqdPpsGjRImzatAlmsxkZGRm45ZZbIi2LEuWENI9hoNA8ht5p\naVH7rFVssXSWl5gwwRQ15SW8cTr5EYDBAKSmcmKQ2Ol0Yu3atTAajZDL5ZgxYwbWrVsXFuOwZ88e\nvPLKK2huboZGo8HChQtx5513hvy+A6Wurg6NjY0YP358UEc1lOBA8xgoQYMQoKlJIxqBruUlzj+/\nFhkZ4S8vEQxcLv7/mBggLY1fi6Bre//ee++huLhY3N69ezf27t2LOXPmhFzfnDlzwHEcXn75Zbjd\nbhQWFuLw4cM444wzQn7vgZCRkSEmklKkA8dxcDgcSElJibSUgKCGIQBCHWMgBKiv1/mMCABgwgQ+\no3jhwlNITbX7NKBSinsI9KZJWPRIMAZ6fd9BY+9ZVwDgdrvR0NAwIE0D8Qdv3LgRbW1tAACLxYJX\nX30V69evH9D9g6UpHEhRV7RpcrvdIIQgMTERkyZNirqFgahhiCAcB9TWxohGoLy8s7xEfn4rfv/7\nk1FVXqInhCCyVgukpvJxA39HOAsWLMCBAwdgMpkAAGlpaUGtB9MfNpvNZ9tqtYIQIrqyWJbFoUOH\n4PF4UFBQQCsGU+BwOKBSqTBy5EikpaVBFo3DeVDDEBDBmGlTXW0QcwhOnIgddHkJqY0WAGDChAlw\nOPiyE/HxBMnJZEAL18+cORN33HEHtm3bBplMhhtuuAGpqakD0jSQ3mZaWhpOnTolbo8YMUI0Ch6P\nB2vXrkVxcTE4jkNubi7++c9/+pSWD4WmcCBFXVLWxLIsnE4n4uLiMG7cuCER46GGIYT0VV5i1qxG\nXHttWb/lJaIJl4sPIuv1wOjRHLTawV/zggsuwAUXXDD4Cw2Ahx9+GM8++yyampoQHx+P+++/X3xt\n27ZtOHTokFhKvrS0FB9++CFuvvnmiGilhB+XywWGYZCUlIRRo0ZF5VICvUENQwD058+PRHmJSMcY\nhLiBTscbA4MBOHSoCKNHS6uHNxAfdUxMDJ544okeXzObzeg6oa+joyPkmsKBFHVJRRMhBE6nE2q1\nGo2Njbj00ksll/QYDKhhGAThKC8hRYS4gUbDl6FISgp+5rHUueiii7Bt2zbU19cDAJKTk8VlaylD\nD5Zl4XK5EB8fj5ycHOj1elit1iFpFACaxxBQHkNf5SWys81RVV4iUARjoFTyaxaMGEHXNj516hTe\ne+89cByHq666Cvn5+ZGWRAkygrtoxIgRyMzMHHRWeaiheQxhQCgvIbiGIlFeIpIImcgKBb+sZXIy\nNQbejB49Go8++mikZVCCjOAu0mq1GDduHJKSkobsyKA3qGHwwmxW/eYW4kcFXctLOJ2FyM/PjrRM\nH0IRY3A6+RpFBgPBmDEEGk1g50vFH+wN1eQ/UtQViCahYWcYBgqFwu9SJh6PBx6PBwkJCcjLy4O2\nn9kT3ssPDzWGtWFoblbh0KHu5SUmTDBjzpzSbuUlysqG7ujA7eZHCHo9kJHBQa+PtCIKJTAcDgfk\ncjkSEhKQm5sLjUaDkpISuFyuPo2Dw+GAQqFAamoqMjIyJFkTK9wM2xgDIcC0aUokJtrFtYqjtbzE\nQBEWtomJARISCOLjh18QmRLduN1ucBwHg8GAkSNHIi4uzud1QghKSkpgt9t9ppMKpSoMBgMyMzOR\nkJAQbukhgcYYBgnDAH//+5GoK6I3WLxnFCUn8zOKaAeJEk14PB64XC4YDAZkZGQgOTm51wxjhmEw\nadIklJWVoaOjAwzDgGVZJCYmIj8/H5pA/aTDBNo/DICysuORltANfzQRwscNWJafUZSXx2HCBA4p\nKaExCkVFRcG/6CChmvxHiroKCwvhcDhACEFqaipmzJiBKVOmICUlpd+yEwzDIC8vD8nJyUhPT8eM\nGTOQk5MzaKOwe/fuQZ0vZcI6YtiyZQtYlp/XP378eEyZMiWctx92eGcijxrFIYBqDRSKJBDiBjEx\nMSgoKBhUYz527NggKhvahDXGsH37dixYsKDf46SaxxANeFcwTU7mM5GH2Uw7SpQjzCiKi4tDWlpa\nt7gBpXeiMsbAsiy++OILEEIwduzYsDT+w4HBVDClUCKFMK2UEAKFQgG1Wg2dTodRo0YhMTFx2OUO\nSFEijK4AABEBSURBVImwGoaFCxeKf2/bti2ctw4Kka5L5A3H8cbg5MnjmDUrB0lJBFJJyoz2efDh\nQoqagNDo4jgOLpcLHMdBpVJBo9FAp9MhPj4eer2+35LlUswZkKKmYBGxpqS/SoTeD10I8gR7GxgB\noDOAKzT6vW0L+Ht8KLadTuDEiePQ6VjMm5cLlrWgvv4g6us7ywALwcNIbRuNxh5fJ4Tg008/RUdH\nBxYsWCDWFgqHPqPRKJnn0zW4KxU9/X1+/m4fOHAAHo8HU6dOhUqlwrFjx6DRaLBgwQLodDr8/PPP\ncDgcmDx5MgD/fq/FxcUhbw8Cbz8gKT3BNFJhjTFUVVVhzJgxAICtW7fi0ksv7fE4GmPwxTtukJIS\nnclnx48fx7p169Dc3AwASE1NxfPPP4/MzMwIK6MMBpfLBZZlIZPJoFarodVqodfrER8fD61WG7UL\n1UQrURljqKqqwr59+wBIc+ENKTHU4gZbt24VjQIANDY24rvvvsONN94Ykvvt3r0bR48exbRp0zBt\n2rSQ3GM40Vs8IDY2FgaDARqNhsYEhhBhNQxz584N5+2CTjjWfHY6+QqmcXF8BdP+1v6Qop+6J01J\nSUk+2zKZDMnJySG5/7///W9s3boVdrsdW7duxapVq5CXlxcVz0kKFBYWIj8/f8DxgFAgRX++FDUF\nC4mEK4c3Lhc/pdRgGLr5BitXrkRhYSGOHTsGmUyGM844A4sXLw76fTiOw549e2C32wEAFosFO3bs\nQF5eXtDvNRTweDxwu91gGEY0AnFxccjPz4dOp5N8mWlKaKCfegAEc7TgXado1CiC2FgyoHwDKfY4\ne9KkUqnw4osvoqysDDKZDBMmTAib/5kQEjXPKdQ4HA4wDNNnPECK60pIsWcuRU3BghqGMMJx/Ohg\nuNYpksvlIW90ZDIZZs6ciW+//RYOhwMxMTGYN29eSO8ZDTidTiiVSuTk5NAcAUq/RHE4M/wMtFaS\n08mPDvT64NcpkmJdm0hrWrNmDe6++25ceumluO+++3D99ddHXFNPhEOT0+kEy7LIzs7GWWed5dei\nM1KsAUQ1hRc6YggRdH2DyMEwDC666CJcdNFFkZYSMVwuF2QyGcaNG4cRI0ZEWg4lyhi26zEAwc9j\nEKaY6nRAYiJd34ASfoRA8ujRo5GSkhJpOZQwE5V5DEMRYV1kpZI3BlIqTUEZ2rAsKy5WTwiBSqXC\nqFGjkJaWFmlplCiH9mcDwDvGIMQNdDqCCRM45OVxSE0Nv1EYrr7zQIlGTSzLwuFwwOFwwG63+0wr\n1ev1SEtLw8SJE1FQUIBZs2Zh2rRpQTEKUvSdU03hhfZtA4DjGDid/BTTtDRa0poyODweDxwOh7it\nUCigVCqhVCqhUqmg1WoRExMDjUYDlUpFy0tQwgaNMfQTY/BeCjMxkSAxkcYNKP3Dsiw8Hg84jhPL\nSCiVSigUCqhUKigUCsTExECn00GtVkOlUtEppJRBQ2MMIUSIGygUfGmK5GSCCFQBoEQhbrcbCQkJ\nUKvVPr19mkFMiSZo39cLl6tzdDB+PIeJEzlkZHQahWj0U0eC4arJ4XBgwoQJyM7OFheb6aushFR9\n1FLURTWFl2HfjfEuTZGZSRAXN7DSFBRKTEwMXYaSMiQY1jGGH34ohcvlHHalKSjBx+FwYMqUKYiJ\niYm0FMowJlgxhmHtSkpNJUErTUEZetjtdjAM4zNzqCcIIYiNjaVGgTJkGLaGwel0oqamBjabze9z\nhqvvPFCiXZPD4YBCocDUqVMxdepUTJw4EXq9HhzHwW63w+VydTt+3LhxAWuSqo9airqopvAyLGMM\nJSUluOmmm1BXVwe9Xo+bbroJ559/fqRlUSKM2+2GTCZDfn4+YmNjxf1xcXFi7MDj8aCtrQ0tLS2w\nWq1wuVxISkqCRqOJlGwKJegMyxjDokWL8PPPP4vbmZmZ2LBhA00gGiIQQuBwOCCTyfzOD7Db7cjI\nyMDo0aMDyidwOp1QKBSQU38kRQLQPIZB0NV9JJQd0A3FpdOGEULtoISEBOTl5UGhUODgwYN9LkXp\ndrshl8sxderUAX3+arV6MJIpFEkyLLvIEyb4rsSWkpLiV6MQ7b7zcBFsTYQQ9DWw9Xg8cLlciI+P\nx/Tp05GXlwetVgulUonJkyfD4XCgqKgIHMfB6XTCbrfDbrfD6XQiLS0NZ511VkQ6BVL1UUtRF9UU\nXsI+YmhoaMDOnTshl8sxb948pKenh1sCXn31VWg0Ghw+fBgGgwH33ntv2DVQ/IMQApZlER8fD4vF\nIs4QksvlogsnPT0d6enpPboCdTodJk6ciJMnTyIpKQkGg4FmI1Mo/RD2GMNXX32FpUuXAgA2bdqE\nZcuWdTsmXHkMx44dg9MZvPUYKMHH6XSioKBAdNlwHEdjQRRKL0RtHoP3kL0v3y+FYrfbkZ+f7+PH\np0aBQgk9Yf+VeQ9QlEpluG8/KIaDPz8Y+KvJ7XaLvn6GYcT1iQF+pJCdnQ2DwRAUTVL0B0tREyBN\nXVRTeAm7YRB++AD6nBbo/dB3794d0u2ioiKfxoxuD27baDT2+DrLsrDb7SgqKsKxY8eQmZmJgoIC\nuFwudHR0YPr06UhKSsK+fftQW1srrlUcjM+7uLh4UOcPp+3i4mJJ6aGfX2DbwSDsMYYvv/wSy5cv\nByEEW7duxZIlS7odQ2MMQwuHwwG5XI7k5GSMHDmyXxciIYSuTUChDICozWOYNWsWNm7cCEII5s+f\nH+7bU8KEkFNgMBiQm5uLhIQEv8+lRoFCiSxhdyVlZGRg5cqVWLVqFVJSUsJ9+0ERzf78cOF0OlFY\nWIjk5GRMnz4dkydPDsgohAop+oOlqAmQpi6qKbzQidyUPnG73eIUUblc3uOsII/HA7fbjdjYWIwd\nOxZutxtjxoyJgFoKhRIMhmWtJAEaY+gZt9sNj8cDg8GAlJQUJCcng+M4FBYW+sQHHA4HlEolUlJS\nkJ6eThPGKJQIE7UxBoo0EWICOp0OGRkZSE1N9WnoZTIZcnNzceTIEcjlcsTGxmLcuHE+VUgpFMrQ\ngGYLBYDU/PnA4DQJ6wtwHIfk5GRMmzYNU6dOxciRI3vs/cfFxWHy5MmYMWNGt9LU3kjR90o1+Y8U\ndVFN4YWOGIYZQklqpVKJ+Ph4jBw5Elqt1u/z6ZrGFMrQh8YYhkmMQcgliIuLQ3p6etAyiikUinSg\nMQZKv7hcLhBCYDAYMGbMGMTHx9McAQqF0i80xhAA0RBjEOoPKRQKZGVlifGAhISEsBkFKfpeqSb/\nkaIuqim80BHDEIBlWTidTsTExGDkyJFISUmhU0cpFMqAoTGGKI0xCLkGWq0WCQkJSE9Pp2XMKZRh\nDo0xDEOcTicIIdDr9UhJScGIESOirnQ5hUKRPjTGEADhjjEIU0vdbjc0Gg1ycnIwc+ZMTJ48GRkZ\nGVAqlZL0c1JN/iFFTYA0dVFN4YWOGCSGkIGsUqkQFxcX1MVqKBQKxR9ojEECMQaXywWWZRETE4P4\n+Hikpqb6LGdJoVAo/kBjDFGOw+EAwzDQ6/VIT09HUlISnUlEoVAkAY0xBEAw6hIJM4ny8vIwc+ZM\nTJo0qVvBukCQop+TavIPKWoCpKmLagovtIsaQjweD1wuF7RaLeLj45GWlgadThdpWRQKhdInNMYQ\n5BiDEC/Q6/VITEzEiBEjaH4BhUIJCzTGIBEIIXA6nZDJZNDr9cjMzERCQgLkcnmkpVEoFMqAoDGG\nABBiDCzLwuFwiCODiRMnijWJkpOTw2oUpOjnpJr8Q4qaAGnqoprCS1hHDFu2bAHLsgCA8ePHY8qU\nKeG8/aBwu92i2ykxMRFpaWkBrWPw/9u7l5Y2vgAK4EcNiUYEXygW36iE+kbri9JuWnAhrVjorrt+\nAxf9EG678gsUFDSKj+ALoogg2FZaQ7qJRBBUJIRaSSh15r+QDJk2oxl7c2/s//xWk+k4OXOU3E4m\nd0JEdF9IvcawurqK58+f37pdtlxjSNyCorCwEGVlZbwFBRFltXt5jeHq6gozMzPQdR0NDQ1SXvzt\nSFwvyMvLQ1FREWpra1FcXIzcXL7jRkT/H1Jf8YaHhzE2NoZXr17h9PRU5lNbSr5eUFRUhNbWVjx6\n9AgejwelpaWmQSEb31NkpvQwU/qyMRczyZWRt5LOz88xNTVlWjcyMoLa2lrj8draGp49e5by5/f2\n9hCNRkXHIiL6pxUXF6Onp+ev9yP1GkM4HEZdXR0AYGFhASMjI7KemoiI0iT1GkM4HMbu7i4AoKur\nS+ZTExFRmrJy5jMREanDj9sQEZEJBwaiDNA0zZjMmS3ueyZZ+e97JhGkXmM4OTnB+vo68vLy8PTp\nU1RVVVluOzExgebmZgDXn3J6+/YtAPGzp+1kOjw8xN7eHjRNw+DgIGpqamzvQ1YmlT2dnZ1hY2MD\nBQUFaG9vR2Njo+19yMqUidn4Pp8PoVAIo6OjePDgwZ2OQXRXIjKJ7spOJqttVfZkta3Kng4ODvDt\n2zdomoaBgQFUV1cDuENPukRzc3PG8uzs7I3bxmIxY3l5edlYXllZUZZpaWnJWF5cXLzTPmRlUtmT\nz+czlre2tu60D1mZRPeUcHBwoB8fH9+6ndUxiO5KRKZMdJVuJqttVfZkta3Knvx+v7H8N69RUs8Y\nkr+L4LZbUefn5wO4/p9eRUWFsV707Gk7ma6urqBpGnRdh550zd7OPmRlUtmTy+VCLBaD0+nE58+f\n0dfXB6fTqbQnq0yqZ+NbHYPorkRkUt1VKip7sqKypydPnqRcb7cnqQND8gtXuvccCgQCGBgYMB4P\nDw8by8vLy1IztbW1YWJiAgDw5s2bO+1DViaVPT1+/Bg+nw8/f/5ES0sLLi8v4XQ6lfZklUl0T3ZZ\nHYPorkRkUt1VKip7spINPa2urqKvr894bLcn6fdKSsjJyUnrZ+LxuHH28DsRfwh2Mu3v7+Pdu3fQ\nNA0LCwt48eKF7X3IypRMdk8Oh8OYvOj1elFYWGh7H7IyJVPxwmJ1DKK7EpEpWba8CKvsKR0qevL7\n/WhubkZ5ebmxzm5PUj+VFIvFAFyPXollAPj69SsCgcAf22ua9scN7MLhsLEcj8elZkqcguXm5pp+\n4Vb7UJlJZU8J0WgUP378MDKq7Mkqk+iebpIql9UxiO5KRCZZXd30+/udyp6sqOxpa2sLlZWVqK+v\nN62325PUM4b+/n58+PABuq6b7pO0s7ODnJwcPHz40LT90dERmpqaTOtEz562k6mhoQEzMzMAgNbW\n1lv3oTKTyp6+fPmCYDAIXdfx+vXrW/ehMlMmZuOvra0hFAohPz8f9fX1xvu+qXJZHYPorkRkEt2V\nnUxW26rsyWpbVT2dnZ1he3sbHo8HwWAQFxcXxtvLdnvizGciIjLhBDciIjLhwEBERCYcGIiIyIQD\nAxERmXBgICIiEw4MRERkwoGBKIX5+XlMTk7i06dPAIBQKITp6Wm8f/8ewPVX0xL9q6ROcCO6L3p7\ne3F0dITu7m4AQGNjI9xuNw4PDwEgo7NsiVTjGQNRCmVlZYhEItA0DePj4zg/P0ckEkFJSQk2NzcR\nDAbh9Xrh9Xrh9/tVxyUSimcMRCm4XC7E43EEg0G8fPkSHz9+hNvtRktLCzweD05PTzE6Oqo6JlFG\n8IyB6AaBQABDQ0OIRqOIRCIoLS1VHYko4zgwEN3g169fcDgccLvd+P79OxwOnmTTv49/5UQWLi4u\nUFdXB+D6LpmTk5PGv3V2dmJ6ehoul8v4pq6Ojg5VUYmE4t1ViYjIhG8lERGRCQcGIiIy4cBAREQm\nHBiIiMiEAwMREZlwYCAiIhMODEREZMKBgYiITP4DCmA2rRYOv7gAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d1d1490>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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NAODw4cOoqKjQ3VbvdiKieAauhrGv5aOU7e9R723T7O9fs7Kv/VvzTCsImkNG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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d6d9a50>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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d8RwCaeE8BLI6FgQiIgLAgqArO55DIP3wKiOyOs5DuMJn54fw/9/vNmx7ubM9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\nCgsCEREBYEEgIqKvsCAQEREA4H8BymNhQBM3kzgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d63ff90>"
       ]
      }
     ],
     "prompt_number": 106
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The point at the upper right exerts enough influence on the slope (via the Normal likelihood) that the value 0 is not in the credible HDI. Kruschke suggests replacing the Normal likelihood with a t-distributed likelihood, whose fatter tails accommodate observations outside the normal distribution. The degrees-of-freedom parameter will be treated as a continuous adjustment of the fatness of the tails, and will be estimated along with the other model parameters, biased towards smaller values: "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def make_t_model(x, y):\n",
      "    \"\"\"\n",
      "    return a dict of model variables for the model constructor\n",
      "    \"\"\"\n",
      "    # priors for the regression coefficients and variance/precision\n",
      "    beta = mc.Container((mc.Normal(\"beta_0\", mu=0, tau=1e-12, value=mean(y)), # population intercept\n",
      "                         mc.Normal(\"beta_1\", mu=0, tau=1e-12, value=0))) # population slope\n",
      "    tau = mc.Gamma(\"tau\", alpha=.001, beta=.001, value=.001)   # population precision\n",
      "    sigma = mc.Lambda(\"sigma\", lambda tau=tau: tau**-0.5)\n",
      "    nuGain = 1\n",
      "    udf = mc.Uniform(\"udf\", 0, 1.0, value=0)\n",
      "    nu = mc.Lambda(\"nu\", lambda udf=udf: 1 - nuGain * np.log(1 - udf)) # nu range [1,infty)\n",
      "\n",
      "    # The distribution of each y_i has mean that is a deterministic function of the x_i\n",
      "    mu = mc.Container([mc.LinearCombination(\"mu_%d\" % i, (1, x[i]), beta)\n",
      "                       for i in x.index])\n",
      "\n",
      "    # likelihood for the data\n",
      "    z_like = mc.Container([mc.NoncentralT(\"z_like_%d\" % i, mu=mu[i], lam=sigma, nu=nu, value=y[i], observed=True)\n",
      "                          for i in y.index])\n",
      "    \n",
      "    # simulate posterior predictions for confidence intervals\n",
      "    z_sim = mc.Container([mc.NoncentralT(\"z_like_%d\" % i, mu=mu[i], lam=sigma, nu=nu) for i in y.index])  \n",
      "    return mc.Model(input=locals())\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 107
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = make_t_model(cig.Wt, cig.Tar)\n",
      "plot_regression(cig.Wt, cig.Tar, M.mu, M.tau, titlestr=\"pre MAP estimate\")\n",
      "show()\n",
      "mc.MAP(M).fit()\n",
      "plot_regression(cig.Wt, cig.Tar, M.mu, M.tau, titlestr=\"MAP estimate\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=123.961284, max=123.961284\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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q2NhY7Nq1C+U3vuDXb9iAvn374s4775S1fteuXXH27FnYbpw91SkoqM6iUJM/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\nG87xAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1158bb690>"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=127.413709, max=127.413709\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Tgh4zOUu1hSE9PR179+5FcHCw5M5YVR2GSuTqDAYDpk2bhmnTpmkdRRE2ux0f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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d085ad0>"
       ]
      }
     ],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = mc.MCMC(input=M, db='ram')\n",
      "S.sample(50000, burn=1000, thin=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 127 of 50000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 243 of 50000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 371 of 50000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 491 of 50000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 618 of 50000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 733 of 50000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 851 of 50000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 982 of 50000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  2%                  ] 1093 of 50000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  2%                  ] 1218 of 50000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 2%                  ] 1335 of 50000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 2%                  ] 1463 of 50000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1581 of 50000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1700 of 50000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1817 of 50000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 3%                  ] 1943 of 50000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2070 of 50000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2185 of 50000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2301 of 50000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 2416 of 50000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 5%                  ] 2544 of 50000 complete in 10.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 2663 of 50000 complete in 11.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 2787 of 50000 complete in 11.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                5%                  ] 2900 of 50000 complete in 12.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3010 of 50000 complete in 12.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3134 of 50000 complete in 13.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3253 of 50000 complete in 13.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3363 of 50000 complete in 14.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 3488 of 50000 complete in 14.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 3612 of 50000 complete in 15.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 3730 of 50000 complete in 15.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                7%                  ] 3852 of 50000 complete in 16.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               7%                  ] 3975 of 50000 complete in 16.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 4099 of 50000 complete in 17.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 4224 of 50000 complete in 17.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 4341 of 50000 complete in 18.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               8%                  ] 4461 of 50000 complete in 18.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4579 of 50000 complete in 19.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4714 of 50000 complete in 19.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4838 of 50000 complete in 20.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 4957 of 50000 complete in 20.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---              10%                  ] 5073 of 50000 complete in 21.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---              10%                  ] 5195 of 50000 complete in 21.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 5305 of 50000 complete in 22.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             10%                  ] 5423 of 50000 complete in 22.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5537 of 50000 complete in 23.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5642 of 50000 complete in 23.6 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5754 of 50000 complete in 24.1 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             11%                  ] 5875 of 50000 complete in 24.6 sec"
       ]
      },
      {
       "output_type": "stream",
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        "\r",
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        "\r",
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        "\r",
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        "\r",
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        "\r",
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        "\r",
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      {
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        "\r",
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      },
      {
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        "\r",
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       ]
      }
     ],
     "prompt_number": 110
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_regression(cig.Wt, cig.Tar, M.mu, M.tau, M.z_sim, titlestr=\"Noncentral T regression with outlier\") \n",
      "show()\n",
      "posterior_hist(M.beta[0].trace(), \"beta0\")\n",
      "legend()\n",
      "show()\n",
      "posterior_hist(M.beta[1].trace(), \"beta1\")\n",
      "legend()\n",
      "show()\n",
      "posterior_hist(M.nu.trace(), \"nu\")\n",
      "legend()\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=4.279330, max=11.527998\n",
        "CI: min=27.605732, max=32.712127\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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5ZWJcT0jVRy1FXaQpuAzorCS5XO52c+E4Dq2trTh9+jR4nodarRbXs42KioLV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\nyGTAoUMHIZO5ntZ4Hjh4MB8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Ns2bNwvTp07F+/Xowxvrd2tE8L6R3ep7Ry3EKt5t9UpIZ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\nnQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d999690>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10cf0d1d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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OHTqkv8GYPXs2FixYICJXZ2cn3nrrLUyePBnV1dXo7e21Nc/WrVv1Ixs/+eQT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\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11096b250>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10dcb7c10>"
       ]
      }
     ],
     "prompt_number": 111
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Repeated Measures"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This final example uses the lung toxin clearance dataset from [H.A.Feldman](). Repeated measurements per subject are modeled via a hierarchic prior on the regression coefficients, and outliers are accommodated via a t-distribution for the likelihoods. There's a small bit of data cleaning to do on the [Feldman table](\"feldman.csv\"), to extract group1 data and exclude missing data\n",
      ". Let's wrangle this with a Pandas Dataframe."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "feldman = pd.read_csv(\"data/feldman.csv\", index_col=0)\n",
      "group1 = feldman.ix[feldman.group == 1]\n",
      "group1 = group1.ix[group1.retention.notnull()]\n",
      "group1.subjID -= 1 # life will be simpler if we can index 0-based on subjID\n",
      "group1.index = range(len(group1.index)) # get a contiguous index\n",
      "group1[:15]"
     ],
     "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>group</th>\n",
        "      <th>subjID</th>\n",
        "      <th>time</th>\n",
        "      <th>retention</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td>  0</td>\n",
        "      <td> 100</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td>  3</td>\n",
        "      <td> 102</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td>  4</td>\n",
        "      <td>  87</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 10</td>\n",
        "      <td>  89</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 15</td>\n",
        "      <td>  57</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 20</td>\n",
        "      <td>  48</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 25</td>\n",
        "      <td>  43</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 30</td>\n",
        "      <td>  33</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td>  0</td>\n",
        "      <td> 100</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td>  3</td>\n",
        "      <td>  95</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td>  4</td>\n",
        "      <td>  91</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>11</th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 10</td>\n",
        "      <td>  62</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>12</th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 15</td>\n",
        "      <td>  52</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>13</th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 20</td>\n",
        "      <td>  55</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>14</th>\n",
        "      <td> 1</td>\n",
        "      <td> 1</td>\n",
        "      <td> 25</td>\n",
        "      <td>  45</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 250,
       "text": [
        "    group  subjID  time  retention\n",
        "0       1       0     0        100\n",
        "1       1       0     3        102\n",
        "2       1       0     4         87\n",
        "3       1       0    10         89\n",
        "4       1       0    15         57\n",
        "5       1       0    20         48\n",
        "6       1       0    25         43\n",
        "7       1       0    30         33\n",
        "8       1       1     0        100\n",
        "9       1       1     3         95\n",
        "10      1       1     4         91\n",
        "11      1       1    10         62\n",
        "12      1       1    15         52\n",
        "13      1       1    20         55\n",
        "14      1       1    25         45"
       ]
      }
     ],
     "prompt_number": 250
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def make_subj_model(df, subj, x, y):\n",
      "    \"\"\"\n",
      "    return a dict of model variables for the model constructor\n",
      "    df: dataframe of observations, each with associated subject id\n",
      "    subj: name of subject id column in df\n",
      "    x: name of predictor column\n",
      "    y: name of observed column\n",
      "    \"\"\"\n",
      "    # population regression parameters beta_0, beta_1\n",
      "    beta_pop_mu = mc.Normal(\"pop_mu\", mu=0, tau=1e-12, value=(0,0), size=2)\n",
      "    beta_pop_tau = mc.Gamma(\"pop_tau\", alpha=.001, beta=.001, value=(.001,.001), size=2)\n",
      "\n",
      "    # subject regression betas are normally distributed around population betas\n",
      "    nsubj = len(df[subj].unique())\n",
      "    beta_subj = mc.Container([\n",
      "     mc.Normal(\"beta_0\", mu=beta_pop_mu[0], tau=beta_pop_tau[0], value=np.zeros(nsubj)*.01, size=nsubj),\n",
      "     mc.Normal(\"beta_1\", mu=beta_pop_mu[1], tau=beta_pop_tau[1], value=np.zeros(nsubj)*.01, size=nsubj)])\n",
      "\n",
      "    # The distribution of each y_i has mean that is a deterministic function of the x_i\n",
      "    # and the subject regression parameters\n",
      "    mu = mc.Container(\n",
      "        [mc.LinearCombination(\"mu_%d\" % idx, (1, row[x]), (beta_subj[0][row[subj]], \n",
      "          beta_subj[1][row[subj]])) for (idx,row) in df.iterrows()])\n",
      "\n",
      "    # each subject has own constant variance prior\n",
      "    m = mc.Gamma(\"m\", alpha=1, beta=.1, value=1)\n",
      "    d = mc.Gamma(\"d\", alpha=1, beta=.1, value=1)\n",
      "    s = mc.Lambda(\"s\", lambda m=m, d=d: m**2 / d**2)\n",
      "    r = mc.Lambda(\"r\", lambda m=m, d=d: m / d**2)\n",
      "    tau_subj = mc.Gamma(\"tau_subj\", alpha=s, beta=r, value=np.ones(nsubj), size=nsubj)\n",
      "    \n",
      "    # likelihood for the data, normally distributed as mu_subj_i, tau_subj\n",
      "    y_obs = mc.Container(\n",
      "        [mc.Normal(\"y_obs_%d\" % idx, mu=mu[idx], tau=tau_subj[row[subj]], \n",
      "         value=row[y], observed=True) for (idx,row) in df.iterrows()])\n",
      "    \n",
      "    # posterior predictions, for generating confidence intervals\n",
      "    y_sim = mc.Container(\n",
      "       [mc.Normal(\"y_sim_%d\" % idx, mu=mu[idx], tau=tau_subj[row[subj]]) \n",
      "\t    for (idx,row) in df.iterrows()])\n",
      "    \n",
      "    return mc.Model(input=locals())\n",
      "\n",
      "def plot_group_regressions(group, title):\n",
      "    colors = ['b', 'k', 'g', 'r']\n",
      "    for id in group.subjID.unique():\n",
      "        idxs = (group.subjID == id) # boolean vector selects subsets of group rows \n",
      "        plot_regression(group.time[idxs], group.retention[idxs], list(group.mu[idxs]), group.tau[idxs].iloc[0], \n",
      "                        y_sim=list(group.y_sim[idxs]), titlestr=title, color=colors[id])\n",
      "    legend()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 289
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M = make_subj_model(group1, 'subjID', 'time', 'retention')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 253
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "group1['mu'] = list(M.mu) # cast container to list\n",
      "group1['tau'] = [M.tau_subj[row['subjID']] for (idx, row) in group1.iterrows()]\n",
      "group1['y_sim'] = list(M.y_sim) # cast container to list\n",
      "print group1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "    group  subjID  time  retention     mu          tau     y_sim\n",
        "0       1       0     0        100   mu_0  tau_subj[0]   y_sim_0\n",
        "1       1       0     3        102   mu_1  tau_subj[0]   y_sim_1\n",
        "2       1       0     4         87   mu_2  tau_subj[0]   y_sim_2\n",
        "3       1       0    10         89   mu_3  tau_subj[0]   y_sim_3\n",
        "4       1       0    15         57   mu_4  tau_subj[0]   y_sim_4\n",
        "5       1       0    20         48   mu_5  tau_subj[0]   y_sim_5\n",
        "6       1       0    25         43   mu_6  tau_subj[0]   y_sim_6\n",
        "7       1       0    30         33   mu_7  tau_subj[0]   y_sim_7\n",
        "8       1       1     0        100   mu_8  tau_subj[1]   y_sim_8\n",
        "9       1       1     3         95   mu_9  tau_subj[1]   y_sim_9\n",
        "10      1       1     4         91  mu_10  tau_subj[1]  y_sim_10\n",
        "11      1       1    10         62  mu_11  tau_subj[1]  y_sim_11\n",
        "12      1       1    15         52  mu_12  tau_subj[1]  y_sim_12\n",
        "13      1       1    20         55  mu_13  tau_subj[1]  y_sim_13\n",
        "14      1       1    25         45  mu_14  tau_subj[1]  y_sim_14\n",
        "15      1       1    30         42  mu_15  tau_subj[1]  y_sim_15\n",
        "16      1       2     0        100  mu_16  tau_subj[2]  y_sim_16\n",
        "17      1       2     3        112  mu_17  tau_subj[2]  y_sim_17\n",
        "18      1       2     4         72  mu_18  tau_subj[2]  y_sim_18\n",
        "19      1       2    10         63  mu_19  tau_subj[2]  y_sim_19\n",
        "20      1       2    15         49  mu_20  tau_subj[2]  y_sim_20\n",
        "21      1       2    20         45  mu_21  tau_subj[2]  y_sim_21\n",
        "22      1       2    25         29  mu_22  tau_subj[2]  y_sim_22\n",
        "23      1       2    30         36  mu_23  tau_subj[2]  y_sim_23\n",
        "24      1       3     0        100  mu_24  tau_subj[3]  y_sim_24\n",
        "25      1       3     3        110  mu_25  tau_subj[3]  y_sim_25\n",
        "26      1       3     4        129  mu_26  tau_subj[3]  y_sim_26\n",
        "27      1       3    10         71  mu_27  tau_subj[3]  y_sim_27\n",
        "28      1       3    15         57  mu_28  tau_subj[3]  y_sim_28\n",
        "29      1       3    25         29  mu_29  tau_subj[3]  y_sim_29\n",
        "30      1       3    30         32  mu_30  tau_subj[3]  y_sim_30\n"
       ]
      }
     ],
     "prompt_number": 278
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mc.MAP(M).fit()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 270
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot_group_regressions(group1, \"MAP estimate\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=201.634374, max=201.634374\n",
        "CI: min=207.652105, max=207.652105\n",
        "CI: min=253.353066, max=253.353066\n",
        "CI: min=240.729917, max=240.729917\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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DXsppLxNympARsngdRttiAeb8wERExF4JC8bZs2f54x//yLPPPkskEmHVqlXp\nyJWR1MOwl3Lay4ScJmSEzO1hJCwYGzZs4Ktf/Sp9+vSJr8UQEZHsk7BgBAKBdiusfT5fF3tLV9TD\nsJdy2suEnCZkhCy+H0Zzc3O7cSwWS1kYERFxr4QFY/DgwWzfvp1IJMKOHTsYnqGVMx3Uw7CXctrL\nhJwmZIQs7mHMmDGD/v37EwgEKCwsdP8lOEREJCWS6mJPmDCBCRMmpDpLxlMPw17KaS8TcpqQEbJ4\nHUYkEmk33rx5c8rCiIiIeyUsGH/605/ajRsaGlIWJtOph2Ev5bSXCTlNyAhZ3MPQp6JERAS66GHU\n1dURiUQ4d+4ctbW1WJZFNBrVEcZlUA/DXsppLxNympARMreH0WnBqKysJBwOc+zYMT744IOWnf3+\nDm9gJCIima/TgnHjjTcCLesw9Akpe5w4cYLBBtxxr6amxoh3csppLxNympARWnoY7k/ZfQl7GCoW\nIiICSRQMaLmPd3l5OZFIhOrq6lRnyljqYdhLOe1lQk4TMkIWX0tqx44dHD16lMOHD+P3+3nnnXfS\nkUtERFwmYcE4evQo06ZNi9+mtWfPnikPlam0DsNeymkvE3KakBGyeB2GLmcuIiKQRMEIBoOEwy2f\nKA6Hw1rIdxnUw7CXctrLhJwmZITM7WEkvPjgnDlz+MMf/kBNTQ3RaJS5c+emI5eIiLhMwoJx8uRJ\nvv3tb6chSubTOgx7Kae9TMhpQkbI4nUYu3btajf++OOPUxZGRETcq9u3aL2wgEjy1MOwl3Lay4Sc\nJmSEzO1hJCwY06ZN489//nM6soiIiIslLBi///3vOXv2LC+++CIvvvgi77//fjpyZSStw7CXctrL\nhJwmZITMXYeRsOl96623ct1118XHF95QSUREskPCgtG2WADcdttttodYu3Yt0WgUgNGjRzNx4kSg\n5d1EWVkZPp+PmTNnMnToUNtfO53Uw7CXctrLhJwmZIQsvB9GOgUCAW655ZaLtpeXl7N48WIAVq9e\nTWlpabqjiYjIeUldrTbVotEoL7/8Mi+99BIVFRXx7fn5+fHHubm5TkSzlXoY9lJOe5mQ04SMkMU9\njHRou3p8/fr18ceWZcUf5+TkpDWTiIi0l9aCUVtbywsvvNBu27x58xje5jPLbQtDa18DwOPxdPnc\n27dvZ/r06fHHgLvGwSCzzvcwWt8ltZ6Pddu4dZtb8pg+1nzaNy4sLHRVnk7HffrQyhW/f7oYd4fH\navs23iHQzxLoAAAKvElEQVSHDh1ixIgRAKxbt4558+YBsGrVKhYuXIhlWaxbt67T+4mXlZVRXFyc\ntryXJBgkb+lSPAZcGkRELk900CDCjzzidIyEKioqmDVrVtL7u+KU1KFDhygvLwdg8uTJ8e0lJSWs\nWLECy7KYPXu2U/Fso2tJ2Us57WVCThMyQuZeS8oVBWPGjBkdbi8qKmLRokVpTiMiIh1xxaeksoXW\nYdhLOe1lQk4TMkIWX0tKREQEVDDSSusw7KWc9jIhpwkZIXPXYahgiIhIUlQw0kg9DHspp71MyGlC\nRlAPQ0REspwKRhqph2Ev5bSXCTlNyAjqYYiISJZTwUgj9TDspZz2MiGnCRlBPQwREclyKhhppB6G\nvZTTXibkNCEjqIchIiJZTgUjjdTDsJdy2suEnCZkBPUwREQky6lgpJF6GPZSTnuZkNOEjKAehoiI\nZDkVjDRSD8NeymkvE3KakBHUwxARkSyngpFG6mHYSzntZUJOEzKCehgiIpLlVDDSSD0MeymnvUzI\naUJGUA9DRESynApGGqmHYS/ltJcJOU3ICOphiIhIllPBSCP1MOylnPYyIacJGUE9DBERyXIqGGmk\nHoa9lNNeJuQ0ISOohyEiIllOBSON1MOwl3Lay4ScJmQE9TBsE4vFiEaj6X5ZERG5TGktGBs2bOA/\n/uM/OHbsWLvtNTU1/OEPf2DlypV89tlnCbebSj0MeymnvUzIaUJGUA/DFnPnzuXmm2++aHt5eTmL\nFy/mG9/4Bu+8807C7SIikn6u6GHk5+fHH+fm5ibcbir1MOylnPYyIacJGSFzexh+pwMAWJYVf5yT\nk5Nwu4gx2vwbFjFdSgpGbW0tL7zwQrtt8+bNY3gnVbdtE9zj8STc3pHt27czffr0+GPAXeNQiAmN\njRQNGsTho0cBuLKoCMB14527djFw0CDX5Ols3LrNLXk6HHs87Ny5s2U+r7ii5e+PHGn5e5eNW7e5\nJU9H4wuzOp2ns/FHx45Rcj6nK37/dDHuDo9lpfctUGVlJX379qXo/H8ugFWrVrFw4UIsy2LdunXM\nnz+/y+0XKisro7i4OC35L1lzM8fvv59h48Y5nSShQ4cOMWLECKdjJKSc9jIhpwkZAfafOsWIn/7U\n6RgJVVRUMGvWrKT3T+spqU2bNlFdXU0gEGDkyJHMmDEDgJKSElasWIFlWcyePTu+f2fbTXXlmDFY\nXle0jbo0fNQoTDiRopz2MiGnCRkBrrr2WjJx8UBaC0Znv/SLiopYtGhR0ttNZQ0YAL17Ox1DRFLM\nGjDA6Qgp4f63uxnkowMHnI6QlP379jkdISnKaS8TcpqQEaByzx6nI6SECoaIiCRFBSONRo8Z43SE\npIwbP97pCElRTnuZkNOEjAATrrnG6QgpoYIhIiJJUcFII/Uw7KWc9jIhpwkZQT0MERHJcioYaaQe\nhr2U014m5DQhI6iHISIiWU4FI43Uw7CXctrLhJwmZAT1MEREJMu54vLm2WL06NF4QiGnYyQ0fuRI\nUE7bKKd9TMgIMGHSJGJOh0gBFYx08fmIXXst9OjhdBIRSTGroMDpCCmhU1JptHv3bqcjJGXnzp1O\nR0iKctrLhJwmZASoePddpyOkhAqGiIgkJe03UEoFI26gFI3iKy/XKSmRLBArKMAyYN2Vq2+glNU8\nHiw33Asjwa1u085NeZSlY8rSbdbAgU5HSAkVjHTxetlWV3dJ99FNt7b3R3cz5bSXCTlNyAjm5Owu\n9TBERCQp6mGIiGSp7vYwdIQhIiJJUcFIo+3btzsdISnKaS/ltI8JGcGcnN2lgiEiIklRD0NEJEup\nhyEiIimhgpFGppzXVE57Kad9TMgI5uTsLhUMERFJinoYIiJZSj0MERFJibQXjFgsRjQaTffLuoIp\n5zWV017KaR8TMoI5ObsrrRcf3LBhA9XV1ZSWllJUVBTfvnbt2ngRGT16NBMnTgSgpqaGsrIyfD4f\nM2fOZOjQoemMKyIibaS9h1FZWUnfvn3bFYyNGzdyyy23XLTvK6+8woIFCwBYvXo1paWlHT6nehgi\nIt1n5P0wotEoL7/8MpZlMWrUqPgv//z8/Pg+ubm5TsUTERFc0vSeO3cuX/va17jjjjs4duxYfHvb\ng5+cnBwnotnKlPOaymkv5bSPCRnBnJzdlZIjjNraWl544YV22+bNm8fw4cMTfm3bwtC2Oe7p4k5b\nffv2paKi4hKSpld+fr5y2kg57WVCThMygjk5+/bt2639U1IwBg4cyH333Zf0/ocOHWLEiBEANDU1\nxbcHg0Gg5Uij9XFHpkyZcolJRUQkWWntYWzatInq6moCgQAjR45kxowZQEvBKC8vB2Dy5Mnx/UtK\nSlixYgWWZTF79ux0RhURkQtkxEpvERFJPVc0vUVExP1UMMQYplwlwJScIt3linUYduhstbgbmLJi\n3c1z2NFVAtw4rx3ldOu87tmzh3379hGLxZg6dSpXXnml6+a0o4xunM+33norviRg+PDhTJkyxXVz\nCR3n7NZ8WhnitddeczpCp9asWRN/vGrVKgeTdM3Nc2hZlrVnzx7ryJEj8bFb5/XCnG6d161bt8Yf\nv/rqq5ZluW9OO8ro1vls9ec//9myLPfN5YVac3ZnPjPmCKOz1eJuYMqKdTfPYUc0r5en9VOKbblt\nTjvK6Nb5PHjwIC+99BILFy4E3DeXrS7M2Z35zJiCMXfu3Pjj9evXO5jkYpYhK9bdPIcd0bzaY+PG\njXz5y18G3DunbTO6dT5HjhzJ/fffz5o1a7jqqqtcO5cX5uzOfBpXMJJZRe6mHw4kv2LdTdw2hx3R\nvF6+rVu3MnbsWAYOHAi4c04vzNiW2+YzEAjQq1cvwJ1z2aptzrYSzadxBaOzVeSdrRZ3g2RXrDvN\nzXPYEc3r5XnjjTcYMmQII0eOjG9z25x2lNGN83nq1Cn69+8PfH6U5ra5hI5zdmc+jSsYnelstbgb\nmLJi3c1z2NFVAtw4rx3ldOO8Hj9+nDfffJMvfOELVFVVUV9fz5IlS1w1p51ldON8vvnmm4RCIQCu\nu+46wJ3/7zvK2Z351EpvERFJihbuiYhIUlQwREQkKSoYIiKSFBUMERFJigqGiIgkRQVDRESSooIh\n0k3r1q3r9O9+/etfc+LEiTSmEUkfFQyRbupq1e6dd95Jv3790phGJH20cE8kSZFIhPXr17Nz5874\nPQPGjh3LNddcQ3NzMxs2bODAgQMsWbKEQYMGAS337HjyyScZMWIEsViM3NxccnNzCQQCLFiwAIBt\n27Zx/PhxcnNzaWpqYu7cufTu3dux71OkMxlzaRCRVPP7/cyfP5+mpiZKS0vb/V1ubi4LFixgy5Yt\n7bYXFhYybtw4Fi1axPHjx9m5cydz5syJX0CzsrISr9fL17/+dQDC4TBr1qyJj0XcRAVDJMX8fn/8\nz9b7IrRevbS6upqmpiZWr14d3//cuXPpDymSBBUMEQdde+211NTUMHXq1Pi2SCTiYCKRzqlgiHTT\nkCFDWL16NV6vl0gkwrRp06itreXAgQNUV1dz5MgRevbsydSpU/F4PFRVVbF3716GDBnCrl27mD59\nOsFgkD179nDNNddw6tSp+PO13kOh9W5oIm6ipreIiCRFH6sVEZGkqGCIiEhSVDBERCQpKhgiIpIU\nFQwREUmKCoaIiCRFBUNERJKigiEiIkn5/64cOfGlJAwhAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1106c6690>"
       ]
      }
     ],
     "prompt_number": 290
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "S = mc.MCMC(input=M, db='ram')\n",
      "S.sample(50000, burn=2000, thin=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 90 of 50000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 179 of 50000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 270 of 50000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 365 of 50000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  0%                  ] 460 of 50000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 554 of 50000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 647 of 50000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 735 of 50000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  1%                  ] 823 of 50000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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     "collapsed": false,
     "input": [
      "plot_group_regressions(group1, \"Subject regressions\")\n",
      "show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "CI: min=17.199729, max=59.267751\n",
        "CI: min=49.853338, max=72.021280\n",
        "CI: min=20.221401, max=69.481680\n",
        "CI: min=66.263943, max=93.399557\n",
        "CI: min=20.185319, max=47.970193"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "CI: min=71.930313, max=83.799921\n",
        "CI: min=24.730844, max=59.288972\n",
        "CI: min=95.238683, max=107.042296\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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KqKpEVaUb89Y0zfU2nF+xJnSCih/DEkhFIa/rpINBimt01ejg7BGhqio+n49Q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\nDz/88KaFk6TGcP3hp2PWPoVfyXuvOoxOT6etxbIs5ubmyOVyWJbVNv1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       "text": [
        "<matplotlib.figure.Figure at 0x1431a5c90>"
       ]
      }
     ],
     "prompt_number": 294
    }
   ],
   "metadata": {}
  }
 ]
}