{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayesian Zig Zag\n", "\n", "Developing probabilistic models using grid methods and MCMC.\n", "\n", "Thanks to Chris Fonnesback for his help with this notebook, and to Colin Carroll, who added features to pymc3 to support some of these examples.\n", "\n", "Copyright 2018 Allen Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# If we're running on Colab, install empiricaldist\n", "# https://pypi.org/project/empiricaldist/\n", "\n", "import sys\n", "IN_COLAB = 'google.colab' in sys.modules\n", "\n", "if IN_COLAB:\n", " !pip install empiricaldist\n", " !pip install pymc3>=3.8" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "import numpy as np\n", "import pymc3 as pm\n", "\n", "import warnings\n", "warnings.filterwarnings(\"ignore\", category=UserWarning)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Simulating hockey\n", "\n", "I'll model hockey as a Poisson process, where each team has some long-term average scoring rate, $\\lambda$, in goals per game.\n", "\n", "For the first example, I'll assume that $\\lambda$ is somehow known to be 2.4. Since regulation play (as opposed to overtime) is 60 minutes, we can compute the goal scoring rate per minute." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.04" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam_per_game = 2.4\n", "min_per_game = 60\n", "lam_per_min = lam_per_game / min_per_game\n", "lam_per_min" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we assume that a goal is equally likely during any minute of the game, and we ignore the possibility of scoring more than one goal in the same minute, we can simulate a game by generating one random value each minute." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "def simulate_game(p, n=60):\n", " goals = np.random.choice([0, 1], n, p=[1-p, p])\n", " return np.sum(goals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And simulate 10 games." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "size = 10\n", "sample = [simulate_game(lam_per_min) for i in range(size)]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we simulate 1000 games, we can see what the distribution looks like. The average of this sample should be close to `lam_per_game`." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2.35, 2.4)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "size = 1000\n", "sample_sim = [simulate_game(lam_per_min) for i in range(size)]\n", "np.mean(sample_sim), lam_per_game" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PMFs\n", "\n", "To visualize distributions, I'll start with a probability mass function (PMF).\n", "\n", "I'll use the `Pmf` object from `empiricaldist`, which is a subtype of a Pandas `Series`.\n", "\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ "0 0.116\n", "1 0.218\n", "2 0.228\n", "3 0.207\n", "4 0.142\n", "5 0.055\n", "6 0.029\n", "7 0.003\n", "8 0.001\n", "9 0.001\n", "dtype: float64" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from empiricaldist import Pmf\n", "\n", "pmf_sim = Pmf.from_seq(sample_sim)\n", "pmf_sim" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the distribution looks like." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "def set_colors():\n", " \"\"\"Set the color cycle for goals\"\"\"\n", " plt.gca().set_prop_cycle(color=['#2ca02c', '#9467bd',])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def decorate_goals(ylabel='PMF'):\n", " \"\"\"Decorate the axes.\"\"\"\n", " plt.xlabel('Number of goals')\n", " plt.ylabel(ylabel)\n", " plt.title('Distribution of goals scored')\n", " plt.legend()" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "pmf_sim.bar(label='simulation')\n", "decorate_goals()\n", "\n", "plt.savefig('zigzag1.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poisson process\n", "\n", "For large values of `n`, the process we just simulated converges to the Poisson distribution with parameter `mu = n * p`, which is also `mu = lam_per_game`.\n", "\n", "We can use NumPy to generate a sample from a Poisson distribution." ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.377" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = 60\n", "p = lam_per_min\n", "mu = n * p\n", "sample_poisson = np.random.poisson(mu, size)\n", "np.mean(sample_poisson)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And confirm that the results are similar to what we got from the model." ] }, { "cell_type": "code", "execution_count": 112, "metadata": {}, "outputs": [], "source": [ "from empiricaldist import Pmf\n", "\n", "def plot_pmf(sample, **options):\n", " \"\"\"Compute and plot the PMF of a sample.\"\"\"\n", " Pmf.from_seq(sample).bar(**options)" ] }, { "cell_type": "code", "execution_count": 113, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_pmf(sample_poisson, label='Poisson sample', alpha=0.7)\n", "decorate_goals()\n", "\n", "plt.savefig('zigzag2.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But plotting PMFs is a bad way to compare distributions. It's better to use the cumulative distribution function (CDF)." ] }, { "cell_type": "code", "execution_count": 114, "metadata": {}, "outputs": [], "source": [ "from empiricaldist import Cdf\n", "\n", "def plot_cdf(sample, **options):\n", " \"\"\"Compute and plot the CDF of a sample.\"\"\"\n", " Cdf.from_seq(sample).plot(**options)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Comparing CDFs makes it clearer that the results from the simulation are consistent with the Poisson model." ] }, { "cell_type": "code", "execution_count": 116, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(sample_poisson, color='gray', label='Poisson')\n", "plot_cdf(sample_sim, label='simulation')\n", "decorate_goals('CDF')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Warming up PyMC\n", "\n", "Soon we will want to use `pymc3` to do inference, which is really what it's for. But just to get warmed up, I will use it to generate a sample from a Poisson distribution." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " goals = pm.Poisson('goals', mu)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000" ] }, "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(trace['goals'])" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.419" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_pymc = trace['goals']\n", "np.mean(sample_pymc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This example is like using a cannon to kill a fly. But it help us learn to use the cannon." ] }, { "cell_type": "code", "execution_count": 119, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_pmf(sample_poisson, label='Poisson', alpha=0.5)\n", "plot_pmf(sample_pymc, label='PyMC', alpha=0.5)\n", "decorate_goals('CDF')\n", "\n", "plt.savefig('zigzag3a.png', dpi=150)" ] }, { "cell_type": "code", "execution_count": 120, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(sample_poisson, label='Poisson')\n", "plot_cdf(sample_pymc, label='PyMC')\n", "decorate_goals('CDF')\n", "\n", "plt.savefig('zigzag3b.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Evaluating the Poisson distribution\n", "\n", "One of the nice things about the Poisson distribution is that we can compute its PMF TBLlytically, and SciPy provides an implementation." ] }, { "cell_type": "code", "execution_count": 121, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy.stats import poisson\n", "\n", "xs = np.arange(11)\n", "mu = 2.4\n", "\n", "ps = poisson.pmf(xs, mu)\n", "set_colors()\n", "plt.bar(xs, ps, label='Poisson PMF')\n", "decorate_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the probability of scoring 4 goals in a game if the long-term rate is 2.4 goals per game." ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.1254084986272838" ] }, "execution_count": 122, "metadata": {}, "output_type": "execute_result" } ], "source": [ "data = 4\n", "poisson.pmf(data, mu)" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.00000000e+00, 1.81555589e-05, 2.50026149e-04, 1.08944747e-03,\n", " 2.96358283e-03, 6.22748873e-03, 1.11145981e-02, 1.77229800e-02,\n", " 2.60231799e-02, 3.58778394e-02, 4.70665182e-02, 5.93114635e-02,\n", " 7.23017337e-02, 8.57142371e-02, 9.92310359e-02, 1.12552785e-01,\n", " 1.25408499e-01, 1.37562022e-01, 1.48815687e-01, 1.59011643e-01,\n", " 1.68031356e-01, 1.75793720e-01, 1.82252178e-01, 1.87391193e-01,\n", " 1.91222339e-01, 1.93780255e-01, 1.95118616e-01, 1.95306276e-01,\n", " 1.94423652e-01, 1.92559429e-01, 1.89807621e-01, 1.86264988e-01,\n", " 1.82028837e-01, 1.77195165e-01, 1.71857150e-01, 1.66103943e-01,\n", " 1.60019753e-01, 1.53683172e-01, 1.47166728e-01, 1.40536620e-01,\n", " 1.33852618e-01, 1.27168093e-01, 1.20530156e-01, 1.13979883e-01,\n", " 1.07552602e-01, 1.01278229e-01, 9.51816428e-02, 8.92830728e-02,\n", " 8.35984979e-02, 7.81400478e-02, 7.29163965e-02, 6.79331437e-02,\n", " 6.31931800e-02, 5.86970320e-02, 5.44431858e-02, 5.04283870e-02,\n", " 4.66479169e-02, 4.30958446e-02, 3.97652554e-02, 3.66484555e-02,\n", " 3.37371552e-02, 3.10226309e-02, 2.84958667e-02, 2.61476786e-02,\n", " 2.39688206e-02, 2.19500757e-02, 2.00823331e-02, 1.83566515e-02,\n", " 1.67643118e-02, 1.52968592e-02, 1.39461360e-02, 1.27043063e-02,\n", " 1.15638747e-02, 1.05176971e-02, 9.55898817e-03, 8.68132323e-03,\n", " 7.87863661e-03, 7.14521711e-03, 6.47570069e-03, 5.86506121e-03,\n", " 5.30859947e-03, 4.80193100e-03, 4.34097292e-03, 3.92193024e-03,\n", " 3.54128163e-03, 3.19576513e-03, 2.88236372e-03, 2.59829116e-03,\n", " 2.34097794e-03, 2.10805767e-03, 1.89735382e-03, 1.70686702e-03,\n", " 1.53476276e-03, 1.37935980e-03, 1.23911899e-03, 1.11263277e-03,\n", " 9.98615235e-04, 8.95892745e-04, 8.03395164e-04, 7.20147598e-04,\n", " 6.45262707e-04])" ] }, "execution_count": 123, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mus = np.linspace(0, 15, num=101)\n", "likelihood = poisson.pmf(4, mus)\n", "likelihood" ] }, { "cell_type": "code", "execution_count": 124, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(mus, likelihood)\n", "plt.xlabel('Goals per game (mu)')\n", "plt.ylabel('Likelihood');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bayesian inference with grid approximation\n", "\n", "Ok, it's finally time to do some inference! The function we just wrote computes the likelihood of the data, given a hypothetical value of `mu`:\n", "\n", "$\\mathrm{Prob}~(x ~|~ \\mu)$\n", "\n", "But what we really want is the distribution of `mu`, given the data:\n", "\n", "$\\mathrm{Prob}~(\\mu ~|~ x)$\n", "\n", "If only there were some theorem that relates these probabilities!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll start with a uniform prior just to keep things simple. We'll choose a better prior later." ] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "101" ] }, "execution_count": 125, "metadata": {}, "output_type": "execute_result" } ], "source": [ "uniform_prior = Pmf(1, mus)\n", "uniform_prior.normalize()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initially `uniform_prior` represents the prior distribution of `mu`." ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [], "source": [ "def decorate_rate(ylabel='PDF'):\n", " \"\"\"Decorate the axes.\"\"\"\n", " plt.xlabel('Goals per game (mu)')\n", " plt.ylabel(ylabel)\n", " plt.title('Distribution of goal scoring rate')\n", " \n", " handles, labels = plt.gca().get_legend_handles_labels()\n", " if len(labels):\n", " plt.legend()" ] }, { "cell_type": "code", "execution_count": 127, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "uniform_prior.plot(label='prior')\n", "decorate_rate()\n", "\n", "plt.savefig('zigzag4.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can update it with the data and plot the posterior." ] }, { "cell_type": "code", "execution_count": 128, "metadata": {}, "outputs": [], "source": [ "data = 4\n", "likelihood = poisson.pmf(data, mus)" ] }, { "cell_type": "code", "execution_count": 129, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.06595319262654087" ] }, "execution_count": 129, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior1 = uniform_prior * likelihood\n", "posterior1.normalize()" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "posterior1.plot(label='posterior')\n", "decorate_rate()\n", "\n", "plt.savefig('zigzag5.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With a uniform prior, the posterior is the likelihood function, and the MAP is the value of `mu` that maximizes likelihood, which is the observed number of goals, 4.\n", "\n", "This result is probably not reasonable, because the prior was not reasonable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A better prior\n", "\n", "To construct a better prior, I'll use a Gamma distribution with parameters chosen to be consistent with previous playoff games." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use `make_gamma_dist` to construct a prior suite with the given parameters." ] }, { "cell_type": "code", "execution_count": 131, "metadata": {}, "outputs": [], "source": [ "from scipy.stats import gamma\n", "\n", "def make_gamma_dist(xs, alpha, beta):\n", " \"\"\"Makes a Pmf based on a gamma distribution.\n", " \n", " xs: places to evaluate the PDF\n", " alpha, beta: parameters of the distribution\n", " \n", " returns: Suite\n", " \"\"\"\n", " ps = gamma(a=alpha, scale=1/beta).pdf(xs)\n", " pmf = Pmf(ps, xs)\n", " pmf.normalize()\n", " return pmf" ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4.4, 1.8)" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "alpha = 4.4\n", "beta = 1.8\n", "\n", "alpha, beta" ] }, { "cell_type": "code", "execution_count": 132, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2.4441837515202747, 1.1644330431484435)" ] }, "execution_count": 132, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mus = np.linspace(0, 10, num=101)\n", "gamma_prior = make_gamma_dist(mus, alpha, beta)\n", "gamma_prior.mean(), gamma_prior.std()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what it looks like." ] }, { "cell_type": "code", "execution_count": 133, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gamma_prior.plot(label='gamma prior')\n", "decorate_rate()\n", "\n", "plt.savefig('zigzag6.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can update this prior using the observed data." ] }, { "cell_type": "code", "execution_count": 134, "metadata": {}, "outputs": [], "source": [ "data = 4\n", "likelihood = poisson.pmf(data, mus)" ] }, { "cell_type": "code", "execution_count": 135, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.10917679489111866" ] }, "execution_count": 135, "metadata": {}, "output_type": "execute_result" } ], "source": [ "posterior2 = gamma_prior * likelihood\n", "posterior2.normalize()" ] }, { "cell_type": "code", "execution_count": 136, "metadata": {}, "outputs": [ { "data": { "image/png": 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3rNhSysS4MOalxzhWp5TRI1kyLYGXNx7m+wvSCQvWP02lBir97xxGjDGsX7+e1atXk5yczPXXX09ExBfzRzY0NJCfn8+qVat48sknuemmm0hMTDynjCOnzrK55CQ/uXKS4zft3TlvPO/sqmDF5lJun9u1lciUUn1P+ziGkdWrV7N69WoyMzO59dZbzwkaYI0rnzVrFrfffjsiwjPPPMP+/fvPSfOXXdbN/1dPH+N4/bJTorggdRRPf3oQj97XoYahP//5z+zZs6fzhG2sXLmSBx/su1vaNHAME4WFhaxfv55Zs2Zx3XXXnXdR+oSEBO68805iYmJYsWIFFRVfzGT79s4KpidH9moI7vncMXc8ZSfP8rc9eje5Gn56Ejg8Hg/XXHMNDzzwQLfy9IYGjmGgsbGRd955h5iYGBYvXtylJqbw8HC++c1vEhoayooVKzh79iwHq+vZfaSGa2Y4f7XRalFmPOOiR/LkumK/HUMpf+hoWvWOpk5/4IEHyMzMZPr06fzkJz/hs88+Y+XKlfz0pz8lOzuboqIiioqKWLx4MbNmzWLevHns3bsXgG9961v86Ec/4vLLL+f+++/n2Wef5b777gPg0KFDLFiwgOnTp7NgwQIOHz7cbp7e0D6OYeCDDz6gpqaG22+/Hbe767/y0NBQrr/+ep555hnefPNNjsVZN5B+ZXpiJzl7zhUg3H5JGv+6Mp9th0+SM3aU346lhqZfvJ3PnvJaR8vMHBPBv351aqfp2k6r/pvf/IbHH3/8S1On33rrrbz55pvs3bsXEeHUqVNERUVxzTXXcPXVV3PdddcBsGDBAh577DHS09PZuHEj3/3ud/nggw8A2L9/P++//z4ul4tnn3328zrcd9993Hrrrdx22208/fTTfP/73+fPf/7zl/L0hl5xDHGHDx9m06ZNzJ49m5SUlM4ztJGcnMzixYvZv/8Ar24oYnbqaBIjR/ihpl/4u1nJjAh0sWJzaeeJlRpA2k6rvmbNmnanTo+IiCAkJIQ777yTN954g5EjR36prNOnT/PZZ59x/fXXk52dzXe+851zmo2vv/76dgPA+vXrWb58OQC33HLLOWt6dJSnu/SKYwgzxvDOO+8QGRnJggULelxObm4uG/eVUZ7n5eYL2x+i66SwYDdfmZ7I2zvL+b9XZxKqQ3NVN3TlysBfujrS0O12s2nTJtasWcMrr7zC73//+8+vJFp5vV6ioqLYsWNHu2V0ddp13zo5NVW7XnEMYQcOHODYsWNcccUVBAUF9bgcEaE2Kh3BYA5v6/ad5j1xwwUp1De18BddYlYNIm2nVV+4cGG7U6efPn2ampoali5dym9/+9vPg0N4eDh1dXUAREREkJaW9vnSscYYdu7c2WkdLr74Yl555RUAXnrppfNO7d5TGjiGsA0bNhAeHs7Uqb3/Brau6CQZMUFUlx3sk/l4cseNYnxMKH/aos1VavBoO636D3/4w3anTq+rq+Pqq69m+vTpXHrppTz00EMA3Hjjjfz6179m5syZFBUV8dJLL/HUU08xY8YMpk6dyltvdb780MMPP8wzzzzD9OnTeeGFF/jd737n+HnqtOpD1NGjR3n88cdZuHDh522uPVVV28Ds/1jDT6+aRFDhR9TW1nLfffcRHBzsUG3b9+hHRfzne3tZ8+NLdW1ydV46rXrvDZhp1UVksYjsE5FCEfnSIGN75b+H7f27RCTH3h4iIptEZKeI5IvIL3zy/FxEjojIDvux1J/nMFht2LCBwMBAcnJyel3W2gPVAFw6KY6lS5dy+vRpPvzww16X25m/m5WEK0BYoVcdSg0ofgscIuICHgGWAJnATSKS2SbZEiDdftwFPGpvbwSuMMbMALKBxfbSsq0eMsZk2493/XUOg1VdXR27d+8mOzubESN6PwJq7f5jxIQFkZkYQVJSEjk5OWzevJmTJ086UNuOxYWHcPnkOF7fekRXCFQDnk6r7ozZQKExptgY0wS8Aixrk2YZ8LyxbACiRCTRfn3aThNoP4Z+m5pDNm/ejNfrZc6cOZ0n7oTXa/iksJp56bEEBFijMy699FJEhLVr1/a6/M7ccEEK1acb+XjfMb8fSw1uw6HZ3V+6+975M3AkAb5tDGX2ti6lERGXiOwAqoDVxpiNPunus5u2nhaRdu8QE5G7RGSLiGw5dmz4fOi0tLSwdetWJk+ezOjRo3tdXl55DSfqm5g/6YuZcCMiIsjNzWXnzp2cOHGi18c4n8smxzJqZCBv7Sz363HU4BYSEsLx48c1ePSAMYbjx48TEhLS5Tz+HCDf3oDmtr/VDtMYY1qAbBGJAt4UkWnGmDys5qx/s9P9G/DfwO1fKsSYJ4AnwOoc7+E5DDolJSWcOXOG7OxsR8pbu98KuvPSY8/ZPnfuXLZu3cratWu59tprHTlWewJdASzJSuTNbUc40+RhZJDe06G+LDk5mbKyMobTl0QnhYSEkJyc3OX0/vwvLAN8b1VOBtp+bew0jTHmlIh8BCwG8owxn89+JyJPAu84WOdBLz8/n6CgICZOnOhIeWv3VzN1TAQxYeeOoAoLC+OCCy5gw4YNzJ07l5gY59bmaGvZjDH878bDrN5TybLsthetSkFgYCBpaToVf1/xZ1PVZiBdRNJEJAi4EVjZJs1K4FZ7dNUcoMYYUyEisfaVBiIyAlgI7LVf+06U9DVgePRGdUFLSwsFBQVMmTKlW3NSdaSuoZlth09y6aTYdvdfcskluN1uPv74414f63wuSB1NYmQIK3doc5VSA4HfAocxxgPcB6wCCoAVxph8EblbRO62k70LFAOFwJPAd+3ticCHIrILKwCtNsa0Xln8l4jstvddDvzQX+cw2Bw8eJCGhgYyM9sOXuuZz4qO4/Ea5ncQOEJDQ5k9ezZ5eXl+7esICBCunp7I2gPHOHWmyW/HUUp1jV8bjO2hsu+22faYz3MD3NtOvl3AzA7KvMXhag4Z+fn5BAcHM2HCBEfKW3fgGKFBrvPOUHvhhReyYcMGNmzYwNKl/rulZll2Ek+uO8hf845y0+yxfjuOUqpzOuXIENHS0sLevXsda6YC2FB8ggvSRhPk7vjPJDw8nKysLLZv386ZM2ccOW57po6JYHxMKG/tOOK3YyilukYDxxBRVFREQ0ODI/NSAZyob6Kw6jQXpHY+pPeiiy7C4/Hgz2ldRISvzhjDxoMnOFrT4LfjKKU6p4FjiNizZw8hISGMHz/ekfK2lFh9FrPTOg8ccXFxTJw4kU2bNvV6ScrzuSZ7DMagM+Yq1c80cAwBvs1UTizSArC55ARBrgCykiK7lP7iiy+mvr6eXbt2OXL89kyIDWNKQjjv5WngUKo/aeAYAo4cOUJjY+Pnq4w5YVPJSWakRBIS2LVAlJqaSkJCAuvXr/fr3btLpiWy5dBJqmq1uUqp/qKBYwgoKipCRBy7AepMk4f8IzVd6t9oJSJcdNFFVFdXU1xc7Eg92rMkKwFjYFX+Ub8dQyl1fho4hoDi4mKSkpK6NdfM+ew4fAqP13QrcABkZmYycuRINm/e7Eg92pMeF8aE2FD+mqeBQ6n+ooFjkGtoaODIkSOOdYoDbCo5gQjkjOv4/o32uN1ucnJy2L9/PzU1NY7Vx5eIsGRaIhuKj3P8dKNfjqGUOj8NHIPcwYMHMcY4dtMfwJaSk0xJiCByRGC38+bmWouF+XNo7pKsBLwGVu+p7DyxUspxGjgGuaKiIoKCgkhKcmbyP0+Ll22HT3JBaveuNlpFRkYyadIktm3b5rehuZmJEYwdPZJ3tblKqX6hgWOQKy4uJi0tzbFhuPnltZxpaul2/4avCy64gDNnzrBnzx5H6tSWiLAkK4HPCqupOdPsl2MopTqmgWMQO3HiBCdPnnS0f2OzfeNfbwLH+PHjiY6O9msn+ZJpiXi8htUF2lylVF/TwDGItQ57dbp/I2X0CBIiez5CS0TIzc2lrKyMo0f905w0IzmShIgQ/qbDcpXqcxo4BrGioiIiIyMdWSK21Y7SU+edDberZsyYgcvlYtu2bQ7U6stEhCunxrP2wDHONrX45RhKqfZp4BikvF4vBw8eZPz48Yi0twJv9x2taeBobQMzkqN6XdaIESPIzMxk165dNDf7px/iqqkJNDR7WXdAlwtVqi9p4BikKisraWxsJDU11bEyd5adAiB7bJQj5eXk5NDY2Eh+fr4j5bU1O200ESFu/qbDcpXqU34NHCKyWET2iUihiDzQzn4RkYft/btEJMfeHiIim0Rkp4jki8gvfPKMFpHVInLA/tn7dpVBqLS0FICxY51b1Ghn6SncAUJmYoQj5Y0bN47o6Gi/NVcFugJYkBHPmoJKPC1evxxDKfVlfgscIuICHgGWAJnATSLSdk3TJUC6/bgLeNTe3ghcYYyZAWQDi+01yQEeANYYY9KBNfbrYae0tJTw8HAiI7s2e21X7Cw7RUZiRJcnNuyMiJCTk0NpaSlVVVWOlNnWlZnxnDzTzOaSk34pXyn1Zf684pgNFBpjio0xTcArwLI2aZYBzxvLBiBKRBLt16ftNIH2w/jkec5+/hxwrR/PYcA6fPgwKSkpjvVveL2GXaU1zEhxLhCB1UkeEBDgt6uOSyfHEuwO4G97dHSVUn3Fn4EjCSj1eV1mb+tSGhFxicgOoApYbYzZaKeJN8ZUANg/49o7uIjcJSJbRGTLsWNDq/O0pqaG2tpaUlJSHCuzuLqeukaPIx3jvkJDQ8nIyGDXrl1+uZN8ZJCbeekx/C2/0q/TuSulvuDPwNHeV+G2/9kdpjHGtBhjsoFkYLaITOvOwY0xTxhjco0xubGxsd3JOuD5q38DIDslyrEyW82cOZOzZ8+yd+9ex8sGuDIzgSOnzrKnotYv5SulzuXPwFEG+H4lTgbKu5vGGHMK+AhYbG+qFJFEAPunfxrPB7DDhw8TGBhIfHy8Y2XuLDtFWLCb8bFhjpXZavz48URGRrJjxw7HywZYkBFHgMDf8nV0lVJ9wZ+BYzOQLiJpIhIE3AisbJNmJXCrPbpqDlBjjKkQkVgRiQIQkRHAQmCvT57b7Oe3AW/58RwGpNLSUpKSkhybnwqsK46spEhcAc70mfgSEbKzsykqKvLLdOvRYcHMGjdKZ8tVqo/4LXAYYzzAfcAqoABYYYzJF5G7ReRuO9m7QDFQCDwJfNfengh8KCK7sALQamPMO/a+B4FFInIAWGS/HjYaGxuprKx0tH+j0dPCnopaZvihmapVdnY2gN+uOhZlxrOnopayk2f8Ur5S6gtufxZujHkXKzj4bnvM57kB7m0n3y5gZgdlHgcWOFvTwePIkSMYYxzt3yioqKO5xZDt8IgqX1FRUaSlpbFjxw7mz5/v2GiwVgsz4vmPd/eypqCK2y5OdbRspdS59M7xQebw4cMAJCcnO1Zma8e4P684wOokP3XqFCUlJY6XPT7WWlJWm6uU8j8NHINMaWkpcXFxjq0vDlbgiAsPJiHCuTLbM2XKFIKDg/3YXJXAhuLj1JzVNTqU8icNHIOI1+ulrKzM0f4NgF1HapieHOl481FbgYGBZGVlsWfPHhoaGhwvf1FmHB6v4aN9w26gnVJ9SgPHIFJdXU1TU5OjgeNMk4eiY6eZluS//g1f2dnZeDwe8vLynC87ZRQxYUG8X6CBQyl/0sAxiJSXW7e4jBkzxrEyCypqMQamjembwDFmzBhiY2PZuXOn42W7AoQFU+L5aG8VTR6d9FApf9HAMYiUl5cTFBREdHS0Y2XmHbHutu6rK47WezrKysrwx1QwizLjqWv0sPHgccfLVkpZNHAMIhUVFSQmJhIQ4NyvLe9IDTFhQcRHBDtWZmemT5+OiPilk3xuegwhgQE6ukopP9LAMUi0tLRw9OhREhMTHS03r7yWqWP83zHuKywsjPT0dHbt2oXX62yTUkigi3npsby/Ryc9VMpfNHAMEseOHcPj8Tjav9HQ3MKByjqmJTmzcFN3ZGdnc/r0aYqKihwve1FGPOU1DTrpoVJ+ooFjkPBHx/j+yjo8XtNnHeO+Jk2axMiRI/3SXHVFRhwiaHOVUn6igWOQKC8vJzg4mNGjRztWZl93jPtyuVxkZWWxb98+zpxxdn6pmLBgcsaO4v0CDRxK+YMGjkGioqKCMWPGONoXkVdeQ0SIm+RRIxwrszuys7NpaWnxyz0dCzPiyTtSS/mps46XrdRwp4FjEPB4PH7pGM8/UsO0pL7tGPeVkJBAQkKCX5qrFmVaa5Ws0asOpRyngWMQqKqqwuv1Otq/0dzipeBoXb80U/nKzs6moqKCykpnP+AnxIaSFhPK37SfQynHaeAYBFo7xpOS2i7Z3nOFVadp8niZOqbvR1T5ysrKIiAgwPGrDhFhUWY8G4qPU9egkx4q5SS/Bg4RWSwi+0SkUEQeaGe/iMjD9v5dIpJjb08RkQ9FpEBE8kXkH3zy/FxEjojIDvux1J/nMBCUl5czYsQIIiOduzrIO2KtxDe1H0ZU+Ro5ciSTJ09m9+7dtLS0OFr2wox4mlsMa/dXO1quUsOd3wKHiLiAR4AlQCZwk4hktkm2BEi3H3cBj9rbPcCPjTEZwBzg3jZ5HzLGZNuPcxaKGorKy8sd7xjPL69lZJCLtJhQx8rsqRkzZlBfX09hYaGj5c4aN4pRIwP5256jjpar1HDnzyuO2UChMabYGNMEvAIsa5NmGfC8sWwAokQk0RhTYYzZBmCMqcNaeta5dppBpLm5maqqKkf7NwDyy2vISIzwyxrj3TVx4kRCQ0Mdb65yBQgLMuL5cG8VzS066aFSTvFn4EgCSn1el/HlD/9O04hIKtYysht9Nt9nN209LSKj2ju4iNwlIltEZIs/JtPrK1VVVRhjHB1R5fUa9pTXMq2f+zdauVwupk+fzv79+6mvr3e07EWZ8dQ2eNh08ISj5So1nPkzcLT3Vbbt5EHnTSMiYcDrwA+MMa3zRzwKTACygQrgv9s7uDHmCWNMrjEmNzY2tptVHziOHrWaWRISEhwrs/TkGeqbWsgcIIEDrNFVXq+X3bt3O1ru/PRYQgID+Fu+Nlcp5RR/Bo4ywHfFoWSgvKtpRCQQK2i8ZIx5ozWBMabSGNNijPECT2I1iQ1ZlZWVBAUFERUV5ViZe8qtGJyZ2L8d477i4uIYM2YM27dvd3RywhFBLuZOjGW1TnqolGP8GTg2A+kikiYiQcCNwMo2aVYCt9qjq+YANcaYCrF6gZ8CCowxv/HNICK+bTZfA5y/7XgAOXr0KAkJCY52jO+pqMUVIKTHhzlWphOys7OpqqqioqLC0XKvzLQmPcwv10kPlXKC3wKHMcYD3AeswurcXmGMyReRu0XkbjvZu0AxUIh19fBde/slwC3AFe0Mu/0vEdktIruAy4Ef+usc+psxhsrKSuLj4x0td095LRNiQwkJdDlabm9NmzYNl8vleCf5gow4AgS9GVAph7j9Wbg9VPbdNtse83lugHvbyfcJ7fd/YIy5xeFqDlgnT56kqanJ0f4NsK44LkxzbrJEp4wYMYKMjAx2797NlVdeidvtzJ9ndFgws8aNYvWeSn60aJIjZSo1nOmd4wOYPzrGT9Q3UVHTMKA6xn1lZ2fT0NDA3r17HS33yswECipqKT3h7Ey8Sg1HGjgGsKNHjyIiODkqrKBi4HWM+0pLSyMiIsLx5qrWSQ+1uUqp3tPAMYBVVlYSExNDYGCgY2W2jqjKSAx3rEwnBQQEkJ2dTVFRETU1NY6VmxoTyqT4MB2Wq5QDNHAMYK0jqpy0p6KWhIgQosOCHS3XSdnZ2QDs3LnT0XKvmprA5pITHD/d6Gi5Sg03GjgGqLNnz1JbW+uXEVUDtX+j1ahRo0hLS3P8no6rpibgNejKgEr1kgaOAcofHeMNzS0UHjtNZuLADhwAM2fO5NSpUxw8eNCxMqeOiSApagSr8jVwKNUbGjgGqNbA4eQVR2HVaVq8hoxBEDimTJlCSEgI27dvd6xMEWHxtAQ+OVDN6UaPY+UqNdxo4BigKisrCQsLIyzMubu7P59qZIA3VQEEBgaSlZVFQUEBZ886t274VVMTaGrx8uHeKsfKVGq40cAxQPmrY3xkkItxo0c6Wq6/5OTk0NLSwq5duxwrc9a4UcSEBbFKR1cp1WMaOAaglpYWjh075peO8YzECAIGwBocXZGQkEBiYqKjneSuAGtJ2Q/3VtHQ7OyKg0oNFxo4BqDq6mq8Xq+jgcMYQ0FF7YC9f6MjM2fOpLKy0tGJD6+amkB9UwufFemSskr1xHkDh4j8zef5z/xfHQVW/wY42zFedvIsdY2eAXvHeEeysrJwu91s3brVsTIvnhBDeLCb9/K0uUqpnujsisN3rovr/VkR9YXKykoCAgKIjo52rMz8AX7HeEdCQkKYNm0aeXl5NDY6c+NekDuABRlx/G1PpS4pq1QPdBY4dOWbflBVVUVsbCwul3PTnhdU1BIgMCVh4I+oamvWrFk0NTWRl+fc0itLsxI5daaZ9UXHHStTqeGis8AxXkRWisjbPs8/f/RFBYcjv6zBUVFLakwoI4IG1hocXZGUlERcXJyjzVXzJ8USGuTir3nOLhql1HDQWeBYhrWm9//n89z3cV4islhE9olIoYg80M5+EZGH7f27RCTH3p4iIh+KSIGI5IvIP/jkGS0iq0XkgP1zVNdPd+A7e/YsdXV1xMXFOVpuQUXtoLhjvD0iwqxZs6ioqKC8vO3qwz0TEuhiQUY8q/Ir8WhzlVLdct7AYYz5uPUB7AH2tNnWIRFxAY8AS4BM4CYRyWyTbAmQbj/uAh61t3uAHxtjMoA5wL0+eR8A1hhj0oE19usho6rKujHNycBRc7aZspNnB8Ud4x2ZPn06brebbdu2OVbm0qwETtQ3sfHgCcfKVGo46GxUlYjIv4pINbAX2C8ix0TkX7pQ9myg0BhTbIxpAl7BumrxtQx43lg2AFEikmiMqTDGbAMwxtRhLT2b5JPnOfv5c8C1XajLoOGPEVV7P1+DY/AGjtZO8t27dzvWSX7Z5DhGBrn4y25trlKqOzprqvoBMBe4wBgTbYwZBVwIXCIina31nQSU+rwu44sP/y6nEZFUYCaw0d4Ub4ypALB/tvvVXETuEpEtIrLl2LFjnVR14KisrCQkJITwcOdGP32+eNMgmGrkfHJycmhqamL37t2OlBcS6OLyKXGsyjtKi1fHgSjVVZ0FjluBm4wxn09RaowpBm62951Pe7cnt/3vPG8aEQkDXgd+YIyp7eR45xZizBPGmFxjTK6TK+j5W1VVFfHx8Yg4d3f3nopaRocGERc+cNfg6Irk5GTi4+PZsmWLY3eSfyUrkeP1TWw8qKOrlOqqzgJHoDHmS7fXGmOOAZ0tS1cGpPi8Tgba9mx2mEZEArGCxkvGmDd80lSKSKKdJhEYMrPVGWOoqqryQ8d4HZmJEY4Go/4gIlxwwQVUVlZSVlbmSJmXTY4lJDCAd7W5Sqku6yxwNPVwH8BmIF1E0kQkCLgRaDuEdyVwq92XMgeoMcZUiPUJ9xRQYIz5TTt5brOf3wa81Uk9Bo2amhqampocDRyeFi/7KusG3Y1/HcnKyiI4OJjNmzc7Ut7IIDcLpsTz191HdXSVUl3UWeCYISK1IlJnP2pbXwNZ58tojPEA9wGrsDq3Vxhj8kXkbhG52072LlAMFAJPAt+1t18C3AJcISI77MdSe9+DwCIROQAssl8PCf7oGC+urqfJ4x3UI6p8BQUFMWPGDPbs2UN9fb0jZX51xhiO1zexvlibq5TqCvf5dhpjenW3mDHmXazg4LvtMZ/nBri3nXyf0H7/B8aY48CC3tRroGoNHE5ecQyVjnFfubm5bNq0ie3btzN37txel3fZ5FjCgt2s3FHOvPTB0x+mVH/pbDhuiIj8QER+b49SOm+gUb1TVVVFVFQUwcHOdWLvKa8lyBXAhFjnFoTqb7GxsaSmprJ161a83t43L4UEurhyajzv5R+l0aNTrSvVmc6aqp4DcoHdwFK6cLe46jl/dIzvqaglPT6MQNfQmkE/NzeXU6dOUVhY6Eh518wYQ12Dh4/3DZ6h20r1l84+TTKNMTcbYx4HrgPm9UGdhiWPx0N1dbWjgeOLNTiGTjNVqylTphAeHs7GjRs7T9wFl0yMYdTIQN7epaOrlOpMZ4GjufWJ3dmt/KS6uhpjjKMd48fqGqk+3TSo7xjviMvlIjc3l+LiYpy4wTPQFcDSrETe31PJmSb9U1fqfLo6qqp1JNV0n1FW3bohT52fP+aoal2DY+oQ6hj3NWvWLFwul2NXHV+dMYazzS28XzBkbg1Syi86m+TQZYyJsB/hxhi3z/Oh+WnUT/yzeFMNABlDNHCEhoaSlZXFrl27OHv2bK/Lm506moSIEFbuOOJA7ZQauoZWj+kg5o/Fm/ZU1DJ29EgiQjq7yX/wuvDCC2lubnZk1tyAAOGa7DF8tO8YJ+o7u79VqeFLA8cA4Y8RVfnltUO2mapVQkIC48aNY/PmzY4Mzf3azCQ8XsPbO51Z90OpoUgDxwDQ0NBAbW2to4GjrqGZQ8fPDMmO8bYuvPBCampq2Lt3b6/LykiMICMxgje2a3OVUh3RwDEA+KNjvKCiDoCpSUM/cEyePJmoqCg2bNjgSHl/l5PEztJTFB077Uh5Sg01GjgGAP+MqLI6xqeOiXSszIEqICCAOXPmUFpaSmlpaecZOnHNjDEECLy5Ta86lGqPBo4BoLKykqCgICIjnfuQ31NeS/QQWIOjq2bOnElISAifffZZr8uKiwhhXnosb24/glcXeFLqSzRwDADHjh0jLi7O0fUy8stryRwz+Nfg6KqgoCByc3PZu3cvx4/3fpbbr+ckceTUWTaV6HrkSrWlgaOfGWOorKx0tJmqyePlQFXdsGim8nXhhRficrkc6eu4MjOB0CAXb2xzZsEopYYSDRz97PTp0zQ0NDg61ciBqjqaW8yQmkq9K8LCwpg+fTo7duzo9VodI4JcfGV6In/ZVUF9o05BopQvDRz9zB9rcOwZ4lONnM9FF12Ex+Nh06ZNvS7rhgtSqG9q4S868aFS5/Br4BCRxSKyT0QKReSBdvaLiDxs798lIjk++54WkSoRyWuT5+cicqSdlQEHJX/NUTUi0EVqdKhjZQ4WsbGxTJ48mU2bNtHY2NirsnLGjmJCbCivbun9SC2lhhK/BQ4RcQGPAEuATOAmEclsk2wJkG4/7gIe9dn3LLC4g+IfMsZk2493O0gzKFRVVREWFsbIkSMdK3NPeS0ZieG4AoZHx3hb8+bNo6GhgS1btvSqHBHhxgvGsvXQSQqr6hyqnVKDnz+vOGYDhcaYYmNME/AKsKxNmmXA88ayAYgSkUQAY8xaYMgPaXF6qhGv11qDY7j1b/hKSkpi/PjxrF+/nubm5s4znMfXcpJwBwivbtarDqVa+TNwJAG+/21l9rbupmnPfXbT1tMiMqq9BPZSt1tEZIsT6zX4g9fr/XworlNKjtdT1+hhelKUY2UORvPmzaO+vp7t27f3qpyYsGAWZcbz+rYjNHl6PxeWUkOBPwNHe+0kbe+m6kqath4FJgDZQAUdLGdrjHnCGJNrjMmNjY3tpMj+cfLkSTwej6MjqnYfse4Yn5Y0vIbitjVu3DhSUlL47LPPaGnp3Tri37gghRP1TawpqHSodkoNbv4MHGVAis/rZKDtlKNdSXMOY0ylMabFGOMFnsRqEhuU/DGiandZDcHuANLjwxwrczASEebNm0dNTQ27du3qVVnz02NJjAzhZW2uUgrwb+DYDKSLSJqIBAE3AivbpFkJ3GqPrpoD1Bhjzjv2sbUPxPY1IK+jtANdZWUlIoKTV0S7jtSQkRhBoEtHWk+cOJHExETWrVvXq6sOV4BwwwUprN1/jJLq3t0fotRQ4LdPF3uN8vuAVUABsMIYky8id4vI3Xayd4FioBDr6uG7rflF5GVgPTBZRMpE5A5713+JyG4R2QVcDvzQX+fgb1VVVURHRxMY6MxCS16vIf9IDdOTh3czVSsR4bLLLuPkyZPs3LmzV2XdNHss7gDhxQ2HHKqdUoOX25+F20Nl322z7TGf5wa4t4O8N3Ww/RYn69ifKisrSUxM7DxhFxVX11Pf1ELWMO/f8JWenk5SUhJr165lxowZPV5hMT4ihKumJrBiSyk/vnIyI4KcW6lRqcFG2zP6SVNTEydPnnS0YzzP7hjP0iuOz4kIl19+OTU1Nb1eXvaWi8ZR2+Bh5U6dbl0Nbxo4+knrHeNOBo5dZTWEBAYwMXZ4d4y3NX78eFJSUli3bh0eT8/nnbowbTST4sN4fv0hrItlpYYnDRz9pHVEldNXHJmJEbi1Y/wcrVcddXV1vbqbXES45aJU8str2Xb4lHMVVGqQ0U+YfuL04k0tXkNeeQ3Tk6McKW+oSUtLIy0tjXXr1vVqDquvzUwiLNjNC+tLnKucUoOMBo5+UllZSXx8vGMLLR2sPs2ZppZhf+Pf+SxcuJAzZ87w6aef9riMsGA3181K5i+7K6isbXCwdkoNHho4+kHr4k1O928AOhT3PMaMGcPUqVPZsGEDdXU9n7Tw25ek0uI1PPtZiXOVU2oQ0cDRD2pra2lsbHR8qpERgS4maMf4eV1xxRW0tLTw0Ucf9biMcdGhXDU1gZc2HNJFntSwpIGjH/hrqpGpYyKG7VTqXTV69Ghyc3PZvn071dXVPS7n7+ePp7bBwwpdq0MNQxo4+oHTgcPT4iW/vFb7N7po/vz5BAYGsnr16h6XkTN2FLPGjeLpTw/S4tWhuWp40cDRD6qqqoiKiiIkJMSR8vZV1nG2uYWZY6McKW+oCw0NZf78+ezfv5/CwsIel/P388ZTeuIsq/KPOlg7pQY+DRz9wOmO8dZ7CnLGtrs0iWrHhRdeyOjRo1m1alWPJ0BclBnPuOiRPL62WG8IVMOKBo4+5vF4qK6udrR/Y/uhk8SEBZM8aoRjZQ51brebq666iurqajZt2tSjMlwBwl3zx7Oz9BSfFPa8v0SpwUYDRx+rrq7GGOPwFcdJcsZGOXZPyHCRnp7OxIkT+fjjj6mv79l06dfNSiYxMoSH1xzQqw41bGjg6GMVFdZyI04FjuOnGyk5foaccdpM1V0iwlVXXUVzczPvv/9+j8oIdru4+9IJbC45yYbiEw7XUKmBSQNHHzt69ChBQUFER0c7Ut527d/olZiYGObMmcOOHTs4dKhna23ccEEKceHBPLzmgMO1U2pg8mvgEJHFIrJPRApF5IF29ouIPGzv3yUiOT77nhaRKhHJa5NntIisFpED9s9B9YlZUVFBQkKCY81K20tP4g4QXYOjFy699FKioqJ45513ejR7bkigi7vmj2d98XE2l+hVhxr6/BY4RMQFPAIsATKBm0Qks02yJUC6/bgLeNRn37PA4naKfgBYY4xJB9bYrwcFr9fL0aNHSUhIcKzMbYdOkZEYoQsL9UJQUBBLly6lurq6x/NYffPCccSEBelVhxoW/HnFMRsoNMYUG2OagFeAZW3SLAOeN5YNQFTrmuLGmLVAe1/flgHP2c+fA671R+X94cSJEzQ3Nzu26p+nxcvOslPk6P0bvZaens7UqVNZt24dx48f73b+EUHWVce6A9WsL+p+fqUGE38GjiTAdz6GMntbd9O0FW+MqQCwf7Y7rlVE7hKRLSKy5dixY92quL+0dow7FTj2VdZxpqlFO8YdctVVV+F2u3n77bd7NELq1otSSYwM4cH39uoIKzWk+TNwtNeI3/a/qStpesQY84QxJtcYkxsbG+tEkb1WUVGBy+UiJibGkfJab/ybmaKBwwnh4eFceeWVHDp0qEf3doQEuvjhwknsLD2ld5OrIc2fgaMMSPF5nQyU9yBNW5WtzVn2z6pe1rPPHD16lPj4eFwuZ/ojrBv/gkgZrTf+OWXmzJmkp6fz/vvv96jJ6us5SaTHhfFfq/bhafH6oYZK9T9/Bo7NQLqIpIlIEHAjsLJNmpXArfboqjlATWsz1HmsBG6zn98GvOVkpf3FGPP5iCqnbC89xcyxo/TGPweJCF/96ldxu9289dZbeL3d+/B3uwL46VWTKT5Wz5+2lvmplkr1L78FDmOMB7gPWAUUACuMMfkicreI3G0nexcoBgqBJ4HvtuYXkZeB9cBkESkTkTvsXQ8Ci0TkALDIfj3g1dTU0NDQ4Fj/xrG6Rg5W1zNL+zccFx4ezpIlSygtLWX9+vXdzr8oM55Z40bx0Or9ul6HGpLc/izcGPMuVnDw3faYz3MD3NtB3ps62H4cWOBgNfuE0x3jG4qtZpQ54525kVCdKysri4KCAj744APS0tIYM2ZMl/OKCP/8lQy+/ofP+P2Hhdy/eIofa6pU39M7x/tIRUUFIuLYVCPri48TFuxm2pgIR8pT52ptsgoLC+P111+nsbGxW/lzxo7i73KS+eO6Yg5W92weLKUGKg0cfeTo0aPExsbidjtzkbeh6Diz00bjdumv0F9GjhzJ17/+dU6ePMm7777beYY27l8ymWC3i1++ne+H2inVf/RTp49UVFQ41kx1tKaB4up6LtJmKr8bN24c8+fPZ9euXezcubNbeePCQ/iHBel8uO8Yawoq/VRDpfqeBo4+UFdXx+nTpx0bUbW+2Fr74aIJGjj6wvz58xk3bhx/+ctfPl/2t6tuuziVCbGh/PKdPTQ092zBKKUGGg0cfcDpjvH1RceJCHGTkaj9G30hICCA6667jpCQEF599VXOnj3b5bxB7gD+bdk0Dh0/w0Or9/uxlkr1HQ0cfaCsrAwRcS5wFB9nzvhoXAF6/0ZfCQsL4/rrr6empoY33nijW/d3XDwxhhsvSOHJdcXsLD3lv0oq1Uc0cPSBsrIy4uPjCQoK6n1ZJ89QeuKsNlP1g5SUFJYsWUJhYSEffvhht/L+01cyiA0P5v7Xd9Hk0TvK1eCmgcPPvF4vR44cISUlpfPEXdA686oGjv4xa9YscnJy+OSTT9ixY0eX80WEBPL/rs1i79E6/vBRof8qqFQf0MDhZ1VVVTQ1NZGcnOxIeeuLjzM6NIhJceGOlKe6R0RYunQpaWlpvP322xw8eLDLeRdmxnPNjDE88mEhu8tq/FhLpfxLA4eflZZas8Y7ccVhjGF90XHmjB9NgPZv9BuXy8U3vvENoqOjefXVV+nOtP2/XDaVmLBgvv/Kdp2ORA1aGjj8rKysjNDQUKKionpdVtGx01TUNHDxBGemZVc9FxISwvLlywkMDOSll16ipqZrVxBRI4N46IZsSo7X868r9cZANThp4PCzsrIyUlJSHJnBdvUeawb5BRntrl2l+lhUVBTLly+noaGBF154gdOnT3cp35zx0Xzv8om8trWMt3Yc8XMtlXKeBg4/qq+v58SJE471b7xfUMm0pAgSI3X9jYEiMTGR5cuXU1tby4svvtjlezy+vyCdWeNG8c9v5lF0rGsBR6mBQgOHH5WVWesxONG/cayukW2HT7Iow7n1PJQzxo4dyw033EB1dTUvvfQSDQ0NneZxuwJ4+KaZBLkDuOv5LdQ1NPdBTZVyhgYOPyotLSUgIMCRG/8+3FuFMbAwU5upBqIJEyZw3XXXUVFRwfPPP8+ZM2c6zZMUNYJHludQcvwMP3x1B16vrlOuBge/Bg4RWSwi+0SkUEQeaGe/iMjD9v5dIpLTWV4R+bmIHBGRHfZjqT/PoTfKyspITEwkMDCw12WtLqgkKWoEmTrNyIA1ZcoUbrzxRqqqqnjuuee61Odx0YRo/uXqTN4vqOKh93VKEjU4+C1wiIgLeARYAmQCN4lIZptkS4B0+3EX8GgX8z5kjMm2H92f77oPtLS0cOTIEUf6N842tbDuwDEWZsTpMrEDXHp6OsuXL+fEiRM8++yznDp1qtM8t140jm/kJvM/HxTymi43qwYBf15xzAYKjTHFxpgm4BVgWZs0y4DnjWUDECUiiV3MO6BVVlbi8XgcCRyfFlbT0OxlYaYzi0Ap/xo/fjy33HIL9fX1PPXUU59PctkREeHfrp3GJROjuf/1XXy4t6qPaqpUz/gzcCQBpT6vy+xtXUnTWd777Katp0VkQC66fejQIcDqOO2t9wsqCQ92c2GaTjMyWIwdO5bbb78dl8vFM888w4EDB86bPtjt4rGbZ5GRGM53X9rGtsMn+6imSnWfPwNHe20qbXv/OkpzvryPAhOAbKAC+O92Dy5yl4hsEZEt3bmz1ymFhYXExsYSEdG7Pgmv1/B+QRWXTo4lyK1jGQaT2NhY7rjjDqKjo3n55Zf57LPPMKbjDvDwkECe+dZs4iKCuf3ZzRRU1PZhbZXqOn9+EpUBvuNQk4HyLqbpMK8xptIY02KM8QJPYjVrfYkx5gljTK4xJjc2NrZXJ9JdTU1NHDp0iAkTJvS6rA3Fx6k+3ciVU3UY7mAUHh7Ot7/9baZMmcLq1at54403aG7ueOhtbHgwL9x+ISFuF8uf3EB+uc5ppQYefwaOzUC6iKSJSBBwI7CyTZqVwK326Ko5QI0xpuJ8ee0+kFZfA/L8eA49cujQIVpaWpg4cWKvy3plcykRIW6u1P6NQSsoKIjrr7+eK664gry8PJ566imOHz/eYfqx0SN59TtzGBnkZvmTG3VCRDXg+C1wGGM8wH3AKqAAWGGMyReRu0XkbjvZu0AxUIh19fDd8+W18/yXiOwWkV3A5cAP/XUOPVVYWIjb7WbcuHG9KqfmTDPv5R/l2plJhAS6HKqd6g8iwrx58z6/y/zxxx9nx44dHTZdjYsO5ZW75hAe4mb5HzewsbjjQKNUX5PztbkOFbm5uWbLli19drz/+Z//ITo6muXLl/eqnOc+K+FfV+bzzvfmMi0p0qHaqf5WW1vLm2++SUlJCdOmTWPp0qWMGNH+NDJHTp3l1qc2UnriLL++fjrLstuOL1HKf0RkqzEmt+127W112IkTJzhx4oQj/Ruvbi5lWlKEBo0hJiIigltuuYXLL7+cPXv28Mgjj1BQUNBu2qSoEbxxzyXMHBvFP7yyg0c+LDxvB7tSfUEDh8OKiooAet2/kXekhj0VtdyQ68zKgWpgCQgIYP78+fz93/894eHhrFixgj/96U/U1dV9KW3kyECev2M212aP4der9nHfy9s5rWt5qH6kgcNhhYWFjBo1itGjR/eqnFc3lxLsDuAabZoY0hISErjzzju54oor2LdvH7///e/59NNPaWlpOSddsNvFQzdkc//iKfx1dwXX/P4T9h39cpBRqi9o4HCQx+Ph4MGDTJgwoVdTg5xtauHPO46wZFoCkSN6P8+VGthcLhfz5s3j3nvvJS0tjffff59HH32UgoKCc5qlRIR7LpvAS3fOofash2WPfMILGw5p05Xqcxo4HHT48GGam5tJT0/vVTkvbCihrsHDzXN6NypLDS6jRo3ixhtvZPny5YgIK1as4Omnn6akpOScdBdNiObd788ld9xo/u+f87jlqU0cOdW1dUCUcoIGDgft3r2bwMBAUlNTe1xGXUMzj35UxPxJseSm9q65Sw1O6enp3HPPPXz1q1+lpqaG5557jmeffZbi4uLPry7iIkJ44Y7Z/Pu109h2+CRXPbSWZz89iKfF28+1V8OBBg6HNDQ0kJeXR1ZWFkFBQT0u56lPDnLyTDM/vXKyg7VTg01AQAA5OTl873vf46qrruLEiRO88MILPPXUU+Tn59PS0oKIcPOccaz6wXyyU6L4+dt7uPp/PmGD3vOh/Mzd3xUYKnbt2oXH42HWrFk9LuNEfRN/XHeQJdMSyErWIbgKAgMDmTNnDrm5uezcuZNPP/2U1157jYiICHJzc5k5cyYpo8N44Y7ZrMo/yr+9U8CNT2xgUWY8P75yElMSdP0W5TwNHA4wxrB161YSExMZM2ZMj8t57OMi6ps8/GjRJAdrp4YCt9vNrFmzmDlzJoWFhWzcuJEPPviAjz76iEmTJjFz5kwWZUzg0klx/HFdMU+sK2bJ79Zx9fQx3Hf5RCYnhPf3KaghRAOHA8rKyqiqquLqq6/ucRmlJ87w3GclfG1mEunx+k+u2hcQEMCkSZOYNGkS1dXVbNu2jZ07d7J3715GjhxJZmYm10ybxs1zLuOPnxzkmU9LeHtnOfMnxfL389KYOzFGFwNTvaaBwwFbt24lKCiIadOm9Sh/o6eFe/93G0HuAL3aUF0WExPDlVdeyYIFCzhw4AB5eXns2LGDLVu2EBoaypTJk3nh+nQ+OSq8uKmUW57axPiYUG64IIWv5yQTGx7c36egBikNHL109uxZ8vPzmTFjBsHBPftH/I+/FLCrrIbHb5lF8qiRDtdQDXUul4spU6YwZcoUmpqa2LdvH/v27SMvL49t27bhdru5N2UcR4OTWF8p/Oqve/n1qn1cOimWq2cksjAjnvAQvV9IdZ0Gjl7atGlTrzrF39lVznPrD3Hn3DSu0jU3VC8FBQWRlZVFVlYWHo+HkpISCgsLKSoqovFgETlARkQE5cGp7Cg5xpq9VQS5A7hkQjRXTInj8ilx+uVFdUoDRy9UVFSwdu1apk6dSmJiYucZ2th66CQPvL6bnLFR3L9kih9qqIYzt9vNxIkTP583raamhpKSEg4dOsShQ4cYzwmOBYVS4h3N9qImPtx3DN7KZ2xUMBdPjOGS9Dhmp40mPiKkn89EDTQaOHqoubmZN954g9DQUL7yla90O/8b28p44PXdJEaF8PvlOQS69JYa5V+RkZHMmDGDGTNmAFBfX09ZWRllZWWUl1dQcOQ4B04HU1EbzutbzvDKliMAjAqGyTHBZCVFMDM1llkTEoiPbH8aeDU8aODoodWrV1NdXc0tt9zS4VoK7WnyePnN6v089nERF0+I5pHlOYwK7fkNg0r1VGhoKJMnT2byZOtmU2MMtbW1VFZWUnG0km0l1eQdPUNJrSGvfCQbjjTCpmPAHkYEtBAX4mVMmIuxo0JIjQllQnwk6YmjiBsdyciRI3X01hDm18AhIouB3wEu4I/GmAfb7Bd7/1LgDPAtY8y28+UVkdHAq0AqUAJ8wxhz0p/n4cvr9bJp0yY2b97MnDlzGD9+fJfynW708PLGwzz1yUGO1jbwzQvH8vNrpuqVhhowRITIyEgiIyOZNGkSl863trcGlJLyY+woqWJPRS0lJzyUnzZsP+ZlfVUT7GsCTgIlBOEhLKCJCLeXyCAYNcJF9Eg3o0YGEhMeQmx4CDHhI4iOGElE2EiCg4MJDg4mJCSEoKAgAgL0f2Kg81vgEBEX8AiwCCgDNovISmPMHp9kS4B0+3Eh8ChwYSd5HwDWGGMeFJEH7Nf3++s8Whlj2LdvH2vWrKG6upq0tDQWLFjQbtqG5haO1zdRduIM20tPsfXQSTYUH6euwcNF46P5z+umc+mkWH9XWSlHtAaUGZGRzMj48jozx+vOUlBWzYHyk5RU11FxqoHKuiaqz7RQ1GA4fVqA1quPBvtxCgA3LQTRQpC0ECgtBNJCcIAh2IX1cAcQ4hb7ZwDBgQGEBLoIdtuPQOsREugi0O0iONBNkNv1xSPQhdsVQKDbTaA7gEC3i0DXF9vcrgACAs59iMiXfrZ97vsYjvx5xTEbKDTGFAOIyCvAMsA3cCwDnjfWzG0bRCRKRBKxriY6yrsMuMzO/xzwEX4KHD96ajUfHzyN1+vFGIMBXK4xhIWmE3gsiGd/9wkY8BpDc4uh0eOlobnlS4vspEaP5KqpCdwyZxwzUqL8UVWl+k10+AjmZqQwN6P9Rcc8LV5O1DdxvL6JY3UNVJ2qp7ruLMfrznLidCN1Dc3UNng43ejhbJOXMx4vpzyGxiZoOgse09GHs9d+NPeq/oIBDGI/F5/tck4a+CIEfvG69YlvLaXNz9YnX6Qxn786J18Hp9rRO9Bh2PLZ8fOvTOaaizI7Stkj/gwcSUCpz+syrKuKztIkdZI33hhTAWCMqRCRuPYOLiJ3AXcBjB07tkcnEB85guTwswS4gnC5XAQFBREVGfnFtwz7jyVAhCB3AEHuAILdAcSEBRMdGkR8RAhZyZHEhOmNVmr4crsCiIsIIS4ihIzE7s+d1eI1NHpaaGj2cra5hSaPl0ZPC43NXppbvDR5vJxtaqax2UNjk4fG5haaWlpobm6hydOCx+vF4/HS7PXiafHS4vXS0mKsn17rp9cY+7nBGIPXGLxe60uh9ZrPvzx6vQYvBmNvAzuM+KRp/dm609jpfdNaP75YS8X4ZDg3TfvOXYal4zVZokKdHxXnz8DRXjBse3YdpelK3vMyxjwBPAGQm5vbo5Vu7r9ubk+yKaUc5AoQRga5GaljSAYMf/ZClQG+167JQHkX05wvb6XdnIX9s8rBOiullOqEPwPHZiBdRNJEJAi4EVjZJs1K4FaxzAFq7Gao8+VdCdxmP78NeMuP56CUUqoNvzVVGWM8InIfsAprSO3Txph8Ebnb3v8Y8C7WUNxCrOG43z5fXrvoB4EVInIHcBi43l/noJRS6stkOCx0n5uba7Zs2dLf1VBKqUFFRLYaY3Lbbtc7bZRSSnWLBg6llFLdooFDKaVUt2jgUEop1S3DonNcRI4Bh3qYPQaodrA6g4Ge8/Cg5zw89OacxxljvjSx3rAIHL0hIlvaG1UwlOk5Dw96zsODP85Zm6qUUkp1iwYOpZRS3aKBo3NP9HcF+oGe8/Cg5zw8OH7O2sehlFKqW/SKQymlVLdo4FBKKdUtGjjOQ0QWi8g+ESm01zcf0kQkRUQ+FJECEckXkX/o7zr1BRFxich2EXmnv+vSF+wlml8Tkb327/qi/q6Tv4nID+2/6TwReVlEnF8Wr5+JyNMiUiUieT7bRovIahE5YP8c5cSxNHB0QERcwCPAEiATuElEnF24d+DxAD82xmQAc4B7h8E5A/wDUNDflehDvwPeM8ZMAWYwxM9dRJKA7wO5xphpWEs13Ni/tfKLZ4HFbbY9AKwxxqQDa+zXvaaBo2OzgUJjTLExpgl4BVjWz3XyK2NMhTFmm/28DusDJal/a+VfIpIMfAX4Y3/XpS+ISAQwH3gKwBjTZIw51a+V6htuYISIuIGRfHk10kHPGLMWONFm8zLgOfv5c8C1ThxLA0fHkoBSn9dlDPEPUV8ikgrMBDb2c1X87bfAPwLefq5HXxkPHAOesZvn/igiof1dKX8yxhwB/j+shd8qsFYa/Vv/1qrPxNurqmL/jHOiUA0cHZN2tg2LscsiEga8DvzAGFPb3/XxFxG5Gqgyxmzt77r0ITeQAzxqjJkJ1ONQ88VAZbfrLwPSgDFAqIjc3L+1Gtw0cHSsDEjxeZ3MELy8bUtEArGCxkvGmDf6uz5+dglwjYiUYDVFXiEiL/ZvlfyuDCgzxrReSb6GFUiGsoXAQWPMMWNMM/AGcHE/16mvVIpIIoD9s8qJQjVwdGwzkC4iaSIShNWZtrKf6+RXIiJYbd8Fxpjf9Hd9/M0Y8zNjTLIxJhXr9/uBMWZIfxM1xhwFSkVksr1pAbCnH6vUFw4Dc0RkpP03voAhPiDAx0rgNvv5bcBbThTqdqKQocgY4xGR+4BVWKMwnjbG5PdztfztEuAWYLeI7LC3/ZMx5t3+q5Lyg+8BL9lfiIqBb/dzffzKGLNRRF4DtmGNHNzOEJx6REReBi4DYkSkDPhX4EFghYjcgRVAr3fkWDrliFJKqe7QpiqllFLdooFDKaVUt2jgUEop1S0aOJRSSnWLBg6llFLdooFDDSoiEi8i/ysixSKyVUTWi8jXelhWqu9MosOJWD6w567qbVlBIrLWngdKDQMaONSgYd+89WdgrTFmvDFmFtaNe8n9WrEuGIAfqkuBnU5MKWNPAroGuKHXtVKDggYONZhcATQZYx5r3WCMOWSM+R8AEQkRkWdEZLc9gd/l9vZUEVknItvsx5emmxCRqSKySUR2iMguEUlvJ81pEflvu4w1IhJrb58gIu/ZV0DrRGSKvf1ZEfmNiHwI/GebskaKyAr7WK+KyEYRybX3PSoiW+z1I37hk6dERP7DvsraIiI5IrJKRIpE5G6fdD8Vkc122b+gfd/EvovYfn/22hMe5onISyKyUEQ+tddxmG2n+7mI/MTnOHn2ZJhgBfRvdnAsNcRo4FCDyVSsu387ci+AMSYLuAl4TqwFe6qARcaYHKxvxQ+3k/du4HfGmGwgF2tOp7ZCgW12OR9j3ZkL1l3I37OvgH4C/MEnzyRgoTHmx23K+i5w0hgzHfg3YJbPvn82xuQC04FLRWS6z75SY8xFwDqs9Reuw1o75ZcAInIlkI61LEA2MEtE5rdzLpcAvpM7TsRap2M6MAVYDsy1z+ef2snfVh5wQRfSqSFgoF0+K9VlIvII1odbkzHmAvv5/wAYY/aKyCGsD+5DwO9FJBtosbe1tR74Z3t9jjeMMQfaSeMFXrWfvwi8Yc8kfDHwJ6slDYBgnzx/Msa0tFPWXKwPaowxeSKyy2ffN0TkLqz/z0SshcRa97fOl7YbCLPXTakTkQYRiQKutB/b7XRhWIFkbZvjj7bztjpojNkNICL5WIv/GBHZDaS2U/9zGGNaRKRJRMLblKuGIA0cajDJB/6u9YUx5l4RiQG22Jvamwof4IdAJdZqdwFAQ9sExpj/FZGNWIs6rRKRO40xH3RSH2OXd8q+UmlPfQfb262riKRhfcu/wBhzUkSeBXyXOW20f3p9nre+dtvl/soY83gndfeISIAxpnUdkrZl+R6n9XPCw7mtFG2XXw2mnfdWDT3aVKUGkw+AEBG5x2fbSJ/na7Hb2UVkEjAW2AdEAhX2h+QtWJNWnkNExgPFxpiHsb7VT2+bBuv/5Tr7+XLgE7tz+aCIXG+XIyIyowvn8gnwDTtPJpBlb4/ACjY1IhKPtXRxd6wCbrevhBCRJBFpb/GefViLOnVHCfYU7CKSg7W+BfbraKB12nI1xGngUIOGsWbkvBar3f+giGzCWg7zfjvJHwCX3bzyKvAtY0yjvf02EdmA1UzV3lXADUCeWLMCTwGebydNPTBVRLZiddT/0t7+TeAOEdmJdVXUlSWG/wDE2k1U92M1RdUYY3ZiNTPlA08Dn3ahrM/ZK9v9L7Defh9eA8LbSfoXrJlUu+N1YLT9Ht0D7PfZdzmgsygPEzo7rlJdJCKnjTFhDpXlAgKNMQ0iMgFrOOske2ir34m1qM/zxphFDpX3BvAzY8w+J8pTA5v2cSjVP0YCH4q14qIA9/RV0ABr/WkReVJEInp7L4dY63r8WYPG8KFXHEoppbpF+ziUUkp1iwYOpZRS3aKBQymlVLdo4FBKKdUtGjiUUkp1y/8PCV7JsHe4708AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "gamma_prior.plot(color='gray', label='prior')\n", "posterior2.plot(label='posterior')\n", "decorate_rate()\n", "\n", "plt.savefig('zigzag7.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Back to PyMC\n", "\n", "Previously we used PyMC to draw a sample from a Poisson distribution with known `mu`.\n", "\n", "Now we'll use it to draw a sample from a gamma distribution of `mu`, with known `alpha` and `beta`.\n", "\n", "And then use that value of `mu` to draw a sample from a Poisson distribution.\n", "\n", "Here are the parameters we used to create the gamma prior:" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4.8 2\n" ] } ], "source": [ "print(alpha, beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the PyMC model looks like:" ] }, { "cell_type": "code", "execution_count": 142, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " mu = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distribution of `mu` from this model is the prior. Let's see what it looks like:" ] }, { "cell_type": "code", "execution_count": 143, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.445926077198612" ] }, "execution_count": 143, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior_pymc = trace['mu']\n", "np.mean(sample_prior_pymc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And compare it to a sample from the gamma prior." ] }, { "cell_type": "code", "execution_count": 144, "metadata": {}, "outputs": [], "source": [ "sample_prior_gamma = gamma_prior.sample(1000, replace=True)" ] }, { "cell_type": "code", "execution_count": 145, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_prior_gamma, label='prior gamma')\n", "plot_cdf(sample_prior_pymc, label='prior pymc')\n", "decorate_rate('CDF')\n", "\n", "plt.savefig('zigzag10.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks pretty good." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prior predictive\n", "\n", "The distributions of `goals` from this model is the prior predictive." ] }, { "cell_type": "code", "execution_count": 146, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.43" ] }, "execution_count": 146, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior_pred_pymc = trace['goals']\n", "np.mean(sample_prior_pred_pymc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And let's compare it to a prior predictive distribution estimated by sampling." ] }, { "cell_type": "code", "execution_count": 147, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.492" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior_pred = np.random.poisson(sample_prior_gamma)\n", "np.mean(sample_prior_pred)" ] }, { "cell_type": "code", "execution_count": 148, "metadata": {}, "outputs": [], "source": [ "def plot_goals(sample, pos='left', **options):\n", " options['align'] = 'edge'\n", " if pos == 'left':\n", " options['width'] = -0.45\n", " else:\n", " options['width'] = 0.45\n", " \n", " cdf = Cdf.from_seq(sample)\n", " plt.plot(cdf.qs, cdf.ps, **options)" ] }, { "cell_type": "code", "execution_count": 150, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(sample_prior_pred, label='prior pred grid')\n", "plot_cdf(sample_prior_pred_pymc, label='prior pred PyMC')\n", "decorate_goals('CDF')\n", "\n", "plt.savefig('zigzag11.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks good." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## When do we get to inference?\n", "\n", "Finally, we are ready to use PyMC for actual inference. We just have to make one small change.\n", "\n", "Instead of generating `goals`, we'll mark goals as `observed` and provide the observed data, `4`.\n", "\n", "And instead of called `sample_prior_predictive`, we'll call `sample`, which is understood to sample from the posterior distribution of `mu`." ] }, { "cell_type": "code", "execution_count": 151, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [mu]\n", "Sampling 2 chains, 0 divergences: 100%|██████████| 2000/2000 [00:00<00:00, 2301.77draws/s]\n", "The acceptance probability does not match the target. It is 0.8821095734410509, but should be close to 0.8. Try to increase the number of tuning steps.\n" ] } ], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " mu = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu, observed=4)\n", " trace = pm.sample(500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With `goals` fixed, the only unknown is `mu`, so `trace` contains a sample drawn from the posterior distribution of `mu`. We can plot the posterior using a function provided by PyMC:" ] }, { "cell_type": "code", "execution_count": 152, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000" ] }, "execution_count": 152, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(trace['mu'])" ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with model:\n", " pm.plot_posterior(trace)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can extract a sample of `mu` from the trace." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.9224513318372063" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pymc = trace['mu']\n", "np.mean(sample_post_pymc)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And compare it to the sample we drew from the grid approximation:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.9052" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post = posterior2.sample(1000, replace=True)\n", "sample_post.mean()" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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gsiZVaVunIrHR9oFfEoXyrKGb85muwAOFvd38vrmHSs5TIUWEvG76ExMTw+zZs5k0aRLDhw/n3XffPfZN/6hAIED58uVZuHBhrusoXbr0SefKa5kT3ZwoISEh1+KRc92mePH5A+w9nMHBHRvI3LqMpHVjKbNrHhWydlAOKAcs1XpMLtedHWddRcMzytGmWlmurVyaSqXjSIjN/T03JVOJuLK4ONi8eTMzZ87kwgsv5IsvvqBDhw40btyYjRs3snbtWho0aMAnn3zCxRdfzKFDhzhy5AhdunThggsuoEGDBgCULVuWtLQ0AJKSkqhbty4jR46kR48eqCqLFy+mZcuWJ8zRrl07hg8fzu23385nn31Ghw4d8s3eoUMHRowYQceOHVm+fDlLlizJd5nzzz+fhx56iD179pCUlMTIkSPzzWYKX2paJlNXp7Jx92G27DvClr1HSNmXTv3D83kzdhANZC8ABzWRX7UFWeU74W/QmYbNzqPJWdVpZt/wDVYICk2TJk346KOPuO+++2jYsCF9+vQhISGBoUOH0qNHj2MHi3v37s3evXvp1q0bGRkZqCr//e9/Abjpppv461//Sv/+/Rk1ahSfffYZffr04ZVXXiE7O5ubbrop3w/b/v37c/fdd/PGG28cO1icn/vvv5+ePXvSokULWrduTYsWLShXrtwJl6levTovvfQSF154IdWrV6dNmzb4/f6Cv2DmlO07nMUPy3bw7eJtzFy3B9UALaM3cmWpZdwRvYEGuoZycXs4HF+VpU1fQqo1JaFWazpVq0ycteWbXITdPYuTk5M1541pVqxYQZMmTTxK5Jw11LVrV5YuzbU3jWLP7/eTnZ1NQkIC69ato1OnTqxevZq4uLiQb9vr9y6cLNt2gP6T1jBpxS58AaVxpRj+Xfozmh6YSkzmfmemSg2hRhs4sw00vhLK1zrhOk3kEJF5qpqc2zTbIzAcOXKEjh07kp2djaoyaNCgIikCpmDW7EzjnYlLWb18IcnxmxlTfQN1Ew5Rev8qZNcuaHI1nN0FGl0GiRW9jmvCkBWCQlCnTp2w3RsA59iE3f6zePEHlPmb9zFixgqqLR/Gv6K/JjHePWvsSAVIqA+1zoNWt0LjLt6GNWHPCoExxcTBjGymrU5l/qJFVFw/loa+tbwRPRdiIFC2BrR/EOr+CSo3gmi7jMoUHisExngsI9vPe1PX88PPU3lARvBC9CxnfGJlspreSVzza4mqd4m3IU2JZoXAGA9NWrGTv3+znGb7J/N9XH8AtEoT5Or+JNQ6z+N0JlJYITDGAxt3H+Yf3y5n3apFPFB2OjfGjYEqTeDmz5GK9byOZyKMFYJiJBy6oTanZ+v+dEZ99z0JK0dzU9ROOiXMQ7ICcPaVcP0QiC3UPjqNKRArBMVIce+G2py6nQczGDBlLV/N3sDEmCeoEb0bf7naRDX+K7R/GJKqex3RRDD7NCgE4d4N9bBhwxgzZgyZmZls2LCBW265hRdffJG//e1vVK5c+ViHdM899xzVqlWjRYsWvPjii1SrVo2FCxfSvXt3mjdvTr9+/UhPT2fs2LHUr1+fnTt30rt3b9avXw/AoEGDaNeuXdG/QR7y+QO8N209/SetoYWuYnriQCpk74ZbRxHdsLPX8YwBSmIh+P5p2JF/Xzkn5YzmcMW/TjhLOHdDDTB79myWLl1KYmIibdu25corr+See+6he/fuPPTQQwQCAYYPH87s2bNZsmQJixYtYsWKFVSsWJF69erRq1cvZs+eTb9+/XjnnXd4++23efDBB7n44osZM2YMfr+fQ4cOFc77ESbWpx7isZGLWLF5J/3PmMBl+4dDfDXoNgSsCJhixDoeKSQ5u6GePn06q1atOq4b6mnTppGUlHSsG+rRo0eTmJh43PqCu6Fu1aoV9913H9u3/367hhN1Q33LLbcATjfU06dPz3cZgM6dO1OpUiVKlSpF9+7dmT59OnXq1KFSpUosWLCAiRMn0rp1aypVqgRA27ZtqV69OvHx8dSvX59LL70UgObNm7Nx40YAJk+eTJ8+fQCnO+v8+i8qKQIB5aufpjPznbv4YNfNrEy4yykCjS6H/5sHzY7v1tsYL5W8PYJ8vrmHSjh3Q51XfnDuUTxs2DB27NjB3XfffWx68N3IoqKijj2PiorC5/MVKFtJtCstgxc+/4XHtz5Ig6ht+JNqQduHnDOCzr4i5LccNOZU2B5BITnaDTWQazfUwB+6oT5w4ABdunTh7bffPvZhn1c31ODcM2DRokX55jjaDTVQ4G6oAX788Uf27t17rI3/6N7Ntddeyw8//MCcOXO47LLLCv6C4DRtDRo0CHA6tjt4sHDvHFfczFq/h7fefoM3t91Kg6ht6EVPEv3IEvjTY043EFYETDFlhaCQHO2GukWLFuzdu/e4bqibN29OVFQUvXv3Ji0tja5du9KiRQsuvvjiP3RD/cYbb9C6dWvWrVvHZ599xocffkjLli0555xz+Prrr/PN0b9/f4YOHUqLFi345JNP6NevX4Hyd+jQgdtvv51WrVpx3XXXkZzsdFIYFxdHx44dueGGG/JsVspLv379mDJlCs2bN+fcc89l2bJlJ7V8uFBV3pu6jl4fTOWJwIfEJlWFnt8iHZ+1D38TFqwb6kIQ7t1QDxs27NhZRzkFAgHatGnDyJEjadiwYaFv2+v37nQdSM/miZGLmL18LT+VeYnKvu1wwyfQtOCn8xpTFKwbanNKli9fTteuXbn22mtDUgTC3Yy1uxkyYhQ9MkYxqNQCon0+6Pq2FQETdmyPwHgqHN+79Cw/r/+wkgUzf2JE/CvESQBJvgta3eLcFMaYYigi9ghU1W6mHmbC7UsIwILN+3j8ywXccWAgL8X/iJaqhPT6ESrV9zqaMaesRBwsTkhIYM+ePWH5wRKpVJU9e/aQkBAefeukZ/l5bfwKbho0jbsyPqJnzI/QuCvSe5oVARP2SsQeQc2aNUlJSSE1NdXrKOYkJCQkULNmTa9j5OvXtbt5ZvQSau2fxfzEgZT2H3DuDNZtgJ0VZEqEElEIYmNjqVu3rtcxTAmz/0gW//xuBSPnpXB3uXk8n/AOUfFl4dqvoP6frQiYEqNEFAJjCltaRjZXvTudvfsP8HXtMbTYOwGp2hhu+wrKVPU6njGFygqBMbl4c+Jqtu47zOyzv6Lyxm+gxrlwzSArAqZEskJgTA7zN+1l9W/fMbr6AipvHA9//htc9LjXsYwJGSsExgTJ9gcY8+VQPo/7J+wF2j/k9BVkTAlmhcCYIKO/G88/jryMP7oU0Q8vgrLVvI5kTMiViOsIjCkMG3YfJmbu+wBE3z7KioCJGFYIjMG5wO350Yu4RBaQcfY1UKdg3XcbUxKEtBCIyOUiskpE1orI07lMLyci34jIIhFZJiJ3hTKPMbnx+QP0+2k1f97cn0pykIRmV3kdyZgiFbJjBCISDQwAOgMpwBwRGaeqy4NmewBYrqpXiUgVYJWIfKaqWaHKZUywWev38MLXy6iTOpn34r5HW9+B2K0kTYQJ5cHi84C1qroeQESGA92A4EKgQFlxeosrg3OeRuTe59AUmZ0HM3h1/Aq+XriNC5P28k6ZoWh0BeTKN+2KYRNxQlkIagBbgp6nAOfnmOddYBywDSgL3KiqgZwrEpF7gXsBateuHZKwJnJ8v2Q7T4xaTJY/wKMX1+SB7QOJ3rwf7v0ZYuK8jmdMkQvlMYLcvlbl7B70MmAhcCbQCnhXRJKOW0j1fVVNVtXkKlWqFHZOEyECAeWtiavo89l8GlYrw48Pd+DBrPeJ3jwdruoPZ7b2OqIxnghlIUgBagU9r4nzzT/YXcBodawFNgCNQ5jJRKi0jGzu/WQe/Sevpce5NRl+7wWctXwwLPgU2vSEc3t6HdEYz4SyaWgO0FBE6gJbgZuAW3LMsxnoBPwiItWAs4H1IcxkItDG3Yf568dzWb/7MC9d1ZSe7eogi7+Eya/AWe3h6v5eRzTGUyErBKrqE5G+wAQgGhiiqstEpLc7fTDwD2CYiCzBaUp6SlV3hyqTiTxb9h7h+sEz8QcCfHL3ebSrEQ3Db4VV30HVc+DKt7yOaIznQtrFhKqOB8bnGDc4aHgbcGkoM5jIdeBINncNm0OWz8/o+9vRoGpZGNQBdi2HJlfDte9BXKLXMY3xnPU1ZEqkLF+A+z6dy6Y9h/nknvOdIrB9EexcAh2fg4uf9DqiMcWGFQJT4qgqT3+1mN/W7+XtG1txQb1KzoTVE5yf53T3LpwxxZD1NWRKnP/+tIbRC7byWOdGXNO6hjMyfR/82h+qNoUKdTzNZ0xxY4XAlCjjl2yn/6Q19Di3Jn3/3OD3CTMHQlYadH8fom1H2JhgVghMiZGR7eeVb5dzzplJvNq9OXK0q4jda2Hav6HJVXBGc29DGlMMWSEwJcZHMzay7UAGz3VpQmy0+6e9bjIMbg+xiXDBA94GNKaYsn1kUyLsP5LFgClrueTsKrRrUNkZuX0RfNULYhKg9y9Q3vqpMiY3VghMiTBgylrSMn08dXlQDyUTnoOsw3DX91YEjDkBaxoyYW/L3iN8NGMT17WpSZPqbp+FO5fDxl+cm8/XaONtQGOKOSsEJuy99eNqRODRzo2cEfu3wJe3QlwZOO8+b8MZEwasEJiwtnTrAcYu3Mpd7etyZvlSzshf+8He9XD9UChdyduAxoQBKwQmrL3+w0rKlYqlzyX1nRFZR5yupVvdCo2sGytjCsIKgQlb3yzaxi9rdtO3YwPKlYp1Rs4dAr50aHmzt+GMCSNWCExY2nkwg+fHLqVlrfLc2a7O7xPWTIBqzaFOB8+yGRNurBCYsKOqPDFqMZk+P/+9oSUx0UF/xnvWQ7Vz7Ab0xpwEKwQm7Hw2azPTVqfybJcm1KtS5vcJ+zbCwRSoVN+zbMaEIysEJqxs3H2Yf363gj81rMxt55/1+4TsdBhyOcSXg8ZdvQtoTBiyK4tN2PD5Azw6YiGx0cK/r29BVFRQ88+MdyFtO1z3IVRr6l1IY8KQFQITNt6btp75m/fT76ZWVC9XCvw+WD/FuW5g4y9Qu53Tw6gx5qRYITBhYV3qIfr9tIYrmp3B1S3PBFUY2RNWfutcQdz5H3BhX4iy1k5jTpYVAlPsqSrPjl5CfGwUf+92jnOfgVXfO0Xg/N7Q8VlIKOd1TGPCln19MsXeyLkpzNqwl2e7NKFq2QRn5MwBUKoC/OUlKwLGnCYrBKZYS03L5J/jV3BenYrcmFzLGbnmJ+eYwPl9ILaUtwGNKQGsEJhi7eVvl5Oe5efV7s2ds4SyDsO4vpBUEzo87HU8Y0oEKwSm2JqychffLNrGAx0b0KCqe+HYws+d00Q7PAwx8Z7mM6aksEJgiqXDmT6eH7uUBlXL0PuSes7IzDT4+TWofDYk3+1tQGNKEDtryBRLr32/gq370xnZ+0LiY6LBlwVf3AxH9jr3GYiK9jqiMSWGFQJT7Py0fCef/raZey+qR9s6FZ2Rcz90DhB3+Q/Uu9jbgMaUMNY0ZIqVXWkZPPXVYppWT+KxS91bTwYC8Gt/58rhtr28DWhMCWSFwBQbqsoTIxdzKNNHv5taOU1CB7fDgLaQtg2S77LupY0JgZAWAhG5XERWichaEXk6j3kuEZGFIrJMRKaGMo8p3j6asZGpq1N5/somNKxW9vduJPauhyvfhOY9vI5oTIkUsmMEIhINDAA6AynAHBEZp6rLg+YpDwwELlfVzSJSNVR5TPG2akcar36/kj83rsptF7jdS//4AmyZBZc8a01CxoRQKPcIzgPWqup6Vc0ChgPdcsxzCzBaVTcDqOquEOYxxVSWL8BDwxeQlBDDv69v4fQldCAFfhvo7AVc9LjXEY0p0UJZCGoAW4Kep7jjgjUCKojIzyIyT0TuyG1FInKviMwVkbmpqakhimu88t7Udazckca/uregchn3IrEZ7wICHZ+zU0WNCbFQFoLcjuppjucxwLnAlcBlwN9EpNFxC6m+r6rJqppcpUqVwk9qPLMu9RDvTF7LlS2q85em1ZyRaTthwSfQtBtUrOttQGMiQCivI0gBagU9rwlsy2We3ap6GDgsItOAlsDqEOYyxcTR7qUTYqN48aqmR0fCTy+BL9PpXtoYE3Kh3COYAzQUkboiEgfcBIzLMc/XwJ9EJEZEEoHzgRUhzGSKkVy7l57zASz6HNo/aDehN6aIhGyPQFV9ItIXmABEA0NUdZmI9HanD1bVFSLyA7AYCAAfqOrSUGUyxcex7qXrVuSGo91L71jinClU50/Q8XlvAxoTQULaxYSqjgfG5xg3OMfzN4A3QpnDFD//ONq99LXNf78J/c//AgSu6me3nDSmCNl/mylyP6/axbic3UvPes+59WSrW6xJyJgiZp3OmSLlDyj/+HY59aqU/r176e+fhlmDoEoT59aTxpgiZXsEpkh9s2gb61IP8/ilZzt9Ce1Y6hSBszpArx8hvozXEY2JOFYITJHx+QP0m7SGJtWTuPycM5yR8z+G6Hi48ROIL+ttQGMilBUCU2TGLNjKht2HeeQvDZ0DxId3w4pvoH5HSKzodTxjIpYVAlMksv0B+k9eQ/Ma5eh89ArisX2c7qXb5NqziDGmiFghMEVi1LwUtuxN59HOjZxO5TLTYM1EOL8PNL7S63jGRDQrBCbkMn1+3p28lla1ynPJ2W5fUYu/dH5aETDGcycsBCIyMWj4mdDHMSXRiDlb2Lo/nccudfcG/D6Y8ipUbwl1Ongdz5iIl98eQXBXn3Z7KHPSMrL9vDtlLW3rVKBDg8rOyHWT4cge6PCI3XrSmGIgv0KQs9toY07KiLlb2Hkwk0eOHhsAWPWd87P+n70LZow5Jr8ri+uJyDicewscHT5GVa8OWTIT9rL9Ad6bup7ksypwYb1Kzki/DxaPgNoXQkI5bwMaY4D8C0HwrSX/E8ogpuQZu2ArW/en88o1zX7fG1gyErKPQPuHvA1njDnmhIVAVaceHRaRKu44u1ekyZc/oAz6eR1Nqyf9fqaQL8vpZrpCHWh4qaf5jDG/y++sIRGRF0VkN7ASWC0iqSLyQtHEM+Hqh6U7WL/7MA90bODsDRzZC592h8O74PLX7T7ExhQj+R0sfhjoALRV1UqqWgHnLmLtReSRUIcz4UlVGTBlLfWqlObyZmfAgRQYfitsngmXvQaNLvM6ojEmSH6F4A7gZlXdcHSEqq4HbnOnGXOcn1elsnz7QfpcXJ/ozP3wv06wdR5c8TpceL+dMmpMMZPfweJYVd2dc6SqpopIbIgymTCmqrw7ZS01ypfimtY1YNYAOLQD7hwPddp7Hc8Yk4v89giyTnGaiVCzN+xl3qZ93HtRPWLTtsK0N5x7EFsRMKbYym+PoKWIHMS5jgB+v8BMgISQpTJh690pa6lcJo4bk2vA0E6QeQgue9XrWMaYE8jv9FE7tcMU2IrtB/llzW6euOxsEqa/DtsXwSXPQPUWXkczxpzACQuBiCQAvYEGwGJgiKr6iiKYCT9Dpm+gVGw0PatvgRFvQ6PL4aInvY5ljMlHfk1DHwHZwC9AF+AcwC4JNcdJTcvk64XbuLFtLcpM6Q0xCXDlmxBlPZ0bU9zlVwiaqmpzABH5EJgd+kgmHH362yay/AF6tYyDhUudJqFyNb2OZYwpgPy+rmUfHbAmIZOXjGw/n/62iU6Nq3LWnFeckS1v9DaUMabACnrWEDhnCpUKOotIVTUppOlMWPh64Vb2HM6iT+t4GPM1nHun05+QMSYs2FlD5rSoKh9O30DbasK5P7sXmyff420oY8xJyW+PwJgTmr52N6t3HmJyo6+QLZvgxk/tdFFjwoyd0mFOy4fTN3Bx6c3U2/wVXHA/NLnK60jGmJNkewTmlK3dlcbUVTuZWeVTCFSFi5/yOpIx5hRYITCnbPDU9fSIncEZaUuh20BIsHMHjAlHIW0aEpHLRWSViKwVkadPMF9bEfGLyPWhzGMKz5qdafw6fzEvxX8GZ7aBljd7HckYc4pCVghEJBoYAFwBNAVuFpGmecz3OjAhVFlM4fvPxFW8EPc5ib4D0PUtu4LYmDAWyv/e84C1qrpeVbOA4UC3XOb7P+ArYFcIs5hCtGDzPvYsn8oVMgPaPwxntvY6kjHmNISyENQAtgQ9T3HHHSMiNYBrgcEnWpGI3Csic0VkbmpqaqEHNQWnqrz+w0ruTfgJjSsDFz3hdSRjzGkKZSHI7X6EmuP528BTquo/0YpU9X1VTVbV5CpVqhRWPnMKpq3Zzbr16+msM5Gm3SC+jNeRjDGnKZRnDaUAtYKe1wS25ZgnGRguzj1sKwNdRMSnqmNDmMucokBA+fcPK3muzNeIT+0KYmNKiFAWgjlAQxGpC2wFbgJuCZ5BVeseHRaRYcC3VgSKr++WbGfbthSuSZjgXDhWo43XkYwxhSBkhUBVfSLSF+dsoGicm9osE5He7vQTHhcwxUu2P8CbE1dxV4XFkA60uhUkt9Y/Y0y4CekFZao6HhifY1yuBUBV7wxlFnN6/vvjag7s2UHvcl9AlcbQ8FKvIxljColdWWzyNX3Nbj6YuopxVT4iLm0fXPYhRFnHtMaUFHYVkDmh1LRMHhmxkFfKjqFx2kw4pzvU6+h1LGNMIbJCYPIUCCiPjVxEdPoeevi+gdrt4Nr37CpiY0oY+482efpg+nqmrU6lf/MNSMAHXf4NMXFexzLGFDIrBCZXC7fs598/rOL6JqVou3EwVG4E1Zp5HcsYEwJ2sNgcxx9QHhuxkGpJCbxaZhSSmQZ3fG2nixpTQtkegTnO90u3sy71MP9u5yNu6RfQ+nao3tLrWMaYELFCYP5AVRkwZR31q5Sm3d6xEFcWOv/d61jGmBCyQmD+4OdVqazYfpA+lzRAdiyBM1tBQjmvYxljQsgKgTlGVXl3ylpqlC/FNaWXwI7FUDPZ61jGmBCzQmCOmbVhL/M27ePBCysSM+ZeKFcLWt/mdSxjTIjZWUPmmAFT1lK5TDzXZX8LmQfhjrFQsZ7XsYwxIWZ7BAaARVv288ua3TzZ2k/MrAHO7SdrnOt1LGNMEbBCYAAY+PNazk3YRo8Fd4BEw9Xveh3JGFNErGnIsHpnGhOW7eTb2lORPQHo9RNUbex1LGNMEbE9ggjn8wd4dvQSzonfxTm7f4Czu1gRMCbC2B5BhOs/aQ1zN+1lYbX3kAPZkHy315GMMUXM9ggi2Ix1u3lnylqebLyH8gdWQJf/QL2LvY5ljCliVggi1J5DmTzy5ULqVi7NvWWmQ3w5aHad17GMMR6wQhCBVJUnRi1m35Fs3r+sFDHLR0PjKyGxotfRjDEesEIQgYb8upHJK3fxXJcmNFj3CQR8cMlTXscyxnjECkGEWb0zjX99v4LOTatxx/k1YNV4aHQ5VKjjdTRjjEesEESQQEB5+qvFlImP4fXrWiDbFsCRPdDiBq+jGWM8ZIUggnw2ezPzN+/nb12bUrF0HCz/2plQ184UMiaSWSGIEDsOZPDv71fSoUFlrm1dA/w+mDcM6nWE0pW9jmeM8ZAVggjx0rhlZPkD/PPaZogqTHwOsg7BuXd6Hc0Y4zErBBFgwrId/LBsBw//pRFnVSgFk/4OswZDi5ugydVexzPGeMy6mCjh0jKyeeHrpTSpnkSvDnVgbB9YPBwaXgrXDgYRryMaYzxmewQl3L9/WMWutEz+dW0zYn9+xSkCza6Hm7+0ImCMAawQlGgz1u3mk982cVe7urTc/BFMfwvO6gDXDIQoe+uNMY6QfhqIyOUiskpE1orI07lMv1VEFruPGSLSMpR5IsnhTB9PjlpM3cqleTI5Cia/AuVrw+2jISbe63jGmGIkZMcIRCQaGAB0BlKAOSIyTlWXB822AbhYVfeJyBXA+8D5ocoUSV77fgVb96cz6q/JJIzrAfFl4O4JVgSMMccJ5R7BecBaVV2vqlnAcKBb8AyqOkNV97lPfwNqhjBPxJixdjef/raZXhfW4tw5j8H2RXBVf0g60+toxphiKJSFoAawJeh5ijsuL/cA34cwT0Q4lOnjiVGLSa6YydNp/4QV30C7B6HJVV5HM8YUU6E8fTS3U1I01xlFOuIUgg55TL8XuBegdu3ahZWvRHp1/Aq2HUjn27NHEL12InR4BP78gp0hZIzJUyj3CFKAWkHPawLbcs4kIi2AD4BuqrontxWp6vuqmqyqyVWqVAlJ2JJg6upUPp+1mUfaJlJh80/Q8hb4y0t2hpAx5oRC+QkxB2goInVFJA64CRgXPIOI1AZGA7er6uoQZinxdhzI4JEvF9K4ain67n4ZNGD3GDDGFEjImoZU1ScifYEJQDQwRFWXiUhvd/pg4AWgEjBQnKYLn6omhypTSeXzB/i/L+aTke1n6IV7iZowHzq94Jwuaowx+QhpFxOqOh4Yn2Pc4KDhXkCvUGaIBP+ZuJo5G/cxsHtdqs+4EZJqwAX3ex3LGBMmrK+hMDd55U4GT13HzW1r0WXV87B/M9w5HmJLeR3NGBMm7ChiGNu6P51HRyyiafUkXq4+A9ZNgta3QZ32XkczxoQRKwRhyucP0Pfz+fj8ygedY4id+BSc2Qa69vM6mjEmzFjTUJgaNmMjCzbvp9+NLTlz+m0QHQ83fgrR9pYaY06O7RGEoS17j/DmxNV0alyVqytthW0L4JKnodyJLtw2xpjc2dfHMKOqPD92KVEC/+h2DjL8UohPguS7vI5mjAlTtkcQZsYt2sbU1ak8ftnZnDnnNdi5BM67F0pV8DqaMSZMWSEII/uPZPHyN8tpWbMcPfkWZvSHuhfDJc94Hc0YE8asaSiMvDp+BfvTs5jY5HuifvwQGneF6z6wA8TGmNNiewRhYsa63YyYu4Wh9aZSaemH0Pp26DHMLhwzxpw2+yoZBn5bv4f7PpnHI0k/c1HK/6DWBdDlDYiO9TqaMaYEsEJQzI1fsp1nh//GM6W/4Wb/N84xgdvHWtfSxphCY4WgGPtoxkZe/2YekxKfp3rWNmh5M1z6ihUBY0yhskJQDKkq/5m4igFT1vJ55S+ofmgbXPchNL/e62jGmBLICkExcyA9mydGLmLi8p0MqDuDdtt/hDY9rQgYY0LGCkExsmzbAe7/bD5b96XzcZvVXLR8ANT/M3R92+toxpgSzApBMTFizhb+9vVSKiTGMfX8OdRY8BbElYWbh9sxAWNMSFkh8FiWL8Dfxi7ly7lb6FC/Eu+dNYnSM96C6i3huiEQE+91RGNMCWeFwEP7j2Rx3yfzmLVhL6+fe5AbDvRDZsyC+p3g5i+sCBhjioQVAo9s2H2Yu4fN4fC+XfzSYCy1ln0HZarBFW84PYnaxWLGmCJihcADs9bv4b5P53G7fssj8V8QlZIFyffApf+AuNJexzPGRBgrBEVIVRk+ZwsvfL2U50uPpWfWl5BYFbq/55wdZIwxHrBCUEQOpGfz7OglTFyyhSeqL6Lnvi+h2fVwdX/bCzDGeMoKQRGYt2kvj3w+j+6Hh/Ofsj9Rat9+qNQQrnrbioAxxnNWCEIoI9vP+9PW02/SGp4t/TX3xIwCLQVX9YNWt9oBYWNMsWCFIATSMrL59LfNfDh9A7sPZfJQo73cs3k4xCbCM1vtAjFjTLFihaAQ7T6UyZDpG/jkt02kZfi4rH48L9X7njO2ToDSVeGvk6wIGGOKHSsEhSAQUL6Ys5l/jV/JoSwfXc45g+cr/Ej1FUNh6w44+0po/xCUr+11VGOMOY4VgtO0LvUQz4+aj2yZyb8qrqRj+d0k7loPa1Ogzp+g27vQsLPXMY0xJk9WCE5FIMCBLUtZNuVL0tbPZmDUCirEpaFHYpGk5nBWO+dx7p0g4nVaY4w5ISsE+UjLyGbd5hR2bVhCxtalVNw9h4ZHFlKNvbQDUuPPJPHMc6HJFUiLGyCxoteRjTHmpIS0EIjI5UA/IBr4QFX/lWO6uNO7AEeAO1V1figzFcR7U9cxc/0eorYt4L7MIZwftfLYtL1RFdhZ5mxW1bqMik0uplmLcz1Maowxpy9khUBEooEBQGcgBZgjIuNUdXnQbFcADd3H+cAg92doBfxwZC8c2Q1H9sBh96c7fO7y1bTLSKWpbwVZcWVY1+QRkuq0odJZ51CxUj0qitAk5CGNMaZohHKP4DxgraquBxCR4UA3ILgQdAM+VlUFfhOR8iJSXVW3F3qaNT/CD884H/7p+wHNfb74ciSXrgyVzoAKN1PqosepX7FuoccxxpjiIpSFoAawJeh5Csd/289tnhrAHwqBiNwL3AtQu/YpnoJZqgKc0QwSK0NiJShd2WnPT6zsDleCUhUhJu7U1m+MMWEqlIUgt9Nlcn4NL8g8qOr7wPsAycnJeXyVz0fNZOgx7JQWNcaYkiyUl7mmALWCntcEtp3CPMYYY0IolIVgDtBQROqKSBxwEzAuxzzjgDvEcQFwICTHB4wxxuQpZE1DquoTkb7ABJzTR4eo6jIR6e1OHwyMxzl1dC3O6aN3hSqPMcaY3IX0OgJVHY/zYR88bnDQsAIPhDKDMcaYE7OuMI0xJsJZITDGmAhnhcAYYyKcFQJjjIlw4hyvDR8ikgpsKoJNVQZ2F8F2Clu45obwzW65i164Zvcy91mqWiW3CWFXCIqKiMxV1WSvc5yscM0N4Zvdche9cM1eXHNb05AxxkQ4KwTGGBPhrBDk7X2vA5yicM0N4Zvdche9cM1eLHPbMQJjjIlwtkdgjDERzgqBMcZEOCsEOYjIEBHZJSJLvc5yMkSklohMEZEVIrJMRB7yOlNBiEiCiMwWkUVu7r97nelkiEi0iCwQkW+9znIyRGSjiCwRkYUiMtfrPAXl3s52lIisdP/WL/Q6U0GIyNnua330cVBEHvY611F2jCAHEbkIOIRzL+VmXucpKBGpDlRX1fkiUhaYB1yjqsvzWdRTIiJAaVU9JCKxwHTgIVX9zeNoBSIijwLJQJKqdvU6T0GJyEYgWVXD6qIsEfkI+EVVP3Dvc5Koqvs9jnVSRCQa2Aqcr6pFcXFsvmyPIAdVnQbs9TrHyVLV7ao63x1OA1bg3P+5WFPHIfdprPsIi28nIlITuBL4wOsskUBEkoCLgA8BVDUr3IqAqxOwrrgUAbBCUCKJSB2gNTDL4ygF4javLAR2AT+qaljkBt4GngQCHuc4FQpMFJF5InKv12EKqB6QCgx1m+M+EJHSXoc6BTcBX3gdIpgVghJGRMoAXwEPq+pBr/MUhKr6VbUVzj2rzxORYt8kJyJdgV2qOs/rLKeovaq2Aa4AHnCbRIu7GKANMEhVWwOHgae9jXRy3Oasq4GRXmcJZoWgBHHb2L8CPlPV0V7nOVnubv7PwOXeJimQ9sDVblv7cODPIvKpt5EKTlW3uT93AWOA87xNVCApQErQHuMonMIQTq4A5qvqTq+DBLNCUEK4B10/BFao6lte5ykoEakiIuXd4VLAX4CVnoYqAFV9RlVrqmodnF39yap6m8exCkRESrsnFOA2rVwKFPuz5FR1B7BFRM52R3UCivXJELm4mWLWLAQhvmdxOBKRL4BLgMoikgK8qKofepuqQNoDtwNL3PZ2gGfd+0YXZ9WBj9wzKaKAEaoaVqdihqFqwBjnuwMxwOeq+oO3kQrs/4DP3CaW9cBdHucpMBFJBDoD93mdJSc7fdQYYyKcNQ0ZY0yEs0JgjDERzgqBMcZEOCsExhgT4awQGGNMhLNCYDwlItVE5HMRWe92dzBTRK49xXXVCbdeYwuLOCa7/fGc7rriRGSaiNjp5RHCCoHxjHsR3FhgmqrWU9VzcS7OqulpsAIohh+SXYBFhdGtiKpmAZOAG087lQkLVgiMl/4MZKnq4KMjVHWTqr4Dx+5VMNTtN3+BiHR0x9cRkV9EZL77aJdzxSJyjnufg4UislhEGuYyzyERedNdxyQRqeKOry8iP7h7KL+ISGN3/DAReUtEpgCv51hXooiMcLf1pYjMEpFkd9ogEZmb834L7j0BXnX3guaKSBsRmSAi60Skd9B8T4jIHHfded2v4Vbg66DXZ6XbKdtSEflMRP4iIr+KyBoROc+d7yUReTxoO0vdDgvBKdC35rEtU9Koqj3s4ckDeBD47wmmPwYMdYcbA5uBBCARSHDHNwTmusN1gKXu8DvAre5wHFAql/Vr0DwvAO+6w5OAhu7w+TjdRwAMA74FonNZ1+PAe+5wM8CH098/QEX3ZzROX0ot3OcbgT7u8H+BxUBZoApOh3bgdP/wPiA4X9y+BS7KZfubgLJBr4MPaO4uMw8Y4q6jGzDWne8l4PGgdSwF6gRlTfX6b8QeRfMobru3JoKJyACgA85eQlt3+B0AVV0pIpuARjgfeu+KSCvA747LaSbwnHvPgNGquiaXeQLAl+7wp8Bot/fWdsBItwsGgPigZUaqqj+XdXUA+rlZl4rI4qBpN7hdPcfgdKnRFOdDH2Cc+3MJUEade0mkiUiG2wfTpe5jgTtfGZziNy3H9iu6yx61QVWXAIjIMmCSqqqILMEpFCekqn4RyRKRsjnWa0ogKwTGS8uA644+UdUHRKQycPTWiZLrUvAIsBNoifONNyPnDKr6uYjMwrlxzAQR6aWqk/PJo+769qvTLXZuDucxPtesIlIXZ2+hraruE5FhOHs1R2W6PwNBw0efx7jrfU1V38snu09EolT16L0Rcq4reDtH/+99/LF5ODgXOAXwuNfWlDx2jMB4aTKQICJ9gsYlBg1Pw22nFpFGQG1gFVAO2O5+6N2O04zxByJSD1ivqv1xvnW3yGX7UcD17vAtwHR1DrZuEJEe7npERFoW4HeZDtzgLtMUp1kGIAmneBwQkWo43RCfjAnA3e6eCiJSQ0Sq5jLfKpwbt5yMjbjdOItIG6Du0QkiUgmnaSj7JNdpwpAVAuMZVVXgGuBiEdkgIrOBj4Cn3FkGAtFuc8aXwJ2qmumO7ykiv+E0C+X2Lf1GYKk4PbE2Bj7OZZ7DwDkiMg/nwPXL7vhbgXtEZBHOXku3Avw6A4EqbpPQUzhNPwdUdRFOs84ynHb6XwuwrmNUdSLwOTDTfR1G4RxHyOk7nF5zT8ZXQEX3NeoDrA6a1hEo7j3XmkJivY+aiCUih1S1TCGtKxqIVdUMEamPc8C5kTqnYoaciFQHPlbVzoW0vtHAM6q6qjDWZ4o3O0ZgTOFIBKaIc5c4wTkbqEiKAICqbheR/4lIkp7mtQTi9PU/1opA5LA9AmOMiXB2jMAYYyKcFQJjjIlwVgiMMSbCWSEwxpgIZ4XAGGMi3P8D4plPoisNciMAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_post, label='posterior grid')\n", "plot_cdf(sample_post_pymc, label='posterior pymc')\n", "decorate_rate()\n", "\n", "plt.savefig('zigzag12.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, it looks pretty good." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Posterior predictive\n", "\n", "To sample from the posterior predictive distribution, we can use `sample_posterior_predictive`:" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1000/1000 [00:00<00:00, 2524.62it/s]\n" ] } ], "source": [ "with model:\n", " post_pred = pm.sample_posterior_predictive(trace, samples=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what it looks like:" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.95" ] }, "execution_count": 53, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pred_pymc = post_pred['goals']\n", "np.mean(sample_post_pred_pymc)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.888" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pred = poisson(sample_post).rvs()\n", "sample_post_pred.mean()" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(sample_post_pred, label='posterior pred grid')\n", "plot_cdf(sample_post_pred_pymc, label='posterior pred pm')\n", "decorate_goals()\n", "\n", "plt.savefig('zigzag13.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks pretty good!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two teams\n", "\n", "We can extend the model to estimate different values of `mu` for the two teams." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [mu_TBL, mu_BOS]\n", "Sampling 2 chains, 0 divergences: 100%|██████████| 2000/2000 [00:00<00:00, 2169.16draws/s]\n", "The acceptance probability does not match the target. It is 0.8810527302399683, but should be close to 0.8. Try to increase the number of tuning steps.\n" ] } ], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " mu_BOS = pm.Gamma('mu_BOS', alpha, beta)\n", " mu_TBL = pm.Gamma('mu_TBL', alpha, beta)\n", " goals_BOS = pm.Poisson('goals_BOS', mu_BOS, observed=3)\n", " goals_TBL = pm.Poisson('goals_TBL', mu_TBL, observed=2)\n", " trace = pm.sample(500)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use `traceplot` to review the results and do some visual diagnostics." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with model:\n", " pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior distribitions for `mu_BOS` and `mu_TBL`." ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "mu_TBL = trace['mu_TBL']\n", "plot_cdf(mu_TBL, label='mu_TBL posterior')\n", "\n", "mu_BOS = trace['mu_BOS']\n", "plot_cdf(mu_BOS, label='mu_BOS posterior')\n", "\n", "decorate_rate('CDF')\n", "np.mean(mu_BOS), np.mean(mu_TBL)\n", "\n", "plt.savefig('zigzag14.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the basis of one game here's the probability that Boston is the better team." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.617" ] }, "execution_count": 59, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(mu_BOS > mu_TBL)" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.0" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(mu_BOS == mu_TBL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predictions\n", "\n", "Even if Boston is the better team, that doesn't mean they'll win the next game.\n", "\n", "We can use `sample_posterior_predictive` to generate predictions." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1000/1000 [00:00<00:00, 1443.61it/s]\n" ] } ], "source": [ "with model:\n", " post_pred = pm.sample_posterior_predictive(trace, samples=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior predictive distributions of goals scored." ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "goals_BOS = post_pred['goals_BOS'].flatten()\n", "goals_TBL = post_pred['goals_TBL'].flatten()" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(goals_TBL, label='TBL')\n", "plot_cdf(goals_BOS, label='BOS')\n", "decorate_goals('CDF')\n", "\n", "plt.savefig('zigzag15.png', dpi=150)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the chance that Boston wins the next game." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.475" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "win = np.mean(goals_BOS > goals_TBL)\n", "win" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The chance that they lose." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.338" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lose = np.mean(goals_TBL > goals_BOS)\n", "lose" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the chance of a tie." ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.187" ] }, "execution_count": 66, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tie = np.mean(goals_BOS == goals_TBL)\n", "tie" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Going hierarchical\n", "\n", "So far, all of this is based on a gamma prior. To choose the parameters of the prior, I used data from previous Stanley Cup finals and computed a maximum likelihood estimate (MLE). But that's not correct, because\n", "\n", "1. It assumes that the observed goal counts are the long-term goal-scoring rates.\n", "2. It treats `alpha` and `beta` as known values rather than parameters to estimate.\n", "\n", "In other words, I have ignored two important sources of uncertainty. As a result, my predictions are almost certainly too confident.\n", "\n", "The solution is a hierarchical model, where `alpha` and `beta` are the parameters that control `mu` and `mu` is the parameter that controls `goals`. Then we can use observed `goals` to update the distributions of all three unknown parameters.\n", "\n", "Of course, now we need a prior distribution for `alpha` and `beta`. A common choice is the half Cauchy distribution (see [Gelman](http://www.stat.columbia.edu/~gelman/research/published/taumain.pdf)), but on advice of counsel, I'm going with exponential." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a PyMC model that generates `alpha` and `beta` from an exponential distribution." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " alpha = pm.Exponential('alpha', lam=1)\n", " beta = pm.Exponential('beta', lam=1)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the distributions of `alpha` and `beta` look like." ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.9842304166724799" ] }, "execution_count": 68, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_prior_alpha = trace['alpha']\n", "plot_cdf(sample_prior_alpha, label='alpha prior')\n", "sample_prior_beta = trace['beta']\n", "plot_cdf(sample_prior_beta, label='beta prior')\n", "\n", "plt.xscale('log')\n", "plt.xlabel('Parameter of a gamma distribution')\n", "plt.ylabel('CDF')\n", "np.mean(sample_prior_alpha)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have `alpha` and `beta`, we can generate `mu`." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " alpha = pm.Exponential('alpha', lam=1)\n", " beta = pm.Exponential('beta', lam=1)\n", " mu = pm.Gamma('mu', alpha, beta)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the prior distribution of `mu` looks like." ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "12.976167851569219" ] }, "execution_count": 70, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_prior_mu = trace['mu']\n", "plot_cdf(sample_prior_mu, label='mu prior hierarchical')\n", "decorate_rate('CDF')\n", "np.mean(sample_prior_mu)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In effect, the model is saying \"I have never seen a hockey game before. As far as I know, it could be soccer, could be basketball, could be pinball.\"\n", "\n", "If we zoom in on the range 0 to 10, we can compare the prior implied by the hierarchical model with the gamma prior I hand picked." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_prior_mu, label='mu prior hierarchical')\n", "plot_cdf(sample_prior_gamma, label='mu prior gamma', color='gray')\n", "plt.xlim(0, 10)\n", "decorate_rate('CDF')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Obviously, they are very different. They agree that the most likely values are less than 10, but the hierarchical model admits the possibility that `mu` could be orders of magnitude bigger.\n", "\n", "Strange as it sounds, that's probably what we want in a non-committal prior.\n", "\n", "Ok, last step of the forward process, let's generate some goals." ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " alpha = pm.Exponential('alpha', lam=1)\n", " beta = pm.Exponential('beta', lam=1)\n", " mu = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the prior predictive distribution of goals." ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [], "source": [ "sample_prior_goals = trace['goals']" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.944" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(sample_prior_goals, label='goals prior')\n", "decorate_goals('CDF')\n", "np.mean(sample_prior_goals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To see whether that distribution is right, I ran samples using SciPy." ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "import scipy.stats as st\n", "\n", "def forward_hierarchical(size=1):\n", " alpha = st.expon().rvs(size=size)\n", " beta = st.expon().rvs(size=size)\n", " mu = st.gamma(a=alpha, scale=1/beta).rvs(size=size)\n", " goals = st.poisson(mu).rvs(size=size)\n", " return goals[0]\n", "\n", "sample_prior_goals_st = [forward_hierarchical() for i in range(1000)];" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "6.937" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "set_colors()\n", "plot_cdf(sample_prior_goals, label='goals prior')\n", "plot_cdf(sample_prior_goals_st, label='goals prior scipy')\n", "decorate_goals('CDF')\n", "plt.xlim(0, 50)\n", "plt.legend(loc='lower right')\n", "np.mean(sample_prior_goals_st)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Hierarchical inference\n", "\n", "Once we have the forward process working, we only need a small change to run the reverse process." ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [mu, beta, alpha]\n", "Sampling 2 chains, 1 divergences: 100%|██████████| 3000/3000 [00:02<00:00, 1444.74draws/s]\n", "There was 1 divergence after tuning. Increase `target_accept` or reparameterize.\n" ] } ], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " alpha = pm.Exponential('alpha', lam=1)\n", " beta = pm.Exponential('beta', lam=1)\n", " mu = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu, observed=[3, 3])\n", " trace = pm.sample(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the posterior distribution of `mu`. The posterior mean is close to the observed value, which is what we expect with a weakly informative prior." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.865235353825642" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_post_mu = trace['mu']\n", "plot_cdf(sample_post_mu, label='mu posterior')\n", "decorate_rate('CDF')\n", "np.mean(sample_post_mu)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Two teams\n", "\n", "We can extend the model to estimate different values of `mu` for the two teams." ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [mu_TBL, mu_BOS, beta, alpha]\n", "Sampling 2 chains, 0 divergences: 100%|██████████| 3000/3000 [00:03<00:00, 861.25draws/s]\n" ] } ], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " alpha = pm.Exponential('alpha', lam=1)\n", " beta = pm.Exponential('beta', lam=1)\n", " mu_BOS = pm.Gamma('mu_BOS', alpha, beta)\n", " mu_TBL = pm.Gamma('mu_TBL', alpha, beta)\n", " goals_BOS = pm.Poisson('goals_BOS', mu_BOS, observed=[3, 3])\n", " goals_TBL = pm.Poisson('goals_TBL', mu_TBL, observed=[2, 3])\n", " trace = pm.sample(1000, nuts_kwargs=dict(target_accept=0.95))" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with model:\n", " pm.traceplot(trace)" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with model:\n", " pm.plot_posterior(trace['mu_BOS'])" ] }, { "cell_type": "code", "execution_count": 82, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "with model:\n", " pm.plot_posterior(trace['mu_TBL'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior distribitions for `mu_TBL` and `mu_BOS`." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2.5273712319352972, 2.857168894779832)" ] }, "execution_count": 83, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sample_post_mu_TBL = trace['mu_TBL']\n", "plot_cdf(sample_post_mu_TBL, label='mu_TBL posterior')\n", "\n", "sample_post_mu_BOS = trace['mu_BOS']\n", "plot_cdf(sample_post_mu_BOS, label='mu_BOS posterior')\n", "\n", "decorate_rate('CDF')\n", "np.mean(sample_post_mu_TBL), np.mean(sample_post_mu_BOS)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the basis of one game (and never having seen a previous game), here's the probability that Boston is the better team." ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.603" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(sample_post_mu_BOS > sample_post_mu_TBL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More background\n", "\n", "But let's take advantage of more information. Here are the results from the seven most recent Stanley Cup finals, ignoring games that went into overtime." ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [], "source": [ "data = dict(BOS13 = [2, 1, 2],\n", " CHI13 = [0, 3, 3],\n", " NYR14 = [0, 2],\n", " LAK14 = [3, 1],\n", " TBL15 = [1, 4, 3, 1, 1, 0],\n", " CHI15 = [2, 3, 2, 2, 2, 2],\n", " SJS16 = [2, 1, 4, 1],\n", " PIT16 = [3, 3, 2, 3],\n", " NSH17 = [3, 1, 5, 4, 0, 0],\n", " PIT17 = [5, 4, 1, 1, 6, 2],\n", " VGK18 = [6, 2, 1, 2, 3],\n", " WSH18 = [4, 3, 3, 6, 4],\n", " BOS19 = [2, 7, 2, 1, 5, 1],\n", " STL19 = [2, 2, 4, 2, 1, 4],\n", " BOS20 = [3, 2],\n", " TBL20 = [2, 3],\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's how we can get the data into the model." ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "Multiprocess sampling (2 chains in 2 jobs)\n", "NUTS: [mu_TBL20, mu_BOS20, mu_STL19, mu_BOS19, mu_WSH18, mu_VGK18, mu_PIT17, mu_NSH17, mu_PIT16, mu_SJS16, mu_CHI15, mu_TBL15, mu_LAK14, mu_NYR14, mu_CHI13, mu_BOS13, beta, alpha]\n", "Sampling 2 chains, 0 divergences: 100%|██████████| 3000/3000 [00:13<00:00, 224.03draws/s]\n" ] } ], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " alpha = pm.Exponential('alpha', lam=1)\n", " beta = pm.Exponential('beta', lam=1)\n", " \n", " mu = dict()\n", " goals = dict()\n", " for name, observed in data.items():\n", " mu[name] = pm.Gamma('mu_'+name, alpha, beta)\n", " goals[name] = pm.Poisson(name, mu[name], observed=observed)\n", " \n", " trace = pm.sample(500, nuts_kwargs=dict(target_accept=0.95))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior means." ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.479121501369579" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_mu_BOS = trace['mu_BOS20']\n", "np.mean(sample_post_mu_BOS)" ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.4738678038205064" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_mu_TBL = trace['mu_TBL20']\n", "np.mean(sample_post_mu_TBL)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are lower with the background information than without, and closer together. Here's the updated chance that Boston is the better team." ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4935" ] }, "execution_count": 92, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(sample_post_mu_BOS > sample_post_mu_TBL)" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_cdf(trace['alpha'], label='alpha')\n", "plot_cdf(trace['beta'], label='beta')\n", "\n", "plt.xlabel('Parameter of a gamma distribution')\n", "plt.ylabel('CDF')\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "4.360177013060098" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(trace['alpha'])" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.7947170342792527" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(trace['beta'])" ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.475142954843771" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(trace['alpha'] / trace['beta'])" ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.6342667744048895" ] }, "execution_count": 97, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(trace['alpha'] / trace['beta']**2)" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.9" } }, "nbformat": 4, "nbformat_minor": 4 }