{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Bayesian Zig Zag\n", "===\n", "\n", "Developing probabilistic models using grid methods and MCMC.\n", "\n", "Thanks to Chris Fonnesback for his help with this example, and to Colin Carroll, who added features to pymc3 to support some of these examples.\n", "\n", "To install the most current version of pymc3 from source, run\n", "\n", "```\n", "pip3 install -U git+https://github.com/pymc-devs/pymc3.git\n", "```\n", "\n", "Copyright 2018 Allen Downey\n", "\n", "MIT License: https://opensource.org/licenses/MIT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/home/downey/anaconda3/lib/python3.6/site-packages/h5py/__init__.py:36: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " from ._conv import register_converters as _register_converters\n" ] } ], "source": [ "from __future__ import print_function, division\n", "\n", "%matplotlib inline\n", "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n", "\n", "import numpy as np\n", "import pymc3 as pm\n", "\n", "import matplotlib.pyplot as plt" ] }, { "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, we'll assume that `lambda` is known (somehow) to be 2.7. Since regulation play (as opposed to overtime) is 60 minutes, we can compute the goal scoring rate per minute." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(0.045000000000000005, 0.0020250000000000003)" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lam_per_game = 2.7\n", "min_per_game = 60\n", "lam_per_min = lam_per_game / min_per_game\n", "lam_per_min, lam_per_min**2" ] }, { "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": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.24854258, 0.52875352, 0.22484978, 0.86150742, 0.43267598,\n", " 0.09555405, 0.27335867, 0.19562018, 0.73189681, 0.21946824,\n", " 0.39113398, 0.57423922, 0.41425276, 0.28758257, 0.33677518,\n", " 0.35294738, 0.88576287, 0.40491434, 0.86364665, 0.27271087,\n", " 0.79620178, 0.24828994, 0.09181572, 0.52995806, 0.9398433 ,\n", " 0.03559086, 0.49451461, 0.10388974, 0.76300647, 0.59411612,\n", " 0.00578253, 0.17309223, 0.0694602 , 0.40727806, 0.35595972,\n", " 0.86150781, 0.40107466, 0.39114327, 0.37708123, 0.81982997,\n", " 0.21540224, 0.06370102, 0.03034388, 0.5671709 , 0.14978002,\n", " 0.40609019, 0.03284181, 0.83123708, 0.51662959, 0.16160601,\n", " 0.00672113, 0.14484844, 0.72336197, 0.15782915, 0.50394997,\n", " 0.03168813, 0.03765264, 0.77608364, 0.1249013 , 0.12412637])" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.random(min_per_game)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If the random value is less than `lam_per_min`, that means we score a goal during that minute." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, True, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False, False, False, False,\n", " False, False, False, False, False, False])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.random(min_per_game) < lam_per_min" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we can get the number of goals scored by one team like this:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "3" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(np.random.random(min_per_game) < lam_per_min)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I'll wrap that in a function." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "def half_game(lam_per_min, min_per_game=60):\n", " return np.sum(np.random.random(min_per_game) < lam_per_min)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And simulate 10 games." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[5, 3, 1, 6, 4, 3, 2, 4, 8, 1]" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "size = 10\n", "sample = [half_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": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(2.673, 2.7)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "size = 1000\n", "sample_sim = [half_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), which I'll implement using a `Counter`.\n", "\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "from collections import Counter\n", "\n", "class Pmf(Counter):\n", " \n", " def normalize(self):\n", " \"\"\"Normalizes the PMF so the probabilities add to 1.\"\"\"\n", " total = sum(self.values())\n", " for key in self:\n", " self[key] /= total\n", " \n", " def sorted_items(self):\n", " \"\"\"Returns the outcomes and their probabilities.\"\"\"\n", " return zip(*sorted(self.items()))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are some functions for plotting PMFs." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "plot_options = dict(linewidth=3, alpha=0.6)\n", "\n", "def underride(options):\n", " \"\"\"Add key-value pairs to d only if key is not in d.\n", "\n", " options: dictionary\n", " \"\"\"\n", "\n", " for key, val in plot_options.items():\n", " options.setdefault(key, val)\n", " return options\n", "\n", "def plot(xs, ys, **options):\n", " \"\"\"Line plot with plot_options.\"\"\"\n", " plt.plot(xs, ys, **underride(options))\n", "\n", "def bar(xs, ys, **options):\n", " \"\"\"Bar plot with plot_options.\"\"\"\n", " plt.bar(xs, ys, **underride(options))\n", "\n", "def plot_pmf(sample, **options):\n", " \"\"\"Compute and plot a PMF.\"\"\"\n", " pmf = Pmf(sample)\n", " pmf.normalize()\n", " xs, ps = pmf.sorted_items()\n", " bar(xs, ps, **options)\n", " \n", "def pmf_goals():\n", " \"\"\"Decorate the axes.\"\"\"\n", " plt.xlabel('Number of goals')\n", " plt.ylabel('PMF')\n", " plt.title('Distribution of goals scored')\n", " legend()\n", " \n", "def legend(**options):\n", " \"\"\"Draw a legend only if there are labeled items.\n", " \"\"\"\n", " ax = plt.gca()\n", " handles, labels = ax.get_legend_handles_labels()\n", " if len(labels):\n", " plt.legend(**options)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the results from the simulation look like." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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z4cD68kaSJgGfBk6NiM2dWdbMzHpGkWGxBDhQ0ihJ/YEpwPzSBpKOAL5BFhS/L5l1L3CipMH5ge0T82lmZlYFhR3gjogWSdPJ3uTrgDkRsULSTKAxIuaTDTvtDnxPEsDaiDg1IjZK+ixZ4ADMbD3YbWZmPa/Is6GIiAXAgrJpV5Y8ntTOsnOAOcVVZ2ZmHVVoWFjn+TRRM6tFvtyHmZklOSzMzCzJYWFmZkkOCzMzS3JYmJlZksPCzMySHBZmZpbksDAzsySHhZmZJTkszMwsyWFhZmZJDgszM0tyWJiZWZLDwszMkhwWZmaW5LAwM7Mkh4WZmSX5TnlmneA7GdquynsWZmaW5LAwM7Mkh4WZmSU5LMzMLMlhYWZmSQ4LMzNLcliYmVmSw8LMzJIcFmZmluSwMDOzJIeFmZklFRoWkiZLelbSKkmXVph/vKTHJbVIOrNs3hZJy/Kf+UXWaWZm7SvsQoKS6oAbgL8BmoAlkuZHxMqSZmuBDwEXV+jitYg4vKj6zMys44q86ux4YFVErAaQdAdwGrAtLCJiTT5va4F1mJnZTmp3GErSLSWPz+1k38OAdSXPm/JpHTVQUqOkRyWd3kZ9F+RtGpubmztZnpmZdVTqmMW4kscf72TfqjAtOrH8yIhoAP4euE7S/jt0FjE7IhoiomHo0KGdLM/MzDoqFRadeXMv1wSMKHk+HFjf0YUjYn3+72pgEXDETtRiZmY7IXXMYrik68n2ElofbxMRH2tn2SXAgZJGAb8BppDtJSRJGgz8KSI2SxoCHAdc25Flzcys+6XCYkbJ48bOdBwRLZKmA/cCdcCciFghaSbQGBHzJR0N/AAYDLxf0tURcShwCPCN/MB3H2BW2VlUZmbWg9oNi4i4dWc6j4gFwIKyaVeWPF5CNjxVvtzDgG8+bGZWI9oNi9SX4SLi1O4tx8zMalFqGOpdZKe/fhd4jMpnOJmZWS+XCot3kH0DeyrZwen/BL4bESuKLszMzGpHu6fORsSWiLgnIs4FjgVWAYskXdgj1ZmZWU1IXu5D0gDgZLK9i3rgemBesWWZmVktSR3gvhUYA9wNXB0RT/VIVWZmVlNSexbnAJuAg4CPS2r9RreAiIi3FlmcmZnVhtT3LHxzJDMzSw5DDQQ+AhwA/ILsW9gtPVGYmZnVjtSew61AA7Ac+FvgS4VXZGZmNSd1zGJ0RIwFkHQzsLj4kszMrNak9izeaH3g4Sczs11Xas9inKRX8scCdsuf+2woM7NdSOpsqLqeKsTMzGqXT401M7Mkh4WZmSU5LMzMLMlhYWZmSQ4LMzNLcliYmVmSw8LMzJIcFmZmluSwMDOzJIeFmZklOSzMzCzJYWFmZkkOCzMzS3JYmJlZksPCzMySCg0LSZMlPStplaRLK8w/XtLjkloknVk271xJz+U/5xZZp5mZta+wsJBUB9wAnASMBqZKGl3WbC3wIeA7Zcu+HfgMcAwwHviMpMFF1WpmZu0rcs9iPLAqIlZHxJ+BO4DTShtExJqI+AWwtWzZ9wH3RcTGiPgDcB8wucBazcysHUWGxTBgXcnzpnxa0cuamVk3KzIsVGFadOeyki6Q1Cipsbm5uVPFmZlZxxUZFk3AiJLnw4H13blsRMyOiIaIaBg6dGiXCzUzs/YVGRZLgAMljZLUH5gCzO/gsvcCJ0oanB/YPjGfZmZmVVBYWERECzCd7E3+aeDOiFghaaakUwEkHS2pCfgg8A1JK/JlNwKfJQucJcDMfJqZmVVB3yI7j4gFwIKyaVeWPF5CNsRUadk5wJwi6zMzs47xN7jNzCzJYWFmZkkOCzMzS3JYmJlZksPCzMySHBZmZpbksDAzsySHhZmZJTkszMwsyWFhZmZJDgszM0tyWJiZWZLDwszMkhwWZmaW5LAwM7OkQu9nYWbFuWze8h5b1zVnjO2xdVlt8p6FmZklOSzMzCzJYWFmZkkOCzMzS3JYmJlZksPCzMySHBZmZpbksDAzsySHhZmZJTkszMwsyWFhZmZJDgszM0tyWJiZWZLDwszMkgoNC0mTJT0raZWkSyvMHyBpbj7/MUn1+fR6Sa9JWpb/3FhknWZm1r7C7mchqQ64AfgboAlYIml+RKwsaXYe8IeIOEDSFOALwFn5vOcj4vCi6jMzs44rcs9iPLAqIlZHxJ+BO4DTytqcBtyaP74LOEGSCqzJzMy6oMiwGAasK3nelE+r2CYiWoCXgb3yeaMkPSHpp5L+qtIKJF0gqVFSY3Nzc/dWb2Zm2xR5W9VKewjRwTYvACMjYoOko4D/kHRoRLyyXcOI2cBsgIaGhvK+O8W3qDQza1uRexZNwIiS58OB9W21kdQX2BPYGBGbI2IDQEQsBZ4HDiqwVjMza0eRYbEEOFDSKEn9gSnA/LI284Fz88dnAvdHREgamh8gR9J+wIHA6gJrNTOzdhQ2DBURLZKmA/cCdcCciFghaSbQGBHzgZuBb0taBWwkCxSA44GZklqALcBHImJjUbWamVn7ijxmQUQsABaUTbuy5PHrwAcrLPd94PtF1mZmZh3nb3CbmVmSw8LMzJIcFmZmluSwMDOzJIeFmZklOSzMzCzJYWFmZkkOCzMzSyr0S3lm1vv15EU4wRfirBbvWZiZWZLDwszMkhwWZmaW5LAwM7Mkh4WZmSU5LMzMLMlhYWZmSQ4LMzNLcliYmVmSw8LMzJIcFmZmluSwMDOzJIeFmZklOSzMzCzJYWFmZkm+n4WZ9Ro9eW+NXe2+Gt6zMDOzJIeFmZklOSzMzCzJYWFmZkkOCzMzSyr0bChJk4GvAHXATRExq2z+AOBbwFHABuCsiFiTz7sMOA/YAnwsIu4tslYzs+7Sk2dlQc+cmVXYnoWkOuAG4CRgNDBV0uiyZucBf4iIA4D/B3whX3Y0MAU4FJgMfC3vz8zMqqDIYajxwKqIWB0RfwbuAE4ra3MacGv++C7gBEnKp98REZsj4lfAqrw/MzOrAkVEMR1LZwKTI+L8/Pk5wDERMb2kzVN5m6b8+fPAMcBVwKMRcVs+/Wbg7oi4q2wdFwAX5E8PBp4t5Jdp3xDgxSqst5Z5m+zI22RH3iY7qsY22TcihqYaFXnMQhWmlSdTW206siwRMRuY3fnSuo+kxohoqGYNtcbbZEfeJjvyNtlRLW+TIoehmoARJc+HA+vbaiOpL7AnsLGDy5qZWQ8pMiyWAAdKGiWpP9kB6/llbeYD5+aPzwTuj2xcbD4wRdIASaOAA4HFBdZqZmbtKGwYKiJaJE0H7iU7dXZORKyQNBNojIj5wM3AtyWtItujmJIvu0LSncBKoAX454jYUlStO6mqw2A1yttkR94mO/I22VHNbpPCDnCbmVnv4W9wm5lZksPCzMySHBZdJGmypGclrZJ0abXrqTZJIyQ9IOlpSSskfbzaNdUKSXWSnpD042rXUiskvU3SXZKeyf/PvKvaNVWbpE/kfztPSfqupIHVrqmUw6ILOngpk11NC/DJiDgEOBb4Z2+TbT4OPF3tImrMV4B7IuKdwDh28e0jaRjwMaAhIsaQnRQ0pbpVbc9h0TUduZTJLiUiXoiIx/PHfyT74x9W3aqqT9Jw4GTgpmrXUiskvRU4nuxsSCLizxHxUnWrqgl9gd3y75wNosa+W+aw6JphwLqS5034jXEbSfXAEcBj1a2kJlwHfArYWu1Cash+QDPw7/nw3E2S3lLtoqopIn4D/BuwFngBeDki/qu6VW3PYdE1Hbocya5I0u7A94F/iYhXql1PNUk6Bfh9RCytdi01pi9wJPD1iDgC2ATs0sf9JA0mG50YBewDvEXStOpWtT2HRdf4ciQVSOpHFhS3R8S8atdTA44DTpW0hmyo8q8l3VbdkmpCE9AUEa17nneRhceubBLwq4hojog3gHnAu6tc03YcFl3TkUuZ7FLyS8vfDDwdEV+udj21ICIui4jhEVFP9n/k/oioqU+L1RARvwXWSTo4n3QC2dUadmVrgWMlDcr/lk6gxg76F3qnvN6qrUuZVLmsajsOOAdYLmlZPu3yiFhQxZqsdl0I3J5/2FoNfLjK9VRVRDwm6S7gcbIzC5+gxi794ct9mJlZkoehzMwsyWFhZmZJDgszM0tyWJiZWZLDwszMkhwW1itICklfKnl+saSruqnvWySd2R19JdbzwfwKrA8UuI4e+V2s93FYWG+xGThD0pBqF1Iqv0JxR50H/FNEvLeoesy6ymFhvUUL2ZeYPlE+o/zTtKRX838nSvqppDsl/VLSLElnS1osabmk/Uu6mSTpwbzdKfnydZK+KGmJpF9I+seSfh+Q9B1geYV6pub9PyXpC/m0K4H3ADdK+mJZ+z6Svpbf6+DHkha0/j6STsgvxrdc0hxJA1r7y+t6StLs/FvB5XXMkrQyr/3fOre5bVfjsLDe5AbgbEl7dmKZcWT3mxhL9g30gyJiPNklxS8saVcPTCC73PiN+Y1pziO7OujRwNHA/5E0Km8/Hvh0RGx3Tw9J+wBfAP4aOBw4WtLpETETaATOjogZZTWeka9/LHA+8K68r4HALcBZETGW7IoMH82X+WpEHJ3fG2E34JSyOt4OfAA4NCIOAz7X0Q1muyaHhfUa+VVuv0V2E5mOWpLfi2Mz8DzQelno5WRv0K3ujIitEfEc2eUp3gmcCPxDfnmTx4C9gAPz9osj4lcV1nc0sCi/YFwLcDvZvR3a8x7ge/n6fwu0HtM4mOzic7/Mn99a0td7JT0maTlZMB1a1ucrwOvATZLOAP6UqMF2cQ4L622uI/vEX3p/hBby/+v5cEz/knmbSx5vLXm+le2vnVZ+XZwgu1T9hRFxeP4zquQeBJvaqK/S5e1T2lqm4vR8j+NrwJn5Hsc3ge1u0ZkH1XiyqwSfDtzThbpsF+KwsF4lIjYCd5IFRqs1wFH549OAfl3o+oP5sYP9yW7e8yzZhSQ/ml+aHUkHdeAmPo8BEyQNyQ9+TwV+mljmIeB/5evfG5iYT38GqJd0QP78nLyv1mB4Mb+/yA5nP+XT98wv9PgvZENiZm3yVWetN/oSML3k+TeBH0paDPyEtj/1t+dZsjfivYGPRMTrkm4iG6p6PN9jaSb7lN6miHhB0mVkQ0kCFkTEDxPr/j7ZJaufAn5JFjgv5zV8GPhefivOJcCNEbFZ0jfJhtLW5NPL7UG2TQbmdexwYoBZKV911uxNQNLuEfGqpL2AxcBx+fELsx7hPQuzN4cfS3ob2fGWzzoorKd5z8LMzJJ8gNvMzJIcFmZmluSwMDOzJIeFmZklOSzMzCzpvwEYhkJ90v5ZGAAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_pmf(sample_sim, label='simulation')\n", "pmf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Analytic distributions\n", "\n", "For the simulation we just did, we can figure out the distribution analytically: it's a binomial distribution with parameters `n` and `p`, where `n` is the number of minutes and `p` is the probability of scoring a goal during any minute.\n", "\n", "We can use NumPy to generate a sample from a binomial distribution." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.772" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "n = min_per_game\n", "p = lam_per_min\n", "sample_bin = np.random.binomial(n, p, size)\n", "np.mean(sample_bin)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And confirm that the results are similar to what we got from the model." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_pmf(sample_sim, label='simulation')\n", "plot_pmf(sample_bin, label='binomial')\n", "pmf_goals()" ] }, { "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": 14, "metadata": {}, "outputs": [], "source": [ "def plot_cdf(sample, **options):\n", " \"\"\"Compute and plot the CDF of a sample.\"\"\"\n", " pmf = Pmf(sample)\n", " xs, freqs = pmf.sorted_items()\n", " ps = np.cumsum(freqs, dtype=np.float)\n", " ps /= ps[-1]\n", " plot(xs, ps, **options)\n", " \n", "def cdf_rates():\n", " \"\"\"Decorate the axes.\"\"\"\n", " plt.xlabel('Goal scoring rate (mu)')\n", " plt.ylabel('CDF')\n", " plt.title('Distribution of goal scoring rate')\n", " legend()\n", "\n", "def cdf_goals():\n", " \"\"\"Decorate the axes.\"\"\"\n", " plt.xlabel('Number of goals')\n", " plt.ylabel('CDF')\n", " plt.title('Distribution of goals scored')\n", " legend()\n", "\n", "def plot_cdfs(*sample_seq, **options):\n", " \"\"\"Plot multiple CDFs.\"\"\"\n", " for sample in sample_seq:\n", " plot_cdf(sample, **options)\n", " cdf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can compare the results from the simulation and the sample from the biomial distribution." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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R7j7CoSBkFULeWOeROxrCKX69NdPP9Luk4JcNGzbwta99jUAgQDgc5v777+eOO+44qXXMnz+f4uJipk6dypQpU5g58/ibvC+55BJ+8YtfMG3aNCZMmMC8efNa5i1evJhp06Yxc+ZMHnnkkZbpV199NStXrmT69OmICD/84Q8ZMmSIJQWPxOPKvqr6lhPBpeW1HKxudGaqkhqrpKChlPyGMvIbS0iNVgJOf39KUpD0jAjpkRBpkRAp4SASCEL2SDcJjIGcYggn+/cGTb/W58Zonj17trYdZGfLli1MnDjRp4j6P/t8O7e3so63S49QWl5HWUUtjbHWO1HToxXkN5aS5x4JpMSOAhAOiNsNFGpJAqGAOCdos0e1HgnkFEHI28sQTf8nIutUdXZn7exIwZjTsOdIHS9tPcDmPVXOBFUyoocZ7iaAvMYykmPVCJAWCZGWFiI9kkZ6JEQkFHS69wNhyC1uTQLZI53LMo3xgSUFY05B22RQUL+L4pq3yGsoIxKvJSkUcM4BZIVIj2SSGgkSbD7BG4w45wHyxjiPrJHO5ZzG9AL2L9GYk7DnSB0vbdnP5r1uF1C8jqlHljOydiO5qUnk5SeRFskmEkooQBxKhlw3AeSNhawRELDxrUzvZEnBmC7YfaSOlxOSAaoMq3uX6UeWMTQlyrDhWaQlBZ154TTIG+1eGTQGModbEjB9hiUFY06grKKWl7ceYEtzMsC5j2D6kReZEtjJ8KEppCa5VwINmwljL4bMYXYvgOmzLCkY0472kgGqjKrdwILY64zMFVKT0p3pyVkw9VMwxJ97ZIzpTnZM20127tzJlClTjpt+2223sXnzZk+3fdlll3HkyJETtikqKuLQoUOextEflFXU8tuVO/n58vePSQhpsSN8Kvo0N6Wu5Iy8EKnNXUUjz4EFX7eEYPoNO1LwWE+Uz166dKnn2+jvSsudI4Ot+44eMz1AnIuStzGvcSWpwTjgJoPUPJh2LRSM7/lgjfGQHSl0o2g0yqJFi5g2bRqf/OQnqa2tZcGCBTTfbJeens43v/lNpk+fzrx589i/fz8Au3bt4qKLLmLatGlcdNFFlJSUAHDzzTfz+c9/ngsuuIDRo0fzyiuvcMsttzBx4kRuvvnmlu0mHgVcddVVzJo1i8mTJ/PAAw/07AfQB5WW1/Lwax9w34r3j0kIIjA3v5G7Mv/ChbHX3IQAIDD6Ajj/LksIpl/qf0cKT3/Zu3Vf/tMTzt62bRu//vWvmT9/Prfccgv33XffMfNramqYN28e//Ef/8Gdd97Jr371K+6++25uv/12brrpJhYtWsRDDz3El770Jf70pz8BUFFRwcsvv8ySJUu4/PLLee2113jwwQeZM2cO69evZ8aMGcdso72y2ieqoDpQlZbX8tKW/WzbX33MdBGYPjSNjyZvIrtsuTNsY7OMoTD9OmeMXGP6qf6XFHw0YsQI5s+fD8ANN9zAvffee8z8pKQkFi5cCMCsWbNYtmwZACtXruSpp54C4MYbb+TOO+9sWebyyy9HRJg6dSqDBw9m6lSn73ry5Mns3LnzuKRwsmW1B5oTJYNpw7O4eGg9+e8/AQcTxnuSIIz7iHNlkd1kZvo5+xfejdqOWNb2dWL57BOVqU5cLrHEdmKZ68SS281Opaz2QFFyuJaXtu7n3Q6SwYXjshm0dzmsX84xA9Zkj3KODjKH9mzAxvik/yWFTrp4vFRSUsLKlSs5++yzefTRRzn33HN5+umnO13unHPO4bHHHuPGG2/kkUceOeVBbk5UVnugOlEymF6YxQUTBjGosQze/CnUJlydFUyCMz4GRefZjWdmQOl/ScFHEydO5De/+Q2f+9znGDduHJ///Oe7lBTuvfdebrnlFu655x4KCgr4n//5n1Pa/onKag80J0oGMwqzWXBGAYOSFTb/GUpeP3bh/PHOlUVp1u1mBh4rnW061Zc+39LyWpZt3s97B9pPBhecMYiCjAjs2wgbHof6ytZGoRSYfBWMOMvuSDb9jpXONgPOWyUVPLGujMTfOcclg4ajsO4x2PPmsQsPmQpTPgkp2T0btDG9jCUF0y/sOFjNH95sTQgiMGNENhdMcJOBKpSthY1PQVNN64JJ6U6JiqHT7ejAGPpRUlDV4672MaevL3QvHqiq53erSoi595cNzoxw/VmjnGQAUFcB7zwBBzYdu2DhHJh8NSSl9WzAxvRi/SIpJCcnc/jwYfLy8iwxdCNV5fDhwyQn997xgI/WN/Hw6zupa3JuMstIDnHzOUVkpyY5Rwe7XoctSyCacGluSg5MuwYG9Y3zJMb0pH6RFAoLCykrK+PgwYN+h9LvJCcnU1hY6HcY7WqMxvntyl1U1DYBkBQUbjp7lJMQqg/C249C+fsJSwgUnQtnLLSB743pQL9ICuFwmOLiYr/DMD0oHlceX1tKWUUd4JwOuHbuSAqzkmH7i7DteYg3tS6QNgimX+uMfmaM6VC/SApm4Hlu4z42ueMjA1w+bRgTs+Pw6o+hsrS1oQRgzEUw/qMQDPsQqTF9iyUF0+e8/v4hXt3eevfxuWPzObswCV7/f1C9v7VhZiHMuA6yemf3lzG9kSUF06ds2VvFM+/sbXk9eVgml03IgFX3tSYECcCEj8GYC61EhTEnyZKC6TPKKmp5bHVJy70IhTkpfHp6PvLG/VC1220lMPMmGHamb3Ea05fZzyjTJ1TUNPLblbtojDkZITctzE1zhpC07lcJ5xAEZlxvCcGY02BJwfR69U0xfrNyJ0frnVLhKeEgi84aTsY7D0PFB60Np30aRszxJUZj+gtLCqZXi8bi/G7VLvZXNQAQDMANc4cxaOsjcPi91oaTPw6jzvEpSmP6D0sKptdSVf60fg/vH2ytVfSJGUMZvesJOLilteHEy2H0+T5EaEz/Y0nB9Forth1k3a6KltcfnpjPmYefgf0bWxuNv8QZJtMY0y08TQoicomIbBOR7SJyVzvzR4rIchF5S0TeEZHLvIzH9B1vlVTwl82t9xzMGpnNBfUvwZ63WhuNudBJCsaYbuNZUhCRIPBz4FJgEnCdiExq0+xu4HFVPRO4FrjPq3hM39FcBrvZmPxUrg69hpStaW1U9CGYeIWVuzamm3l5pDAX2K6qO1S1EXgMuLJNGwUy3edZwB4P4zF9wIGjbcpgZyRxU+ZbBEtXtjYaeTZM+YQlBGM84GVSGA4kFKGhzJ2W6DvADSJSBiwFvtjeikRksYisFZG1Vgm1/6puiPKbNmWwbyvYQlLp31obDZ8NUz9tCcEYj3iZFNr7X9t2xJbrgIdVtRC4DPhfETkuJlV9QFVnq+rsgoICD0I1fnPKYO+kvKa1DPbiIdtJL13e2mjodOfmNCtdYYxnvPzfVQaMSHhdyPHdQ7cCjwOo6kogGcj3MCbTCzWXwS4tby2DfcuwXeTvfrG10eApcOZNlhCM8ZiX/8PWAONEpFhEknBOJC9p06YEuAhARCbiJAXrHxpg2pbB/rtBuxi17y+tDfInwKybIWiluozxmmdJQVWjwO3AC8AWnKuMNonId0XkCrfZV4HPisjbwKPAzdoXBgU23aZtGezLc0qYUr6stUHuGJhzq42FYEwP8fSnl6ouxTmBnDjt2wnPNwPzvYzB9F5ty2Cfl1bC2dUJCSF7FMxdDKGID9EZMzBZB63xRdsy2DNCu/hIwzKk+VqEzEI46+9tLGVjepglBdPjjtQeWwZ7HCVcrS8SFDchZAyFeZ+HpFQfozRmYLKkYHpUfVOMh19vLYNdGCvlWllGUsBNCGkFMO8fIJLuY5TGDFyWFEyPaVsGu6CpjBsCfyE15CaElFw4+wuQnHmCtRhjvGRJwfSItmWwsxv3coM8T1aSmxCSs+Hs2yElx8cojTGWFEyPSCyDndW4n+vizzIoxZ0ZyXCOENLy/AvQGANYUjA9ILEMdkbTIa5uXMKI5lMG4TSY9wVIH+RfgMaYFpYUjKd2HKzmqTd3A5AWrWBhzVOMy3br2YVS4Ox/gMyh/gZpjGlhScF4prkMdjSupEYr+WjlE0zKFQIiEIzAWZ+DrEK/wzTGJLCkYDyRWAY7OXaUCyseZ1oehIICgbCTEHKL/Q7TGNOGJQXT7ZpirWWwI7Eazj/8e6bnxYiEAxAIwdzPQt4Yv8M0xrTDkoLpVqrKk+vKKC2vIxyv49xDjzM9u4n0SAgkALM+AwUT/A7TGNMBSwqmW63ZWcE7ZZWE4/XMP/g4UzJryEkLAwIzF8GQKX6HaIw5AUsKptscqKrnmXf2EIo3cPahJxmffIQhmcmAwJk3wLAZfodojOmEJQXTLZpicR5dXUpTNM6c8qcpZD8jc92CdtOvhcLZ/gZojOkSSwqmWyzdsJd9VfWMrnmLoQ0fMKYgnWBAYMonYOQ8v8MzxnSRJQVz2jbtqWTVjnIymg4xpXIFI3NTSU0KwugLoPg8v8MzxpwESwrmtFTWNvGHdbsJaJRZ5c+SnxJgUEYEMobBGQv9Ds8Yc5IsKZhTFo8rv19bQl1TjAlVKxmkBynKT0OCIZh5IwQ9He3VGOMBSwrmlC3fdoAPDtWS27CbCdWrGFOQTjgocMbHIHOY3+EZY06BJQVzSj44VMNLWw8Qijcwu+IZCrOSyUwOQd5Y51yCMaZPsqRgTlptY5TfrylFFaZWLmdIqIZh2SkQSoYZ17slUI0xfZElBXNSVJWn3txNZV0TQ+reY0zdBkYXpDt5YOqnIDXX7xCNMafBkoI5Kas/KGfTnioisRrOrHiB4vw0IqEADDsThs/yOzxjzGmypGC6bH9VPc9u2AuqnFnxPCPTY+SmJUFylnOUYN1GxvR5lhRMlzRG4zy6uoSmmFJU+w6j4zsZ0VzGYsb1kJTmb4DGmG5hScF0ydINe9lf1UBatILpVcsZW5BOUASKPmSlsI3pRywpmE5t3F3JGx+UIxpnVvmzjM4Jk5IUhPTBMOlKv8MzxnQjSwrmhCpqGnnqzd0AjD+6irHhQxSkR5wBc868EYJhnyM0xnQnSwqmQ04Zi1LqmmJkN+5leu0qivPSnPPJEy6D7BF+h2iM6WaWFEyHXtp6gF2HawnGm5hT8SxjC1IJBQVyimHMRX6HZ4zxgCUF064dB6tZvu0AAFMqVzAhvY6M5BAEI063UcD+6RjTH3n6P1tELhGRbSKyXUTu6qDNp0Vks4hsEpH/8zIe0zW1jVF+v9YpYzGofgfTYxsZlpXizJzycUjL8zdAY4xnPKttLCJB4OfAh4EyYI2ILFHVzQltxgFfB+araoWIDPIqHtM1qsof1pVRVRclHK/jrMrnGT3EPY8weAqMOMvvEI0xHvLySGEusF1Vd6hqI/AY0Pb6xc8CP1fVCgBVPeBhPKYLVu0oZ/Peo+5dyy8wMVecMhZJ6c5Yy3bXsjH9mpdJYThQmvC6zJ2WaDwwXkReE5FVInJJeysSkcUislZE1h48eNCjcM3eyjqWbtgLwIjaTcwMl5CT6l5yOv06iGT4GJ0xpid4mRTa+0mpbV6HgHHAAuA64EERyT5uIdUHVHW2qs4uKCjo9kANNERjPLq6lGhcSY1Wck7dCgpz3fMII8+BIVP8DdAY0yO8TAplQOKF7IXAnnba/FlVm1T1A2AbTpIwPezZd/Zy8GgDonHmHlnKhPywU8YirQAmX+V3eMaYHuJlUlgDjBORYhFJAq4FlrRp8yfgAgARycfpTtrhYUymHe+UHWHNzgoAxlavYWZ6OSnhoHPX8ozrIRTxOUJjTE/xLCmoahS4HXgB2AI8rqqbROS7InKF2+wF4LCIbAaWA19T1cNexWSOV1HTyB/fcspYZDYe4EOx1eSnu0lg3Ecgt9jH6IwxPc2zS1IBVHUpsLTNtG8nPFfgK+7D9LBYXHlsTSn1TXECGuW86ucoLkh2LjDKHukkBWPMgGK3pQ5gL27ZT0l5LQBTqv7K9Ow6QgGBQNi9aznoc4TGmJ5mSWGA2n6gmlfedS7vLajfxfmhTaRH3APHSVdCut1HaMxAZElhAKpuiPKEW8YiHK/nooYXGdpcxqJgIhSd62+AxhjfnDApiMjDCc8XeR6N8VxLGYv6KABzq19iYk7MOY8QToMZ19ldy8YMYJ0dKUxPeP5lLwMxPeP19w+zdd9RAAprt3BZR4dTAAAXYUlEQVRuSglJQfefwfRrIDnLx+iMMX7rLCm0vQPZ9GF7jtTx/MZ9ACRHq7iUV8luLmNROBeGTj/B0saYgaCzS1ILReRenJIVzc9bqOqXPIvMdKuGaIzHVpcQjSuocmH9MoqaC4qk5MKUT/ganzGmd+gsKXwt4flaLwMx3nr67b0crG4E4Iy6t5idfoiABAGBM2+AcLK/ARpjeoUTJgVV/U1PBWK883bpEdbtcspYZDQd4rLQGqeMBcCYCyFvjI/RGWN6k04vSRWRRSLypojUuI+1InJTTwRnTl95QhmLgEa5PPYS+aluQsgcDhMu8zE6Y0xvc8IjBXfn/484ZSjexDm3MBO4R0RQ1d96H6I5VbG48ujqEhqicQDmNLzBxLQqRAQCIeeu5aCnlU6MMX1MZ0cK/wBcrarLVbVSVY+o6svAJ9x5phdbtnkfZRV1AOQ3lnFx0kanjAXAGQshc6iP0RljeqPOkkKmqu5sO9GdlulFQKZ7lByu5ZV3DwEQijfwqcAK0iNut1H+eBi9wLfYjDG9V2dJoe4U5xkfqSpLN+5tef3h+GuMSK53XoRTYcbf2V3Lxph2ddahPFFE3mlnugCjPYjHdINNe6rYddipflpY/y5zk7cj4ub/qZ+ElBwfozPG9GadJYXpwGCgtM30URw/tKbpBWJx5S+bnLuWI7EaLo2/QnLYTQjDZsLwWT5GZ4zp7TrrPvpvoEpVdyU+gFp3null1u4sd25SU2Vu5fOMSHdnJGfB1E/5GpsxpvfrLCkUqepx3UequhYo8iQic8rqm2K8uGU/AIV1W5kR2UM46J47mHEDJKX6GJ0xpi/oLCmcqPZBSncGYk7fq+8dorohRkCjzKz5G4Oz3K+v+DwoGO9vcMaYPqGzpLBGRD7bdqKI3Aqs8yYkcyqq6pt4dbtzCeq4o2sYm9FEUASS0u2uZWNMl3V2ovkfgT+KyPW0JoHZQBJwtZeBmZPz8pYDNETjRGLVzGhYS36ueyA34TII20GdMaZrOiuItx84R0QuAKa4k59172o2vcSBqnrW7CwHYFLV3yjKCTm3IWQMhZFn+xucMaZP6VLhG1VdDiz3OBZzil7YtI+4QlbjfqbGt5KVnOHMmHQVBGwYbmNM19keo4/beaiGzXuPgipTK5czIifFOUoYNAkGneF3eMaYPsaSQh+mqjznDq85pH47Z4T3kR4JgQRg0pU+R2eM6YssKfRhm/ZUUVJeS0CjTK9awfBs9z6EUfMhY4i/wRlj+iRLCn1ULK684JazKK5eT3FKnVPOIpQC4y/xOTpjTF9lSaGPWv1BOYeqGwnH65hSs5Jh2e5lp+M/ApH0Ey9sjDEdsKTQB9U3xXh5q1PO4oyq1xmVKU45i9R8KDrP5+iMMX2ZJYU+6K/vHqS6IUZ6UzkT699mUGbEmTHpChte0xhzWiwp9DGVda3lLKZULqcwJ+KUs8gbC0Om+RydMaavs6TQx7y8dT9NMaWgfiej4zvJT4sA4tyoZqOpGWNOkyWFPsQpZ1GBaJyplcsZmZvq5IERcyF7hN/hGWP6AU+TgohcIiLbRGS7iNx1gnafFBEVkdlextPXPb9pH6owqnYDI0JHyEoJQzDJqqAaY7qNZ0lBRILAz4FLgUnAdSIyqZ12GcCXgDe8iqU/2HGwmi17jxKKNzCp6m+MyHFvVBtzEaRk+xucMabf8PJIYS6wXVV3qGoj8BjQXu2FfwN+CNR7GEuflljOYvzRVQxLiZEWCUJyNoy50OfojDH9iZdJYThQmvC6zJ3WQkTOBEao6jMnWpGILBaRtSKy9uDBg90faS+3YXclZRV1pEYrGV+zjsLmG9UmXg6hJH+DM8b0K14mhfYuhdGWmSIB4L+Br3a2IlV9QFVnq+rsgoKCbgyx94vG4i3lLCZXvsLQjBCRcACyR8LwWT5HZ4zpb7xMCmVA4iUxhcCehNcZOAP3rBCRncA8YImdbD7W6p3llNc0kduwm1EN2xiW5R4l2CWoxhgPeJkU1gDjRKRYRJKAa4ElzTNVtVJV81W1SFWLgFXAFaq61sOY+pT6phgvbzngjpXwMsOyUwgFBYbOgLwxfodnjOmHPEsKqhoFbgdeALYAj6vqJhH5rohc4dV2+5NX3j1ITWOMwrotDInvd8pZBEIw0T4+Y4w3PC2Uo6pLgaVtpn27g7YLvIylr6msbeK17YcIxpuYXPkKhbkpTjmL4vMhLc/v8Iwx/ZTd0dxLvbjFKWcxtnot+cFa8tIikJQO4z7id2jGmH7MkkIvtK+ynnUlFURi1Yw/+gYjmstZTLgMwsl+h2eM6ccsKfRCz2/ciypMqvobecnqlLPIGAojz/Y7NGNMP2dJoZd5/2A12/ZXk9W4n1G1GynMdctZTL4aAvZ1GWO8ZXuZXkRVeX7jvpZLUAvSkkhLCsKgSVAwwe/wjDEDgCWFXuSdMqecxZD67QxqLGN4TgpIACa1VzLKGGO6nyWFXiIai/OXzfsIaJSplSsYkhkhEgrAqPmQMcTv8IwxA4QlhV7ijQ+cchbF1W+RFT/C0KwUCKfChEv9Ds0YM4BYUugF6hpjvLz1AOF4HWccXcnw5nIW4z4CSWl+h2eMGUAsKfQCr7x7gNrGGBOrXiMj0OiUs0grgKIP+R2aMWaAsaTgs8raJl5//zDpTYcprl5PYU4qARGnvlHQ0yokxhhzHEsKPlvmlrOYWrmCjEiA3LQkyBsLQ6b6HZoxZgCypOCjvZV1vFlSQUH9TgbXv09hTgoi4tyoZmMlGGN8YEnBR89v3AfxOFMrl5OdEnbKWYyYC1mFfodmjBmgLCn4ZPuBo7y7v5pRtRvIajrIiNxUCEaconfGGOMTSwo+UFWe27CPULyBiZV/Iz89QmpSEMZeBCnZfodnjBnALCn4YH3pEfZU1jP+6CpStM4pZ5GcDaMv8Ds0Y8wAZ0mhh0VjcZZt3k9qtJKx1WsZkpXslLOYeDmEkvwOzxgzwFlS6GGrdpRTUesMsRmROEOzkiF7JAyf5XdoxhhjSaEnNZezyG3YzfC6rQzLSSEUsEtQjTG9hyWFHrRi2wHqGqNMrXyZ5FCQQRkRGHYm5I72OzRjjAEsKfSYippGXn//MCPqNpPTuJfC3BQCwbBTzsIYY3oJSwo9ZNmW/Wi0kUmVfyU9EiI3NQlGL4DUXL9DM8aYFpYUesCeI3WsLz3C2Oq1pMSOMiInBYmkw9gP+x2aMcYcw5JCD3hu4z4i0aOMP/oGOalhMlPCcMbHIJzsd2jGGHMMSwoee2//UbYfqGZS5auEtJEROamQMQxGzPM7NGOMOY4lBQ/VNcb40/rdZDXuY2TtRgoyIqQkBWHyVRCwj94Y0/vYnskjqsqT60opr25kauVyggEYlp0CgyZDwQS/wzPGmHZZUvDIa9sPs3nvUYbWv0d+Qymj89OIhEMw6Uq/QzPGmA5ZUvDArsM1PLdxL2nRCmZWvMCQzGRnRLVR8yFjsN/hGWNMhywpdLOahiiPri4lGKvn7ENPkRNuYkRuCkQyYMKlfodnjDEnZEmhG6kqj68tpaq2gbmHl5AdL2dsQbpz5/LsWyEpze8QjTHmhDxNCiJyiYhsE5HtInJXO/O/IiKbReQdEXlJREZ5GY/XVmw7yLv7q5l25CUKGnYyuiCdSDgAM/4Ocov9Ds8YYzrlWVIQkSDwc+BSYBJwnYhMatPsLWC2qk4DngR+6FU8Xnv/YDXLtuxndPWbFNe8xbCsFHJSwzD+EiuLbYzpM7w8UpgLbFfVHaraCDwGHHPpjaouV9Va9+UqoE+OWH+0vonfrymloG4H0468RGZyiMKcFKcC6vhL/A7PGGO6zMukMBwoTXhd5k7ryK3Acx7G44l4XHlsdSkc3cfcw0sIB2F0QTqSMxJmXG/jJBhj+pSQh+tub2+o7TYUuQGYDZzfwfzFwGKAkSNHdld83eLFLfsp23+QBYf/QFgbGVOQQSQ9F+Z8FoJhv8MzxpiT4uWRQhkwIuF1IbCnbSMRuRj4JnCFqja0tyJVfUBVZ6vq7IKCAk+CPRXb9h3lla17mXf4j6RGKxmenUJWejrMXQzJmX6HZ4wxJ83LpLAGGCcixSKSBFwLLElsICJnAr/ESQgHPIyl21XWNvH4mhLOrHiB3MbdZKWEGZaTCjNvhKwT9ZIZY0zv5VlSUNUocDvwArAFeFxVN4nId0Wkebixe4B04AkRWS8iSzpYXa8Siyv/t7qEwsOvMaJ2E0mhAGMK0pGJl8OQqX6HZ4wxp8zLcwqo6lJgaZtp3054frGX2/fK8xv30bR7PTOr/oYAYwrSCRedDWMu9Ds0Y4w5LXZH80nauLuSjZs3Mqf8GQAKc1PJHH4GTP2UXWlkjOnzLCmchPKaRp5ZvYV5h58ioFFyUsMMHVoIs2+BoKcHXcYY0yMsKXRRUyzOYyvf48x9T5IcqyYSClA8tACZu9hqGhlj+g1LCl209J09DP3gKbKb9hMQGDs4k/DcW6wUtjGmX7Gk0AVvlx6hav2fGVb3LgAjclNJn3WtjaBmjOl3LCl04sDReta8+gLjj64CIDcticHTPwpF832OzBhjup8lhRNojMZ5dsVrTD7klGRKDgcpmjgbmXSVz5EZY4w3LCmcwPOrNzF21+8JaIyACKOLxxCe8xkI2MdmjOmfbO/WgTff30Pq+l+TFK8DYMSQAjLO+wKEk32OzBhjvGNJoR17j9Sw9+VfkhE9DEBeRiqDL/wCpOb6HJkxxnjLkkIb9U0x3lz6EPl1OwBICQcZeeEtSN5onyMzxhjvWVJIoKq89uKfyD+0GoCgCCPPupKkUWf5HJkxxvQMSwoJ3n7zDdLeay3UOmjCXLLPtCuNjDEDhyUF156yD6hb+SBCHID0wcWMvHCxFbkzxgwolhSAuupKdi39CYG4M/BbKDWb8Qv/CUJJPkdmjDE9a8AnBY01sXnJTwjUlzsTgkkUX/ZPhNNy/A3MGGN8MLCTgirvvvgQ0UPb3QlC3oduJXeYXWlkjBmYBnRS2P/WUiq3vdo6YeJCxk47x7+AjDHGZwM2KdSWvMXuVU+g7uvqQTOZdcEnfI3JGGP8NiCTgh4pZeeyX9AUjQFQlTqSWQs/RygU9DkyY4zx18BLCnVHKHn+pxytqQWgNpTFyI/eTnZ6qs+BGWOM/wZWUog2cnjFfew/sN95GYjAnMVMGDHU58CMMaZ3GDhJQZW6Nb+hZMc2FFAC7B5zDefPmup3ZMYY02sMmKQQ3/osOzespDHm3LH8XsGH+eiCBQQCdseyMcY0GxhJoWwtu9csoaq+CYAP0mdy9kVXkZUS9jkwY4zpXUJ+B9ATdlY0sLeyiQBwILmYgnnXMnZQut9hGWNMrzMgjhQOpE/k1UHXcTAyisMTruOCM4b4HZIxxvRKA+JIYW5xLkMyz+XZDWO4cd4oO49gjDEdGBBJAWBkXip/f/5oxEphG2NMhwZE91EzSwjGGHNiAyopGGOMOTFLCsYYY1pYUjDGGNPC06QgIpeIyDYR2S4id7UzPyIiv3fnvyEiRV7GY4wx5sQ8SwoiEgR+DlwKTAKuE5FJbZrdClSo6ljgv4EfeBWPMcaYznl5pDAX2K6qO1S1EXgMuLJNmyuB37jPnwQuErtEyBhjfOPlfQrDgdKE12XAWR21UdWoiFQCecChxEYishhY7L6sFpFtpxhTftt1DwD2ngcGe88Dw+m851FdaeRlUmjvF7+eQhtU9QHggdMOSGStqs4+3fX0JfaeBwZ7zwNDT7xnL7uPyoARCa8LgT0dtRGREJAFlHsYkzHGmBPwMimsAcaJSLGIJAHXAkvatFkCLHKffxJ4WVWPO1IwxhjTMzzrPnLPEdwOvAAEgYdUdZOIfBdYq6pLgF8D/ysi23GOEK71Kh7XaXdB9UH2ngcGe88Dg+fvWeyHuTHGmGZ2R7MxxpgWlhSMMca0GDBJobOSG/2NiIwQkeUiskVENonIl/2OqSeISFBE3hKRZ/yOpSeISLaIPCkiW93v+my/Y/KaiPyT+296o4g8KiLJfsfU3UTkIRE5ICIbE6blisgyEXnP/ZvjxbYHRFLoYsmN/iYKfFVVJwLzgC8MgPcM8GVgi99B9KCfAs+r6hnAdPr5exeR4cCXgNmqOgXnIhavL1Dxw8PAJW2m3QW8pKrjgJfc191uQCQFulZyo19R1b2q+qb7/CjOzmK4v1F5S0QKgY8BD/odS08QkUzgPJyr+FDVRlU94m9UPSIEpLj3NqVy/P1PfZ6q/pXj79lKLAv0G+AqL7Y9UJJCeyU3+vUOMpFbffZM4A1/I/HcT4A7gbjfgfSQ0cBB4H/cLrMHRSTN76C8pKq7gR8BJcBeoFJV/+JvVD1msKruBedHHzDIi40MlKTQpXIa/ZGIpAN/AP5RVav8jscrIrIQOKCq6/yOpQeFgJnA/ap6JlCDR10KvYXbj34lUAwMA9JE5AZ/o+pfBkpS6ErJjX5HRMI4CeERVX3K73g8Nh+4QkR24nQPXigiv/M3JM+VAWWq2nwE+CROkujPLgY+UNWDqtoEPAWc43NMPWW/iAwFcP8e8GIjAyUpdKXkRr/iliD/NbBFVX/sdzxeU9Wvq2qhqhbhfL8vq2q//gWpqvuAUhGZ4E66CNjsY0g9oQSYJyKp7r/xi+jnJ9cTJJYFWgT82YuNeFkltdfoqOSGz2F5bT5wI7BBRNa7076hqkt9jMl0vy8Cj7g/dnYAn/E5Hk+p6hsi8iTwJs4Vdm/RD8tdiMijwAIgX0TKgH8Bvg88LiK34iTHT3mybStzYYwxptlA6T4yxhjTBZYUjDHGtLCkYIwxpoUlBWOMMS0sKRhjjGlhScH0GSKiIvJfCa/vEJHvdNO6HxaRT3bHujrZzqfcaqbLPdxGj7wX0z9ZUjB9SQPwcRHJ9zuQRG4V3q66FfgHVb3Aq3iMOR2WFExfEsW5Uemf2s5o++tYRKrdvwtE5BUReVxE3hWR74vI9SKyWkQ2iMiYhNVcLCJ/c9stdJcPisg9IrJGRN4Rkc8lrHe5iPwfsKGdeK5z179RRH7gTvs2cC7wCxG5p037gIjc544T8IyILG1+PyJykVvwboNbZz/SvD43ro0i8oB7h2/bOL4vIpvd2H90ch+3GYgsKZi+5ufA9SKSdRLLTMcZZ2Eqzl3e41V1Lk6J7S8mtCsCzscpv/0Ld/CWW3Eqcc4B5gCfFZFit/1c4Juqesw4FSIyDPgBcCEwA5gjIlep6neBtcD1qvq1NjF+3N3+VOA24Gx3Xck4tfWvUdWpOFUIPu8u8zNVneOOK5ACLGwTRy5wNTBZVacB/97VD8wMXJYUTJ/iVnr9Lc5AK121xh1fogF4H2gutbwBZ0fc7HFVjavqezglI84APgLc5JYKeQPIA8a57Ver6gftbG8OsMIt2hYFHsEZ9+BEzgWecLe/D2g+5zABpwDcu+7r3ySs6wIReUNENuAkoMlt1lkF1AMPisjHgdpOYjDGkoLpk36C8ws+ceyAKO6/Z7cbJSlhXkPC83jC6zjH1v9qW/NFccquf1FVZ7iP4oT6/TUdxNdeqfbOdLRMu9PdI4j7gE+6RxC/Ao4ZltJNSHNxKuVeBTx/CnGZAcaSgulzVLUceBwnMTTbCcxyn18JhE9h1Z9y+/bH4Axgsw2niOLn3TLkiMj4Lgxk8wZwvojkuyehrwNe6WSZV4FPuNsfjFMMDWArUCQiY93XN7rrak4Ah9wxM4672sidnuUWQfxHnK4sY05oQFRJNf3SfwG3J7z+FfBnEVmNM35tR7/iT2Qbzg53MPD3qlovIg/idDG96R6BHKSTYRBVda+IfB2nC0iAparaWZnjP+CUgd4IvIuTWCrdGD4DPOEOP7kG+IWqNojIr3C6wHa609vKwPlMkt04jjtBb0xbViXVmF5CRNJVtVpE8oDVwHz3/IIxPcaOFIzpPZ4RkWyc8yH/ZgnB+MGOFIwxxrSwE83GGGNaWFIwxhjTwpKCMcaYFpYUjDHGtLCkYIwxpsX/Bxh4XNBWGFSuAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_sim, label='simulation')\n", "plot_cdf(sample_bin, label='binomial')\n", "cdf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Poisson process\n", "\n", "For large values of `n`, the binomial distribution converges to the Poisson distribution with parameter `mu = n * p`, which is also `mu = lam_per_game`." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.722" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu = lam_per_game\n", "sample_poisson = np.random.poisson(mu, size)\n", "np.mean(sample_poisson)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can confirm that the results are consistent with the simulation and the binomial distribution." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdfs(sample_sim, sample_bin)\n", "plot_cdf(sample_poisson, label='poisson', linestyle='dashed')\n", "legend()" ] }, { "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": 18, "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": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1000" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "len(trace['goals'])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.807" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_pm = trace['goals']\n", "np.mean(sample_pm)" ] }, { "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": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdfs(sample_sim, sample_bin, sample_poisson)\n", "plot_cdf(sample_pm, label='poisson pymc', linestyle='dashed')\n", "legend()" ] }, { "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 CDF and PMF analytically. We can use the CDF to check, one more time, the previous results." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import scipy.stats as st\n", "\n", "xs = np.arange(11)\n", "ps = st.poisson.cdf(xs, mu)\n", "\n", "plot_cdfs(sample_sim, sample_bin, sample_poisson, sample_pm)\n", "plt.plot(xs, ps, label='analytic', linestyle='dashed')\n", "legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can use the PMF to compute the probability of any given outcome. Here's what the analytic PMF looks like:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xs = np.arange(11)\n", "ps = st.poisson.pmf(xs, mu)\n", "bar(xs, ps, label='analytic PMF')\n", "pmf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's a function that compute the probability of scoring a given number of goals in a game, for a known value of `mu`." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def poisson_likelihood(goals, mu):\n", " \"\"\"Probability of goals given scoring rate.\n", " \n", " goals: observed number of goals (scalar or sequence)\n", " mu: hypothetical goals per game\n", " \n", " returns: probability\n", " \"\"\"\n", " return np.prod(st.poisson.pmf(goals, mu))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the probability of scoring 6 goals in a game if the long-term rate is 2.7 goals per game." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.036162211957124435" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "poisson_likelihood(goals=6, mu=2.7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the probability of scoring 3 goals." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.22046768454274915" ] }, "execution_count": 26, "metadata": {}, "output_type": "execute_result" } ], "source": [ "poisson_likelihood(goals=3, mu=2.7)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function also works with a sequence of goals, so we can compute the probability of scoring 6 goals in the first game and 3 in the second." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.008858443486812598" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "poisson_likelihood(goals=[6, 2], mu=2.7)" ] }, { "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!\n", "\n", "The following class implements Bayes's theorem." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "class Suite(Pmf):\n", " \"\"\"Represents a set of hypotheses and their probabilities.\"\"\"\n", " \n", " def bayes_update(self, data, like_func):\n", " \"\"\"Perform a Bayesian update.\n", " \n", " data: some representation of observed data\n", " like_func: likelihood function that takes (data, hypo), where\n", " hypo is the hypothetical value of some parameter,\n", " and returns P(data | hypo)\n", " \"\"\"\n", " for hypo in self:\n", " self[hypo] *= like_func(data, hypo)\n", " self.normalize()\n", " \n", " def plot(self, **options):\n", " \"\"\"Plot the hypotheses and their probabilities.\"\"\"\n", " xs, ps = self.sorted_items()\n", " plot(xs, ps, **options)\n", " \n", "\n", "def pdf_rate():\n", " \"\"\"Decorate the axes.\"\"\"\n", " plt.xlabel('Goals per game (mu)')\n", " plt.ylabel('PDF')\n", " plt.title('Distribution of goal scoring rate')\n", " legend()" ] }, { "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": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([ 0. , 0.4, 0.8, 1.2, 1.6, 2. , 2.4, 2.8, 3.2, 3.6, 4. ,\n", " 4.4, 4.8, 5.2, 5.6, 6. , 6.4, 6.8, 7.2, 7.6, 8. , 8.4,\n", " 8.8, 9.2, 9.6, 10. , 10.4, 10.8, 11.2, 11.6, 12. , 12.4, 12.8,\n", " 13.2, 13.6, 14. , 14.4, 14.8, 15.2, 15.6, 16. , 16.4, 16.8, 17.2,\n", " 17.6, 18. , 18.4, 18.8, 19.2, 19.6, 20. ])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hypo_mu = np.linspace(0, 20, num=51)\n", "hypo_mu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Initially `suite` represents the prior distribution of `mu`." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "suite = Suite(hypo_mu)\n", "suite.normalize()\n", "suite.plot(label='prior')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can update it with the data and plot the posterior." ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "suite.bayes_update(data=6, like_func=poisson_likelihood)\n", "suite.plot(label='posterior')\n", "pdf_rate()" ] }, { "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, 6.\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 scores from previous Stanley Cup finals to estimate the parameters of a gamma distribution.\n", "\n", "Why gamma? You'll see.\n", "\n", "Here are (total goals)/(number of games) for both teams from 2013 to 2017, not including games that went into overtime. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[2.1666666666666665,\n", " 3.1666666666666665,\n", " 2.0,\n", " 1.0,\n", " 1.6666666666666667,\n", " 2.1666666666666665,\n", " 1.0,\n", " 2.0,\n", " 1.6666666666666667,\n", " 2.0]" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" } ], "source": [ "xs = [13/6, 19/6, 8/4, 4/4, 10/6, 13/6, 2/2, 4/2, 5/3, 6/3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If those values were sampled from a gamma distribution, we can estimate its parameters, `k` and `theta`." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "def estimate_gamma_params(xs):\n", " \"\"\"Estimate the parameters of a gamma distribution.\n", " \n", " See https://en.wikipedia.org/wiki/Gamma_distribution#Parameter_estimation\n", " \"\"\"\n", " s = np.log(np.mean(xs)) - np.mean(np.log(xs))\n", " k = (3 - s + np.sqrt((s-3)**2 + 24*s)) / 12 / s\n", " theta = np.mean(xs) / k\n", " alpha = k\n", " beta = 1 / theta\n", " return alpha, beta" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the estimates." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.590040427964036 5.092056864405683\n" ] } ], "source": [ "alpha, beta = estimate_gamma_params(xs)\n", "print(alpha, beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The following function takes `alpha` and `beta` and returns a \"frozen\" distribution from SciPy's stats module:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [], "source": [ "def make_gamma_dist(alpha, beta):\n", " \"\"\"Returns a frozen distribution with given parameters.\n", " \"\"\"\n", " return st.gamma(a=alpha, scale=1/beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The frozen distribution knows how to compute its mean and standard deviation:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.883333333333333 0.6081587702831356\n" ] } ], "source": [ "dist = make_gamma_dist(alpha, beta)\n", "print(dist.mean(), dist.std())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And it can compute its PDF." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.00000000e+00, 6.38558824e-08, 1.47882071e-05, 2.89335244e-04,\n", " 2.05818741e-03, 8.41008968e-03, 2.42005653e-02, 5.46708620e-02,\n", " 1.03457950e-01, 1.71009756e-01, 2.54058869e-01, 3.46221457e-01,\n", " 4.39353435e-01, 5.25141940e-01, 5.96484573e-01, 6.48394461e-01,\n", " 6.78362677e-01, 6.86251605e-01, 6.73866305e-01, 6.44365210e-01,\n", " 6.01647333e-01, 5.49811363e-01, 4.92738384e-01, 4.33813676e-01,\n", " 3.75777888e-01, 3.20683656e-01, 2.69928462e-01, 2.24335393e-01,\n", " 1.84257838e-01, 1.49689963e-01, 1.20370713e-01, 9.58741574e-02,\n", " 7.56829865e-02, 5.92447692e-02, 4.60123559e-02, 3.54707493e-02,\n", " 2.71531125e-02, 2.06485333e-02, 1.56038850e-02, 1.17217339e-02,\n", " 8.75583226e-03, 6.50534975e-03, 4.80865843e-03, 3.53721739e-03,\n", " 2.58989044e-03, 1.88787645e-03, 1.37032322e-03, 9.90624353e-04,\n", " 7.13355115e-04, 5.11779658e-04, 3.65852616e-04, 2.60637420e-04,\n", " 1.85068625e-04, 1.30993248e-04, 9.24350534e-05, 6.50346646e-05,\n", " 4.56267621e-05, 3.19230663e-05, 2.22762016e-05, 1.55048845e-05,\n", " 1.07652488e-05, 7.45664014e-06, 5.15299332e-06, 3.55308296e-06,\n", " 2.44461832e-06, 1.67844019e-06, 1.15005230e-06, 7.86453021e-07,\n", " 5.36780624e-07, 3.65690768e-07, 2.48683805e-07, 1.68818324e-07,\n", " 1.14406721e-07, 7.74040680e-08, 5.22848551e-08, 3.52619808e-08,\n", " 2.37451120e-08, 1.59659882e-08, 1.07198354e-08, 7.18732361e-09,\n", " 4.81225325e-09, 3.21770923e-09, 2.14870341e-09, 1.43301682e-09,\n", " 9.54518898e-10, 6.35022369e-10, 4.21965684e-10, 2.80066266e-10,\n", " 1.85674197e-10, 1.22959061e-10, 8.13389408e-11, 5.37496810e-11,\n", " 3.54815628e-11, 2.33985422e-11, 1.54149991e-11, 1.01455589e-11,\n", " 6.67106332e-12, 4.38237291e-12, 2.87625299e-12, 1.88606377e-12,\n", " 1.23567713e-12])" ] }, "execution_count": 37, "metadata": {}, "output_type": "execute_result" } ], "source": [ "hypo_mu = np.linspace(0, 10, num=101)\n", "ps = dist.pdf(hypo_mu)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(hypo_mu, ps, label='gamma(9.6, 5.1)')\n", "pdf_rate()" ] }, { "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": 39, "metadata": {}, "outputs": [], "source": [ "def make_gamma_suite(xs, alpha, beta):\n", " \"\"\"Makes a suite 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", " dist = make_gamma_dist(alpha, beta)\n", " ps = dist.pdf(xs)\n", " prior = Suite(dict(zip(xs, ps)))\n", " prior.normalize()\n", " return prior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what it looks like." ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prior = make_gamma_suite(hypo_mu, alpha, beta)\n", "\n", "prior.plot(label='gamma prior')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can update this prior using the observed data." ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "posterior = prior.copy()\n", "posterior.bayes_update(data=6, like_func=poisson_likelihood)\n", "\n", "prior.plot(label='prior')\n", "posterior.plot(label='posterior')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The results are substantially different from what we got with the uniform prior." ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "suite.plot(label='posterior with uniform prior', color='gray')\n", "posterior.plot(label='posterior with gamma prior', color='C1')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose the same team plays again and scores 2 goals in the second game. We can perform a second update using the posterior from the first update as the prior for the second." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "posterior2 = posterior.copy()\n", "posterior2.bayes_update(data=2, like_func=poisson_likelihood)\n", "\n", "prior.plot(label='prior')\n", "posterior.plot(label='posterior')\n", "posterior2.plot(label='posterior2')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Or, starting with the original prior, we can update with both pieces of data at the same time." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "posterior3 = prior.copy()\n", "posterior3.bayes_update(data=[6, 2], like_func=poisson_likelihood)\n", "\n", "prior.plot(label='prior')\n", "posterior.plot(label='posterior')\n", "posterior2.plot(label='posterior2')\n", "posterior3.plot(label='posterior3', linestyle='dashed')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Update using conjugate priors\n", "\n", "I'm using a gamma distribution as a prior in part because it has a shape that seems credible based on what I know about hockey.\n", "\n", "But it is also useful because it happens to be the conjugate prior of the Poisson distribution, which means that if the prior is gamma and we update with a Poisson likelihood function, the posterior is also gamma.\n", "\n", "See https://en.wikipedia.org/wiki/Conjugate_prior#Discrete_distributions\n", "\n", "And often we can compute the parameters of the posterior with very little computation. If we observe `x` goals in `1` game, the new parameters are `alpha+x` and `beta+1`." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "class GammaSuite:\n", " \"\"\"Represents a gamma conjugate prior/posterior.\"\"\"\n", " \n", " def __init__(self, alpha, beta):\n", " \"\"\"Initialize.\n", " \n", " alpha, beta: parameters\n", " dist: frozen distribution from scipy.stats\n", " \"\"\"\n", " self.alpha = alpha\n", " self.beta = beta\n", " self.dist = make_gamma_dist(alpha, beta)\n", " \n", " def plot(self, xs, **options):\n", " \"\"\"Plot the suite.\n", " \n", " xs: locations where we should evaluate the PDF.\n", " \"\"\"\n", " ps = self.dist.pdf(xs)\n", " ps /= np.sum(ps)\n", " plot(xs, ps, **options)\n", " \n", " def bayes_update(self, data):\n", " return GammaSuite(self.alpha+data, self.beta+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the prior looks like using a `GammaSuite`:" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.883333333333333" ] }, "execution_count": 46, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma_prior = GammaSuite(alpha, beta)\n", "gamma_prior.plot(hypo_mu, label='prior')\n", "pdf_rate()\n", "gamma_prior.dist.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here's the posterior after one update." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.559076642743212" ] }, "execution_count": 47, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma_posterior = gamma_prior.bayes_update(6)\n", "\n", "gamma_prior.plot(hypo_mu, label='prior')\n", "gamma_posterior.plot(hypo_mu, label='posterior')\n", "pdf_rate()\n", "gamma_posterior.dist.mean()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can confirm that the posterior we get using the conjugate prior is the same as the one we got using a grid approximation." ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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GYywCgQAXX3wxX/nKV0bubBsTD8aqx2gxxsIwLBU25/asUfgr+shLSyYzxdqD2RMIUdUytN/C7+/ksTd/SHsgapjKsheRJuFZTHsNvP4zM8MwDMtQ6clh6DTkX/nKV1i6dCllZWV86Utf4rXXXmPjxo38+7//O6tWreLAgQMcOHCACy+8kNNOO41zzjmH3bt3A3D99dfzxS9+kfPPP58vf/nLPPDAA9x2220AHD58mHXr1lFWVsa6des4cuTIoGPsBINBvvSlL7FixQrKysr46U9/OqzupaWlfOMb3+DUU09lxYoVEb3sethTsQOkp6cDEAqFuPXWW1m2bBkXXXQRH/3oRyP97rjjDk4//XSWL1/OzTffjKqyYcMGNm/ezKc+9SlWrVpFV1cXW7Zs4dxzz+W0007jwx/+MNXV1Y5+nmYH9xTDHgk1Gud2HyLC/Pw0th61dn4fqu8YcmaybedjdASt+6S4fXzilM+yaOGFULEZ3v09waCf99qPIDt+R9mqG2J4NYYJ48+fj5/sj/14yEuDpSe/7bbbBk1Dfu211/KnP/2J3bt3IyI0NzeTnZ3NxRdfzEUXXcRll10GWDu877nnHhYtWsSmTZu49dZbef755wHYu3cvzz77LG63u9+u8Ntuu41rr72W6667jl/96ld87nOf4/HHHz9ujJ1f/vKXHDp0iHfeeYekpCQaGxtHTKGen5/P22+/zd13380PfvAD7r333lG9hX/84x8pLy9n+/bt1NbWsmTJEm644YaI7rffbtWMu+aaa3jyySe57LLL+NnPfsYPfvADVq9ejd/v51/+5V944oknKCgo4JFHHuFrX/sav/rVr0Z1/9FgZhZTiJ5AkLp261eMCBRm+cY0fl5+eqQ9lJNbQyE2HXw6cnzO/I9YhgKgZDW1i9bxk64DPN5TzbMHniRgZheGYRgsPflQacgzMzPx+XzcdNNN/PGPfyQ19fgfM+3t7bz22musX7+eVatW8ZnPfKbfL+j169cPWkHv9ddf56qrrgKsB669JsZQY5599lluueUWkpKs39S5ubkjplD/p3/6JwBOO+20MaUneeWVV1i/fj0ul4vCwkLOP//8yLUXXniBtWvXsmLFCp5//nl27Nhx3Pg9e/bw3nvvccEFF7Bq1Sq+/e1vU1FRMer7jwYzs5hCVDV3R4KRZmR48SaNraykPS9Ueb3lt3C5+mehPXT4Bep6rFxSyS4PpyztXz8gZ955hLb9LwQCtPk72L5rA6eUXT2OV2M4ERgsPflQaciTkpJ48803ee6553j44Yf52c9+Fpkx9BEKhcjOzmbr1q2DyhhtCnO7XkONUdXj9B8phbrX6wXA7XYP6gNJSkoiFApFZPX29g4rt7u7m1tvvZXNmzcze/ZsvvnNb9LdffwPNFVl2bJlvP7668PqFwvGWEwh+i9Bjd653Ud+ejIZviTaugN0+YPUtHYfF3r7+u4/RNqnzFyNLyWn33WPJ5Uz5q7j2QN/BuDVA0+ycvmVuFymHnJCM8xSUTwZLD35UGnI29vb6ezs5KMf/ShnnHEGCxcuBCAjI4O2NitNTWZmJvPmzeOxxx5j/fr1qCrbtm1j5cqVw+rxvve9j4cffphrrrmG3/72t5x99tkj6v6hD32Ie+65h/POOy+yDBVrCvXS0lK2bNnCJz/5SZ544gn8fj8AZ599Ng8++CDXXXcddXV1vPjii1x11VURw5Cfn097ezsbNmyILMfZ35eTTjqJurq6yHvt9/vZu3cvy5YtG7VuIxHXZSgRuVBE9ojIfhE5LhxARLwi8kj4+iYRKbVdKxOR10Vkh4hsF5GxrblMQyqaog7nWaPYXzEQEek3uxi4FFVfv5v9LQesvginL7tqUDmnLf8UXpdVaKmhp4k9+54csy6GE4PB0pMPlYa8ra2Niy66iLKyMs4991zuvPNOAK644gq+//3vc8opp3DgwAF++9vfct9997Fy5UqWLVvGE088MaIeP/nJT7j//vspKyvjoYce4sc/Htl43nTTTcyZM4eysjJWrlzJ7373u3GnUO+boXz605/mpZdeYs2aNWzatCkyq7n00kspKSlh+fLlfOYzn2Ht2rVkZWWRnZ3Npz/9aVasWMHHP/5xTj/99IjM66+/nltuuYVVq1YRDAbZsGEDX/7yl1m5ciWrVq3itddeG1GvsSAjTavGLVjEDewFLgAqgLeAK1V1p63PrUCZqt4iIlcAn1DVy0UkCXgbuEZV3xWRPKBZVYND3W/16tW6efPmuLyWROGHf9tDfbs1bb31vAXMHkWqj4FsOtjA41utcLulxZlcc8bcyLW/vPQNNle/AcBJ2Yu54sKfDinn2Ve+w6sVLwIwK7WQGy+6H3EZF1gisWvXLpYsWTJp9y8vL+eiiy464RMJ/vCHP6S1tZVvfetbw/Zrb28nPT2dhoYG1qxZw6uvvkphYaGjugz2nRCRLaq6eqSx8fzfvQbYr6oHVbUXeBi4ZECfS4AHw+0NwDqxTPCHgG2q+i6AqjYMZyhOBLp6gxFD4RqHc7uP/n6LjuhaaTDAaa2NlCVl4kZYe/Klw8pZW3Yt7nAobWVnDceOvTsufQyG6cw999zDAw88wNVXj+zXu+iii1i1ahXnnHMOX//61x03FLEST5/FLOCo7bgCWDtUH1UNiEgLkAcsBlREngEKgIdV9XsDbyAiNwM3A8yZM8fxF5BI2PM5FWb68LjHZ+cLMrykeNx0+YN09gZp7vSTk5YMTeUU4uIT3mIuyMokbc77h5WTkTmLJblLeK/B+tW4+/DzFBadMi6dDNMTk54cbrnlllFX+nvxxRfjq0yMxHNmMVix54FrXkP1SQLOBj4V/vcTIrLuuI6qv1TV1aq6uqCgIFZ9E5ratmgERNE4/BV9iEi/zXwRI1S/N3IufcbyUS0pnVzyvkh7z7HBo1MMBsP0IJ7GogKYbTsuAQbuTY/0CfspsoDG8PmXVLVeVTuBp4BT46hrwtO3BAXW7CAW7M7xiNPcZizIXzQqOQvnfRB3+CtU01VLc9OhmPQyGAyJSzyNxVvAIhGZJyLJwBXAxgF9NgLXhduXAc+rtYj+DFAmIqlhI3IuMPZMYtOIhvBmPLBCYGPBvvO7oqmLUG8n2lQe7TBKY+H1ZTEvqxQAF0LV0Vdj0stgMCQucfNZhH0Qt2E9+N3Ar1R1h4jcAWxW1Y3AfcBDIrIfa0ZxRXhsk4j8D5bBUeApVf1LvHSdCtTbjEVBunMzi8rmLvYffoknOvdS6kpledZClngzRi3rzDkfYOXebha400jpaIlJL4PBkLjENdZRVZ9S1cWqukBV/zN87vawoUBVu1V1vaouVNU1qnrQNvY3qrpMVZer6v+Np56JTiAYoqnT2rwjguWQjoHsVA9pyVYkU7c/xM6jb9KpQXYG2ziSMrodsH3Mn38By5MySRE3NOyH3s6RBxkMY2AqpCi/6aabBtXRnkRwqmMC46cAjR29kTQf2SmecUdC9SEi/Zai9tVFv+Tzi04fbMjQpGRDdjgSTUNQe0KvFhriQKKnKA8Gg9x7770sXbp0XOOnCsZYTAHq+vkrYluC6mNWOF2IBBqp7aoHLL/D3NlnjV3YzBXRds12J9QzTAOmeoryzs5OPvnJT1JWVsbll1/O2rVr6dv4m56ezu23387atWt5/fXXOe+88yLX7r//fhYvXsy5557Lq69OHz+eyQ01BbBHQuXHGAnVR5/fwtOzla5wYrNZacUkj8FfEaFwBaHdT3Ik1MXeo8/zgZVXkuQ54bOzJBwvHn2RlypeGlXfU2ecyscWfKzfuT8f+DNv174dOT635FzOm33esHKmcoryu+++m5ycHLZt28Z7773HqlWrItc6OjpYvnw5d9xxR78x1dXVfOMb32DLli1kZWVx/vnnc8op02P/kZlZTAHq25yLhOqjb69F0L8bf1BBYX7BOJOOZRTyq2AdD3Yf4fWeWo5UOJuTxjB1mcopyl955RWuuOIKAJYvX05ZWVnkmtvt5tJLj89ysGnTJs477zwKCgpITk7m8ssvP67PVMUYiylAQ4fzy1BZKR4yfUl0BY+gCsGQMq9ozfiEiVCYszByeOTYO47oaJj6jCdF+aWXXsrjjz/OhRdeeFwfe4ryvr9du3ZFrjudonwofD7foAZmoOzphFmGmgL0W4ZyyFgAFKW1UaFW5tlQSJhVPEbnto3SGWVsqXkTgMMNux3Rz+As580+b8Rlo+H42IKPHbc0NRJTOUX52WefzaOPPsr555/Pzp072b59ZH/c2rVr+fznP09DQwOZmZk89thjI+o2VTAziwSn2x+krduK0khyCdkpHsdkZxLdcZ3mzo3JzzDXlvrjaHslfr8JoTVM7RTlt956K3V1dZSVlfHd736XsrIysrKyhh1TVFTEN7/5Tc4880w++MEPcuqp0yfxRNxSlE800zVFeUVTJ3e9YNWYmJHh5V8vWOyY7D89/32e3W/tdZyTvoovX/WjmOT99E+X09jTDMB1Z36N0rnDJyM0xBeTojw2gsEgfr8fn8/HgQMHWLduHXv37iU52Rm/4WQQS4pyswyV4DTEIRKqD3egFsHaIt8TKh60zOpYKM1eSOMxy2Afrt5sjIVhStPZ2cn555+P3+9HVfn5z38+pQ1FrBhjkeD0T/Ph7Bf1YncGhYHZHAv1sDVjKfXtPczIjGEpakYZb/cZi0bjtzjRmeopyjMyMpiOqxXjxfgsEpz6OGzIA6y0HJ0NZHk8FGgK3cmzqG45vhD8WJhbcmakfbStgoA/NnmG2Jkuy8yG2In1u2CMRYJjj4TKc9JYtFrZ4lO9SbQm5ROSJKpbukYYNDxZWXPISc4EIKBBqmu2xKymYfz4fD4aGhqMwTCgqjQ0NODzjX/lwCxDJTCqSl0cNuQB0GIVMUxNdtPsnwkQ88wCYG72AppqrX0W5dVbmD2e9CEGRygpKaGiooK6urrJVsWQAPh8PkpKSsY93hiLBKa9J0BPwErF4U1yke517uPaU/M2nmAHWR4PLR7njMXCmafS1bCPue5UFvX6Y5ZnGD8ej4d58+ZNthqGaYIxFgnMwOp4Tu4Mfa52M3U9jaDgSj4HgLbuAG3dfjJ849/LsWzeB1l2MJw8rfUYhILgGnynq8FgmDoYn0UCY6+OlxdjDQs7/p4O6nuaACs1Qa4tJ1RNrLOL1FxIybHawZ7IcpfBYJjaGGORwPQVPALIddBY1NRuQ7GcnnneHIpz8yLXnFiKIndBtG0v12owGKYsxlgkME2d0WWo7FQHjUVDNPFaYXoxRVnRQkixRkQBkDM30vQ3Hhymo8FgmCoYn0UC02wzFrlpzuWEqmk6EGkXZc+nKCsaTufEzKIzo5BneqqoCHajR6r43OobYpZpMBgmFzOzSGCabctQWSkOzizaon6EwvwlzMz00ec7r2vrwR8MxSQ/OWsOO4MdNGovTb2ttLdVjzzIYDAkNHE1FiJyoYjsEZH9InJcMVwR8YrII+Hrm0SkNHy+VES6RGRr+O+eeOqZiIRCSktX1FhkpzozswgGejkWLqMKUDizDJ/HHXGghxSOtcY2u0jy+ChKLYwcV1abzXkGw1QnbsZCRNzAXcBHgKXAlSIysKL5jUCTqi4E7gS+a7t2QFVXhf9uiZeeiUpLl59QeONtpi8Jj9uZj6qxcR9BDVpyPemkpuYDUGhbioo5IgqYlR2N76+o3xGzPIPBMLnEc2axBtivqgdVtRd4GLhkQJ9LgAfD7Q3AOpmuZabGSLyc23WN+yLtGakzIu1im5O7ygFjUWILx61sPjBMT4PBMBWIp7GYBdiD7CvC5wbto6oBoAXoi+OcJyLviMhLInLOYDcQkZtFZLOIbJ5uKQ3sYbM5Di1BAdS3HI6089KKIu3+M4vYI6JKCk+LtCvbqwgFAzHLNBgMk0c8jcVgM4SBGc2G6lMNzFHVU4AvAr8TkczjOqr+UlVXq+rqgoKCmBVOJJr7zSycMxYFgV6WuTOY4fJSaFsqGhgRFWvyuczM2WQkpQLQG/JTX29SlhsMU5l4GosKYLbtuASoGqqPiCQBWUCjqvaoagOAqm4BDgDOlYibAvSfWTi3DLUkAJf5ZvHZlHmsmhUthZqV4iHFY6Xl6PaH+kXcMRy2AAAgAElEQVRijQdxuSjJmBM5rqh5OyZ5BoNhcomnsXgLWCQi80QkGbgC2Digz0bgunD7MuB5VVURKQg7yBGR+cAi4ITa3dUcD5+FKrQfix5nRCOWRKTf7KImxogogFm5iyLtigYzszAYpjJxMxZhH8RtwDPALuBRVd0hIneIyMXhbvcBeSKyH2u5qS+89v3ANhF5F8vxfYuqNsZL10TE7uB2zGfR2Qih8IwhOR2S0/pdnumwsSiZURZpV7aWxyzPYDBMHnHdwa2qTwFPDTh3u63dDawfZNwfgD/EU7dEZuAeiyynjIV9VpE+87jLhZnOhs8WFZ6CCyGEEuxpI9DTTpI3PWa5BoNh4jHpPhKQtu4AfZuo071uvEnOpPjeXr2JfT1V5Esyi7zLKRpwvcjhvRbJ3gyuzV9NQWcTqZJkVecrOKFcTwbDtMGk+0hAmrvis8fiUOM+tgdaecFfz2E5PqXHjExvNO1He+xpPwDmFqywDAVA85GY5RkMhsnBGIsEpLEjPmGz9R01kXZB9vzjrnuTomk/VKHWVtJ13GTbAuJajLEwGKYqxlgkIM02f0WuQzMLDYWo647mhMrPP2nQfjMznd2cR3Y0fNbMLAyGqYsxFgmIPWzWKed2R8cxuoPWTMHr8pCZMXjh9v5+CwdmFhlF9IqbI8FOXm89QGdHbewyDQbDhGMc3AlIU4fzG/LqG/ZG2vm+PMQ1+O8E+8zCkUJILje/0SaOdlv7MfOr32bRwgtjl2swGCYUM7NIQJr77bFwxljUNe2PtPPSjg+b7cM+s4g1VXlEZma0cl5V/U5HZBoMhonFGIsEQ1X7+SyccnDXt0ZzOhZkzB6yX25aMt4k62vR3hOkrTu2tB8AxXknR9pVzSfURnyDYdpgjEWC0d4TwB+0kvileNz4PM7ssajriKblKrAlEByIiPRbinJidlE8Y0WkXdVeiYZiD8k1GAwTizEWCUZ/f4WDYbO26nh5uQuH7VuY5Y20najJnZd3Esku67W0BzppbauIWabBYJhYjLFIMPptyEtzxl/R091Cm78DALe4yc0Z3lj0d3LHbixc7iSKbbUzqmu2xizTYDBMLMZYJBjxKHrk6qjnSm8JH0qewTkZ83G5hw+CK7JVzTvmgLGA/k7uyoZdjsg0GAwThwmdTTDsCQSzU5yZWXi6mlmcFE7gV7Bi+M70TyhY29ZDMKS4XbFVu52VvwQqXwagqvlQTLIMBsPEY2YWCUaLfUNeikM+C/tGuLQZQ/cLk5Lsjtw7EFLq22PfnFc0c2WkXdVRZZzcBsMUwxiLBKNfanLHjIWtPnna6MrPFmc767fIyZ6Pz205zruDPTSZ2YXBMKUwxiLBiEcdi1C7bWaRPvLMApzPESUuF4sz5nKSO53zPfl42qpjlmkwGCYO47NIIPzBEO09QQBcAhne2D8eDYX4Yc0/8GqIPFcy632ZjMYTYt/J7cTMAuATcz8M+/9uHXQ0OCLTYDBMDMZYJBD2WUVmigdXjE5lgM7OWjpDPXQCHQqelLxRjbNHRDlRCAnon668+ejQ/QwGQ8JhlqESiOZO5/0VjU0HIu1cb86QCQQHkpeWjMdtGavW7gDtPYHYlbGnK285ahXNMBgMUwJjLBKI/mGzzhiLhubySDsvdXTObQCXSwb4LRyYXfiyITkcwhvo7u94NxgMCU1cjYWIXCgie0Rkv4h8ZZDrXhF5JHx9k4iUDrg+R0TaReRL8dQzUWiNQyRUgy21Rm5a4ZjGOl2TGxH2+lJ5oqean3cd4r0jL8Uu02AwTAhxMxYi4gbuAj4CLAWuFJGlA7rdCDSp6kLgTuC7A67fCfw1XjomGvZUH05FQjW0R6OO8jLnDNPzeAptxqLKidoWQJXXx9ZAC7WhHiobdjsi02AwxJ94zizWAPtV9aCq9gIPA5cM6HMJ8GC4vQFYJyICICIfBw4CO+KoY0LREg+fhS2BYG7W3GF6Hk9c0n7Y0pVXtxx2RKbBYIg/8TQWswB7yEtF+NygfVQ1ALQAeSKSBnwZ+NZwNxCRm0Vks4hsrqub+uvfzQ4vQ2koRGN3U+Q4L2/RmMYPlvYjVopmlEXa1Z01hIIOOM4NBkPciaexGCzuc+DTZqg+3wLuVNX24W6gqr9U1dWqurqgYPTO20Sln4PbgQp5bW2V+NV6GPvcXlJT88c0PiXZHSm+5FTaj8ys2WR40gDoDflpaNgTs0yDwRB/4mksKgB7SbYSoGqoPiKSBGQBjcBa4HsiUg58Afh/InJbHHWddLr9Qbr9Vr6kJJeQlhx70aPGpmhVujxvzrhk2J3cVc3O+C2K06ITzKra7Y7INBgM8SWexuItYJGIzBORZOAKYOOAPhuB68Lty4Dn1eIcVS1V1VLgR8B/qerP4qjrpNM6oJRq2HUTE82tRyLtvNTRpfkYSKHT4bNAcc78SLvKOLkNhilB3HZwq2ogPBt4BnADv1LVHSJyB7BZVTcC9wEPich+rBnFFfHSJ9Fx2l8BsCopk8Wpi2gM9eKZuXpcMvrt5HagxCpAUd4SOPQ0AFWtxsltMEwF4pruQ1WfAp4acO52W7sbWD+CjG/GRbkEY2CqD0doryVV3KS6U2CEUqpDURiHHFHFhasi7ZrOY4SCgRELMhkMhsnF7OBOEOxhs07t3qYjGjY72tTkA8lLSyY5nPajrTtAW7d/hBEjk5ZeSJYnA4CABqmtey9mmQaDIb4YY5EgOL4MFQpBp91YjM9n4XIJM+Mxu0iPOrlr63Y6ItNgMMQPM/dPEJwOm+3pOEatv5VcVzKp3mzE4xt50BAUZ6VwtNGKhKpq7mLxzIyY9VtbtJaVnW0Uu1LIUPM1NBgSHfO/NEFwupxqZf1OHuq2oqEWuubwqRhkFWdHndxOzSzmFq2Gw5usgybj5DYYEp1hl6FE5G+29lfjr86Jiao6vgxlzzabnjq6GhZDEY+9FmSVRNttVRCM3RdiMBjix0g+C7tXdNioJcP46fIH8Qetze3eJBc+T+yupMb26P7H3PTimGQVZvnoq8NU395Ltz8YkzwAklOjfhQNQUvF8P0NBsOkMtJTyVSnmQAGFj1yYkNeY8exSDs3Y2BKrrHhcbuYkeH85jyy5xDQEJXBLmqOveuMTIPBEBdG8lnMF5GNWDmc+toRVPXiuGl2AtEShw15jV3RGtd52fOH6Tk6irJ9kU15Vc1dlOanxSzzvSR4vHMfQZSyylf5xJKPxyzTYDDEh5GMhT2l+A/iqciJjNPlVEPBAE29LZHjnJzYjcWs7BTeOdIMQJVDM4usnIUEw5PXirYjI/Q2GAyTybDGQlUjpcxEpCB8burnAk8wWgbkhYqV1tajBNXyK6QnpeL1ZcUsMx5O7sLClbgQQiiNPc10dTaSkprriGyDweAsI0VDiYh8Q0Tqgd3AXhGpE5HbhxtnGBsDkwjGSmNzNNts7jizzQ7EHj57rLWbQDAUs0yPJ5WZtrrg1cfeiVmmwWCIDyM5uL8AnA2crqp5qpqDlT78LBH517hrd4LQr5yqE2Gztgp0uePcuT0Qn8dNbpqlW0jhWFvstS0AijNLI+3KuhOmKKLBMOUYyVhcC1ypqof6TqjqQeDq8DWDA/T3WcS+e7uxrTLSzk0rilleH/025zm0FDUr96RIu7JpnyMyDQaD84xkLDyqWj/wZNhv4VC2uxObUEhp7XbWwe3r7SJPknEh5GaWjDxglBTb0pVXOmUsZkYz0Fa1Vw7T02AwTCYjRUP1jvOaYZS09QToW/5PTXaTnBT7hrxzXemcmzqfkCqhmafFLK+PeKT9yM8/mWSXh96QnzZ/B60tR8nMmj3yQIPBMKGM9GRaKSKtItIW/mvtOwZWTISC051+zm3Hss1aeyxcIiRlFMYuM0xRdv+NeaFQ7Hs2Xe4kilKjOlbVGCe3wZCIDGssVNWtqpmqmhH+y7Qdm2UoB3A6bJbuZggFrLY3A2LINjuQTJ+HDJ81Ge0JhKjvcMbJPcu2abCi3ji5DYZEZKTQWZ+IfEFEfiYiN4uIyVLrMHbntiMV8jps22BS82OXN4BZtqWoiiaH/Bb5S/HhZqE7jYLuDkdkGgwGZxnp4f8g4AdeBj4KLAM+H2+lTiTsYbNO1LE4XLeDSn8jeeKh0JdB7Nvx+lOSk8LumjbAMhanzol9H8fJc97Pkr3PWzmxenqspTSXqctlMCQSI/2PXKqqV6vqL4DLgHPGIlxELhSRPSKyX0S+Msh1r4g8Er6+SURKw+fXiMjW8N+7IvKJsdx3KtHisM9id8MO/t5by8M9lbwbbI9Z3kBKclIj7YqmTkdkulJzkZSw0Qn2QquJijIYEo2RjEXkSaaqgbEIFhE3cBfwEWApcKWILB3Q7UagSVUXAncC3w2ffw9YraqrgAuBX0zXJTCn80LZs83mORg220dJjn2vhTM7uQHInRdtN5U7I9NgMDjGaKOh+iKgymzRUa0jjF0D7FfVg6raCzxM/8SEhI8fDLc3AOtERFS102acfEzjVOlOZ5xtsmWbzc0qjVneQNK8SeSEHfGBkEYy0cZMTmm0bYyFwZBwjDYaqi8CKsnWzhxB9izgqO24Inxu0D5h49AC5AGIyFoR2QFsB24Z68xmKhAIhmjvsV6WSOwO7lAwQKMt22xu7sKY5A3F7NzoUlSlQ05uf1YJW/0t/Lmnht8d/bsjMg0Gg3PE04s4WAWfgTOEIfuo6iZVXQacDnxVRI6LAQ1HaG0Wkc11dVMvGW5rdwANvyMZviTcrtiKHtmzzaa5UxzJNjsY8YiIkswSnvTX8nagmX1dx+hor3FErsFgcIZ4GosKwL4VtwSoGqpP2CeRBTTaO6jqLqADWD7wBqr6S1VdraqrCwoKBl5OeJo7bZFQTuSEsmeb9cUv1bfdb3HUISd3ksdHUerMyHFF1WZH5BoMBmeIp7F4C1gkIvNEJBm4Atg4oM9G4Lpw+zLgeVXV8JgkABGZC5wElMdR10nB6Q15Dc3lkXaeQ9lmB6M4O4W+yq+1bT30BByoyQ2U2Dfn1b3niEyDweAMcTMWYR/DbcAzwC7gUVXdISJ3iEhfOdb7gDwR2Q98EegLrz0beFdEtgJ/Am4dLKHhVKfZYed2Q1tFpJ2XHlvd7eHwedzMyPACoApVzc44uWcXRDPIVDQfcESmwWBwhriGo6rqU8BTA87dbmt3A+sHGfcQ8FA8dUsEWhwOm23oiK7z52XNiVnecJTkpHKs1Ur3UdHUyTwHanKXFJ0GW612ZXsVoWAAl3taRkwbDFMOs012EnE6bLahKzr5ysteELO84YiHkzszazaZnnQA/Bqgtna7I3INBkPsGGMxiTjqswgGOE19rErKYrYrlZzc+SOPiQG7k9upndwAszPnRtpHa952TK7BYIgNM8efRBzdvd1Zz1nJ4QiolFzwpA7fP0aKsnwkuYRASGns8NPREyDNG/vXqST3JHY0WJlnj9Tv5PSYJRoMBicwM4tJoicQpMtvRREluYT0WB+07bXRdvrMofs5RJLbRWFWdOvLkUZnZhdzi6Pm4XDrITTkUDoRg8EQE8ZYTBIDndsisW3Io8NmLNKcT00+GHPzorOXww3OGIuZM8rwuqw9J23+DlqaD40wwmAwTARmGWqScDpslnbbDvb0+O2xsFOal8ar+61cVEcanalD4XInsS5/FaktFcx1p5LeXg+58XXWGwyGkTEzi0miXySUAxvynqh+hUe7K3mut47W5NjDWEeDfWZxtLHLsQy0p88+l2VJmaRLEjSa/RYGQyJgjMUkYV+GcqKOxb72SnYF23jF30AoNX6pPuxk+DzkpkUz0Dq1OY88WyRXgzEWBkMiYIzFJNHY6VyFvK7ORjqC1l4Ht7jJjPOGPDtz86KzmPIGh0qiZs0BV9iAdtZDV7Mzcg0Gw7gxxmKSsCcR7Pt1Pl4am/ZH2nnebFwud0zyxkKpzVgcdigiCncS5JQSVKUy2EVd9RZn5BoMhnFjjMUk0dhh35AX28yiwRYxlJcysdl3S21+iyMNHag6U6dqa3IS3+3cx73dh3nzyEuOyDQYDOPHGItJIBAM0dptGQuR2H0WDa3RGlN56cUxyRorBRleUjzWTKa9J0h9e+8II0ZHZt5i/FgO8yPN+0fobTAY4o0xFpNAc5c/UvQo0+chyR3bx9DQHi0TEo+628MhIv2iopwKoZ1dvBZXuDZWbXcDnfZNhwaDYcIxxmIScNJfAdDQGd1jkZddGrO8sWI3FuX1zvgtPN40itOKIsdHKt9wRK7BYBgfxlhMAk76KzQUoqE7WlwwL2dRTPLGgz0i6rBTEVHA3JzFkXb5sXcck2swGMaOMRaTQJN9ZhGjsWhrq8SvAQBS3D5SJ2j3tp2SnBSSwvXD69p76egJOCK3tOi0SPtgw25HZBoMhvFhjMUk0NQRNRY5MS5D1Tfui7RzfTkxyRovHreLWbaU5YfqnZldzC05C7dYzvO6nkZaW46OMMJgMMQLYywmgSbb7u2cGGcWJSHlet8cPpo8kzW5y2JVbdzMt1XKO1DX7ohMjzeNORlRh/3BIy87ItdgMIwdYywmAfsyVKzGIrmjgbnuVE735FBWeNrIA+LEwhnpkfb+WmeMBcD8/Ghd7kPGb2EwTBrGWEww/mCItm5rTd8lDmScbauOttMLY5MVA3NyU/G4Lb9FfXtvv4ivWJhfcmakfbBpn6lvYTBMEnE1FiJyoYjsEZH9IvKVQa57ReSR8PVNIlIaPn+BiGwRke3hfz8QTz0nEru/IjvVg8sVQx0LVWiriR5nTJ6xSHK7+kVFObUUVVR4KpnuVOa70zjTnU6wpcIRuQaDYWzEzViIiBu4C/gIsBS4UkSWDuh2I9CkqguBO4Hvhs/XAx9T1RXAdcBD8dJzonHSXxHoaqKrt806SPJByuQ4uPuwL0UdqHXGyS0uF5+fdzHX+GbzPk8eSQ37Rh5kMBgcJ54zizXAflU9qKq9wMPAJQP6XAI8GG5vANaJiKjqO6raty15B+ATEW8cdZ0wGjuc81ccObaV73Xu43869/M0nVbukElkQUF0ZrG/rt2xPFGuGUuiB/V7HZFpMBjGRjyNxSzAHutYET43aB9VDQAtQN6APpcC76hqz8AbiMjNIrJZRDbX1dUNvJyQ9N+9HZuxqAtnm23TAL3ejJhkOUFxVgqpyVaoa1t3gNq24z6y8ZEf3ZxHwwEI+ofuazAY4kI8jcVgP3MH/tQcto+ILMNamvrMYDdQ1V+q6mpVXV1QMLHZVsdL/zoWsTm3a1uORNoFE1jDYihcLmG+fXbhVFRUai6khTcbhvyETEEkg2HCiaexqABm245LgKqh+ohIEpAFNIaPS4A/Adeq6rR5OjTbfBYxzyxsCQQLsucP03PiWFhg81s45OQGqMkq4q89x7ir8yDP7f2jY3INBsPoiKexeAtYJCLzRCQZuALYOKDPRiwHNsBlwPOqqiKSDfwF+KqqvhpHHSecxg5nKuRpKERdd33kuCD/5Jj0cooFNif3wboOQiFn/BYtmTN5M9BEvfayp26bIzINBsPoiZuxCPsgbgOeAXYBj6rqDhG5Q0QuDne7D8gTkf3AF4G+8NrbgIXA10Vka/hv4pMeOUy3P0hnbxCAJJeQ6Usat6y2tkq6g5ZPwOtKJjNjYlOTD0VeWnJk70hPIMQRh6rnzS89H49Y71dDTxP19SZXlMEwkYz/aTUKVPUp4KkB5263tbuB9YOM+zbw7XjqNhn037ntQWKIXqpvjEYFFaTkI67E2F8pIiyemc5b5U0A7K5ppdSWCmS8eDypLMhewO6mPQDsPfQc+QkymzIYTgQS4wlzgtDkYGry2sZo9bgCW92HRGBJUWakvbO6zTG5JxWvjbR315i63AbDRGKMxQTS5GTYrK2UaiJEQtlZUJAeSf1R19ZDnUMhtIvmrUPCAXQVHVV0tNeMMMJgMDiFMRYTSGOHc2Gz9kioGdkLYpLlNMlJLhbZHN27a1odkZuWXsjsdGurjqLsO/ScI3INBsPIGGMxgdS3R39h56fHsCFdlWBPa2STSqJEQtmxL0XtqnbGWACcNPPUSHu3KbVqMEwYcXVwG/pjX46ZkRGDsehu4dPeWfiTQ9S7XGRkDNwYP/mcVJiBiJXrsLyhk87eAKnJsX/dFs9bx98PWBHYB1oO4O/pwOON3YFuMBiGx8wsJojeQCiSRNAlMfoswmnJPeKiKHtewkRC2cnweZiTmwpYBmN3jTOO7vz8k8n35gIQ0CAHj7zoiFyDwTA8ifeUmabYl6By05JJcsfw1tvTdGcWx6BVfInbUlRBGQAzXV5c9SYLrcEwEZhlqAnCvgRVEMsSFIC9FnV2YkVC2VlSmMHT71kRS/uOteMPhvDEYiTDrF50EWUNh5nh8kJztZVY0B1jESmDwTAsZmYxQfQzFrE4t4E3ajazP9BOhwYgKzF2bg9GQYaX/HRrua0nEHIssWD2jOXM6NuxHuiGY+85ItdgMAyNMRYTRF27MzOLzvZanmk/wG97KvhR1yFC6TOdUC8uiAjLiqNLUe8ebXZKMMxaHT2u2OyMXIPBMCTGWEwQTi1DVR3bGmnPTCnAleDLL6fMiVbv21ndSrc/6IzgWadF27W70B7nMtwaDIbjMcZiAlDVfg7uWIxFdf2uSLs4qzQWtSaEmZk+irJ8APiDyo6qFmcEpxfQmjGT1/yN/KJzP1t2bXBGrsFgGBRjLCaA5k4//qCVqjvd645pv0F188FIuyhnUcy6TQSrZmdH2u8ccWgpCtiVmc/fe2upCfWwveJlx+QaDIbjMcZiAnDKXwFQ1R4Nmy2asTwmWRPFytnZkfLgB+s7aOlypizqskUfwxXex36kvYLmpkOOyDUYDMdjjMUE4JS/oqO9hha/tTafJG5mFEwNY5GV4mF+OE25qnOO7vSMIuZnzYscb9/3Z0fkGgyG4zHGYgLoHzbrG7ec6pp3I+3C1Jm43FNnm4zd0b3VqagoYMWc8yLtdypeJhQMOCbbYDBEMcZiAnAsEqohWh2uKDNxN+MNxrLizEja8uqWbqpbuhyRu2Txx0hxWwa4qbeVfQefcUSuwWDojzEWE4BTPovq5mjBo+LcxTHpNNH4PG6W2tJ/bDrY6IhcjyeVU4qiRZE273/SEbkGg6E/xljEma7eIG3d1tKIxy1kp4x/X0RVe2WkXTRjRcy6TTRr5+dF2m8faaKr15k9F6uXXh4pirS/5SAN9XtHGGEwGMaKMRZxxr4ElZ/uxeUaX91t7WrhTEmjLCmTme5UCvKXOqXihFGal9pvz8Vb5c7MLnJyF7Aoe2Hk+K2dDzsi12AwRImrsRCRC0Vkj4jsF5GvDHLdKyKPhK9vEpHS8Pk8EXlBRNpF5Gfx1DHe1LV3R9qxLEFJy1HO8OTyCW8xtxS9f0o5t/sQEc5aGJ1dvH6wgVBIHZF9+qKLI+13a96it8e52t8GgyGOxkJE3MBdwEeApcCVIjLw5/CNQJOqLgTuBL4bPt8NfB34Urz0mygcSyDYEPVXkD03Bo0ml7KSbNKS3YC1WXGnQ6nLF8z7ILnebNIlibXuTEImX5TB4CjxnFmsAfar6kFV7QUeBi4Z0OcS4MFwewOwTkREVTtU9RUsozGlqWyOvoQZmTEYC3vdhvyp5dy243G7OH1ebuT49QMNjsgVl4urllzN51Pmc15yPr7Dr0Io5Ihsg8EQX2MxC7AVXqAifG7QPqoaAFqAPEaJiNwsIptFZHNdXV2M6jqPqnK0sTNyPDsndVxyQt2taF8NC3FB3sLhByQ4Z8zPw2Xb0V3V7EwYbd6CC0hKTrcOOuqg4i1H5BoMhvgai8E8uQMXqEfTZ0hU9ZequlpVVxcUFIxJuYmgrq2HnoD16zbd6yY7dXyRULvKn+WHXfvZ0F3JnpR08Ix/Y18ikJXiYfmsrMjxc7uOOSPY44P550eP9z0DIYey3BoMJzjxNBYVwGzbcQlQNVQfEUkCsgBnQmQSgKNN0VnFnNxURMYXCXWo5h06NMiOYBuVKRlOqTepnHdS1LjvrG7jSEPnML3HwLz3g8dKLVLTVsnBPRudkWswnODE01i8BSwSkXkikgxcAQz8n7sRuC7cvgx4XlWdCY9JAI42RpdXSnLHtwQFcKgpum9gfvHaYXpOHYqyUlhZEp1d/G1njTOCPT5a557Bo92V/KK7nCd3/Y5goNcZ2QbDCUzcjEXYB3Eb8AywC3hUVXeIyB0i0hfneB+QJyL7gS8CkfBaESkH/ge4XkQqBomkSniOOOCvaGk+TGOPlUspSdyUzFrjiG6JwAeXzoz4Lg7UdThWdtU771zKsTLbNvW2snXH7x2RazCcyMR1n4WqPqWqi1V1gar+Z/jc7aq6MdzuVtX1qrpQVdeo6kHb2FJVzVXVdFUtUdWd8dTVaXoCQWparUgoESjJSRmXnENHX4m052TMJskzPjmJSH66l9Wl0QSDz+yowYmJpdeXxfvmfjBy/OK+x+nqnDarmwbDpGB2cMeJyqYu+p57MzK8+Dzucck5ZCujOi9/aqQkHwsfOGkmSeHpRUVTF9srnamkt2bl9WSEfRftgU5efOsnjsg1GE5UjLGIE0ebov6K8S5BaSjEIVvywHmzpoe/wk5WqoczbDmjntxW7UjOqGRvBh9ednXk+K3qN6iqMhv1DIbxYoxFnOi3v2Kczu36+l20BSw5PpeXosJTHdEt0Vi3ZAaZPit9SVt3gKe2Vzsid+nij7Mwaz4AivLU5p+aehcGwzgxxiJO2MNmZ+eOz8+w7/CLkfbczLlTMh/UaPB53Fy8qjhyvPlwkyPObnG5uPD0f8Ut1hJgZWcNW7Y9OMIog8EwGMZYxIGWTj+tXdYvWG+Si5kZY99Ep6EQ71a+Gjk+edYZjumXiCwrzmL5rGi9iz+9U0FvIPZ0HXn5izl77rrI8d/2/oHaY+/FLNdgONEwxiIO2GcVs7JTxpWW3N9cTp6/FzeCR5JYsr4K9FYAABQTSURBVOgiJ1VMSC5eWUxKOBCgscPPxnerHImOOuu0z1LgtfJRBTTI0298DwI9I4wyGAx2jLGIA0cc8FckV23lk75ZfDF1IVfMvgCvL2vkQVOcDJ+H/1NWGDnecriJNxyoqOfxpLL+rP/AI0kscKdxqWTAtkdh+uz/NBjijjEWDqOq7LKl3Z6bNw5jEQpC5RYAUsXN/EUfcUq9hOfUOTmcNje69+LJbVUcqu+IWW7BjGXccOrn+JS3hDRJgsrNcPi1mOUaDCcKxlg4TGVzF/XtVnoJb5KLhTPSxy6kdhf0hh28vizIW+SghomNiHDJquLIJsaQwu82HaapI/aUHYWLPozMsfl+tj8G1e/GLNdgOBEwxsJh3j0a3VS2tDgTj3vsb7EefTN6MGs1uE6sj8njdnH12rmkey3/RXtPkHtfOeiIwWD5ZZBZEj5QNm/6EQcPPRe7XINhmnNiPYXijKqyrbI5crxqdvaYZXR1NnLnoT/xVE8NlcEuKDndSRWnDFmpHq5aOzeyu7uxw8//vuyAwUhKhrWfQVPzebm3gb90V/HIW3dy9OirI481GE5gjLFwkEP1HZGQ2bRkNwsKxr4E9faO39EW6uWtQDNPubohs8hpNacM8/LTuPqMqMFo6rQMhr1U7bjwZdJ9+o1sxtpl3xvy8+vX/pOdux+PVWWDYdpijIWDbKuILkGtKMnCPcaQ2Y72Gl4+9Ezk+JQ5H3BMt6nKSYUZxxmMu17Yz86q2Gp3p2QWc837v02a2/KNBDTIY1t/zstv/gQ15VgNhuMwxsIhgiHtlwSvrGTsS1AvbL6LnpC1zJLnzeGU5Vc5pt9Ups9geNyWwegJhHjojcP8bUcNodD4w1/zC5bwz+d/j1xv9LN6/uBf2PDsv9HZXhuz3gbDdMIYC4fYX9tOZzgBXlaKh9IxhszW1Gzl7ZpozegPr7ged1KyozpOZU4qzOAz5y4gx1aa9oU9ddz94v5+ebjGSl7+Ym788F2UZsyJnNvZuJO7/3ozu/Y8EZPOBsN0whgLB1BVXjtQHzkuK8kaUwlVDYX429t3o+Hy4wuy5rFw/occ13OqMys7hds+sLBfOHJlczc/f+kAT2ytpK3bPy65qan5fOpDP+XUmdFggo5gF4++cze/f/o2uhsPDjPaYDgxMMbCAd4+0sTeY9HEd6fMGdsS1JZtv+ZQ62EABOFDp96GnGDhsqMlNTmJf35fKR9aNjOyLKUKbxxs5PvP7OGJrZXjiphK8vj42Pnf5qrV/xqpgwHQ3noU7ys/hi0PQuvAEvIGw4nD9ExjOoG0dPl5cls0pfaZC/Ioyhp9ltl3tv2Gv+yOlv08rXANM2ZOvyJHTuJyCeefNIOVJdls3FrJnrCh9geVNw428uahRk4qzOCU2TmcXJQxpr0uixZeyGeL1/C3N77H1tp3ON+TjwhQ9bb1l1NKzcwl5M45i2RvRpxeocGQeIgTidoSgdWrV+vmzRNb3EZVefC18sjDKi8tmX9ZtxBv0uiq4h3d+xfuf/unkeWn4tSZXPuhn54QeaCcwkqv0sYLe2qpsBWc6sPnsXbRnzQzg0UzMsiy+TxGov7Ye+SVv4bU7oicC6nyo64DdKLMyyzlpKI1LJhzDtnZ88xs0DAlEZEtqrp6xH7GWIwPfzDEszuP8Y99lq9CBD59znzm5aeNMBLobIS9T6NHNvF07zHeDDRRmDKDay64k9TU/DhrPj1RVQ7UtfPinjoO1A2dSyorxcPs3BRKclKZmellRoaPnFTP8D6mpnI4+CJUb2OPv5mHeyqP65KRlEpJ5lyKsxcwI3chM/OXkJk5xxgQQ8KTEMZCRC4Efgy4gXtV9b8HXPcCvwZOAxqAy1W1PHztq8CNQBD4nKo+wzBMlLEIhpQ9NW38ZXsVjR1Rh+pZC/O4qKx4yHGtLUc5Wr2Z0s5W0qreBbUip1SVN5LdrHz/14yhcIiG9h62Hm3m7SNN/T6jofC4hewUD1mpyWSneMjwJZHuSyLdm0Rqshufx02Kx4031En5gSd45fDfOdZdP6LcWe40bso/HVJzwZcNvkzqUOrxk+LNJiUlB583k+TkTLzezGlb3MqQ2Ey6sRARN7AXuACoAN4CrlTVnbY+twJlqnqLiFwBfEJVLxeRpcDvgTVAMfAssFhVhyzOPF5jseWp+6jsreNI8Pj//KpWOU4NQfD/b+/cg+Qqrjv8/WZmn1oh9EbogRaQEC/xEBADjolt/IjjikwFbAxxkcQpygQ7jstO/PojNqnKo8pxxS+cEBuDYzBgTDmqJGWSAipgCouHMCBFvCyBtCC0AiQhrXZe95780b1oZjTyjNDOzmrnfFVTc2/f7r6n7872uX26+xwz8qWE7mIvi2ze/nYCo9N2M3NeQkYitTJJWqaclsmX97GvtI+9xb2MJMFEcknPAlbmKsxM806BM68At3+PO2bG8J4Cz27fw7Pb97LltRGKyeH/3jOCnuRlsoW1FIrPsjfdTkKZsbFJGKSIQevnfem8N88FPJzZyTqNuYRRTb0ZcsqSJUdWWU7KzOGM3AJQFlMWU4bHk1fYbiNABglEBikT6pcQmTfrPTE3nwXZWW/eH+CJ0ovsSQsVco5x4MjqpNyxzM7u/10aYl1xEwVrbtXZaV1LmJ6pnr9bW3gWa3Kl4Fndg/Rov9mwZAmPFX/dVFmA87qXkam41760wJOlF5sqmyPDOT0nVqXtSkd4unTgqLIefermjO6lVWnDyW42lbc3VX5Gpp+TuxZVpb1Ufo2tyWsHlXX+ivNZfOLpTdVfSbPKopWvMucBz5vZpijQbcBq4P8q8qwGvhKP7wS+rWAPWA3cZmYFYLOk52N9D423kOVND/Jq5jU25nY3zgwMJv0MlmYDkMuIxbP6WZfbxdrhnU2VH0pGg7KYdTys+CDMPuEty+78ZiQx/6he5h/Vy28vm0uaGtv35Nn6+ijbdo8y/EaBHXsL7MkfWlzu1GA0cyz0XQJ90JOWyZU2oeIzWPIyxXSYvO0kVxK7ytUd646uAvnswXaIJ8D+/MeUU/aWq1d2bet+lS2ZA+dm6jGzNMTcpPol5IWe7byq5laLHVPcwoy0er/Q8z0vM6KDvrNVMVgYot96qtI29m6lWXV9cuElcra/iyqSsLG3+RVpq/KvYBVKcERFNvY011n3kOGsfHUs+Dcyo2zsbjyiBJhpXZxW2FqVtjM7wsau5uKzHJv2sry4uSptOPdG3X6qL8q6Z/ZieAvKollaqSwWApVPawj4rYPlMbOypN3A7Jj+y5qyC2tvIOlq4GqAJUuW1F5uGd25DDP7u1h4dH9YvtmEq6KcsiwaWMjcOafDCR8ISuIQ9mI4h08mIxbM6DtgtVq+lLBrX4md+4rsHi2xN19mbyF88qWE0WLCaCmhUE4pllPKtbvGMznKPcuhZ3k4BfqBbck+7kv20J/spi/ZS08yQsGeY0b6Ggl5EsuTUCKxEinlAzrRTJ23/akxw+gcibRSWdTrCWt/6wfL00xZzOwG4AYIZqhDFRBg+qrLOKHwOgOlA4d3EmSkN7/7u3McN30mJ02vnps4Nf8qcwpB4+eyXWQyObKZHD3d05nWN5v+aXMZmHaM78iepPR2ZTlmRpZjZjQXKz1JjVKSxo+RpEY5TSknRmrhPDUjtbB6Kk3DN4TvYN7cn2YGliYkSYG0PEo5GSVN8nSRpUc5ZGmY40oTzisMc3oyilmCpUkwk1qCkYZ/HEtJScFS5nXNZlq2cmRhnJt/iXw0Q1k91VNhll7UM5+B7LSq9AvyWyimzZmh5vcupD9T/UwvGt3UdKjcWb1L6M7sN0P1WsJFoy80VRZgoG+QjPYvMMilBS7KDzVVNqcsA31Lq9KOTUa4qPBKU+V7M90M9C6uSjuu/AZdxR1NlR/I9jPQU+1EdFlpJzNKB45Mcsox0Hccc487uam63yqtVBZDQOXTWgTUjiHH8gxJygEzgNebLDsunHL+4UehW0y1sM7UJpsR2UyY+D7SONwdPKe2ufwZh1l+1WGWf1vjLFOWVq7rewRYJmlQUjdwObCmJs8a4Kp4fClwr4XXjjXA5ZJ6JA0Cy4CHcRzHcdpCy0YWcQ7ik8DdhKWzN5rZBknXAY+a2Rrg+8C/xQns1wkKhZjvDsJkeBm49jethHIcx3Fai2/KcxzH6WCaXTrr20sdx3GchriycBzHcRriysJxHMdpiCsLx3EcpyFTZoJb0g6gOccv9ZkDNLeXf2rQae0Fb3On4G0+NI4zs7mNMk0ZZXG4SHq0mRUBU4VOay94mzsFb3NrcDOU4ziO0xBXFo7jOE5DXFns54Z2CzDBdFp7wdvcKXibW4DPWTiO4zgN8ZGF4ziO0xBXFo7jOE5DOl5ZSHq/pGckPS/pC+2Wp9VIWizpPkkbJW2Q9Ol2yzRRSMpKelzSf7RblolA0tGS7pT0dPx7n99umVqNpM/E3/V6ST+W1FxEqyMISTdKGpa0viJtlqT/kfRc/J453vftaGUhKQt8B/hd4BTgo5JOaa9ULacMfNbMTibEcrm2A9o8xqeBje0WYgL5BvBzM1tBiBs0pdsuaSHw58A5ZnYaITTC5e2VqiXcBLy/Ju0LwD1mtgy4J56PKx2tLIDzgOfNbJOZFYHbgNVtlqmlmNk2M1sXj/cQOpAD4ptPNSQtAn4P+F67ZZkIJB0FvIMQMwYzK5rZrvZKNSHkgL4YebOfFkXYbCdmdj8h/k8lq4Gb4/HNwIfG+76driwWAlsrzofogI5zDElLgbOAte2VZEL4J+CvgLTdgkwQxwM7gB9E09v3JE1rt1CtxMxeAr4GbAG2AbvN7L/bK9WEMd/MtkF4IQTmjfcNOl1ZqE5aR6wlljQA/BT4CzN7o93ytBJJHwSGzeyxdssygeSAs4HvmtlZwAgtME1MJqKdfjUwCBwLTJP0h+2VaurQ6cpiCFhccb6IKThsrUVSF0FR3GJmd7VbngngQuD3Jb1AMDW+S9KP2itSyxkChsxsbNR4J0F5TGUuBjab2Q4zKwF3ARe0WaaJYrukBQDxe3i8b9DpyuIRYJmkQUndhMmwNW2WqaVIEsGOvdHMvt5ueSYCM/uimS0ys6WEv/G9Zjal3zjN7BVgq6STYtK7CTHtpzJbgLdJ6o+/83czxSf1K1gDXBWPrwL+fbxvkBvvCo8kzKws6ZPA3YSVEzea2YY2i9VqLgQ+Bjwl6Vcx7Utm9l9tlMlpDZ8CbokvQpuAP26zPC3FzNZKuhNYR1j19zhT0PWHpB8DvwPMkTQE/DXw98Adkj5OUJqXjft93d2H4ziO04hON0M5juM4TeDKwnEcx2mIKwvHcRynIa4sHMdxnIa4snAcx3Ea4srCmZRImi/pVkmbJD0m6SFJl7zFupZWeujsJBS4N/qKOty6uiXdH/0uOR2GKwtn0hE3VP0MuN/MjjezVYTNdIvaK1ljJmFH+gHgifFw6RKdbd4DfOSwpXKOOFxZOJORdwFFM/vnsQQze9HMvgUgqVfSDyQ9FZ3kvTOmL5X0gKR18XOAqwdJp0p6WNKvJD0paVmdPHsl/WOs4x5Jc2P6CZJ+Hkc6D0haEdNvkvR1SfcB/1BTV7+kO+K9bpe0VtI58dp3JT0a4y98taLMC5L+No6mHpV0tqS7Jf1a0icq8v2lpEdi3V+lPlcSd/PG5/N0dCq4XtItki6W9GCMg3BezPcVSZ+ruM/66HQSghK/8iD3cqYwriycyciphF24B+NaADM7HfgocLNCkJth4D1mdjbh7febdcp+AviGmZ0JnEPwoVTLNGBdrOd/CTtkIewG/lQc6XwOuL6izHLgYjP7bE1dfwbsNLOVwN8AqyqufdnMzgFWAhdJWllxbauZnQ88QIhfcCkh/sh1AJLeCywjuNk/E1gl6R112nIhUOlA8URCnIuVwArgCuDtsT1fqlO+lvXAuU3kc6YYk23I7DgHIOk7hA6taGbnxuNvAZjZ05JeJHTWLwLflnQmkMS0Wh4CvhzjW9xlZs/VyZMCt8fjHwF3RS+9FwA/CVYyAHoqyvzEzJI6db2d0DljZuslPVlx7cOSrib8Hy4gBOAauz7mo+wpYCDGHtkjKS/paOC98fN4zDdAUB7319x/Viw7xmYzewpA0gZCwByT9BSwtI78VZhZIqkoaXpNvc4Ux5WFMxnZAPzB2ImZXStpDvBoTKrnWh7gM8B2QlS4DJCvzWBmt0paSwiEdLekPzWzexvIY7G+XXFEUo+Rg6TXlVXSIOFt/lwz2ynpJqAyBGghfqcVx2PnuVjv35nZvzSQvSwpY2ZjcTxq66q8z1h/UKba6lAbmrSHOs/Wmdq4GcqZjNwL9Eq6piKtv+L4fqLdXNJyYAnwDDAD2BY7xo8RnENWIel4YJOZfZPw9r6yNg/h/+LSeHwF8Is4QbxZ0mWxHkk6o4m2/AL4cCxzCnB6TD+KoGB2S5pPCO17KNwN/Ekc8SBpoaR6AW+eIQRCOhReILozl3Q2IT4E8Xw2MOYC3OkgXFk4kw4L3i0/RLDjb5b0MCFU5OdjluuBbDSd3A78kZkVYvpVkn5JMEHVe9v/CLBewePuCuCHdfKMAKdKeoww2X5dTL8S+LikJwijn2ZC8F4PzI3mp88TzEy7zewJgglpA3Aj8GATdb1JjAB3K/BQfA53AtPrZP1PgofSQ+GnwKz4jK4Bnq249k7APRR3IO511nFqkLTXzAbGqa4s0GVmeUknEJaeLo/LUFuOQiCcH5rZe8apvruAL5rZM+NRn3Pk4HMWjtNa+oH7FKITCrhmohQFhHjMkv5V0lGHu9dCIS7Gz1xRdCY+snAcx3Ea4nMWjuM4TkNcWTiO4zgNcWXhOI7jNMSVheM4jtMQVxaO4zhOQ/4fwicrEMa4K/wAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "gamma_prior.plot(hypo_mu, label='prior')\n", "gamma_posterior.plot(hypo_mu, label='posterior conjugate')\n", "posterior.plot(label='posterior grid', linestyle='dashed')\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Posterior predictive distribution\n", "\n", "Ok, let's get to what is usually the point of this whole exercise, making predictions.\n", "\n", "The prior represents what we believe about the distribution of `mu` based on the data (and our prior beliefs).\n", "\n", "Each value of `mu` is a possible goal scoring rate.\n", "\n", "For a given value of `mu`, we can generate a distribution of goals scored in a particular game, which is Poisson.\n", "\n", "But we don't have a given value of `mu`, we have a whole bunch of values for `mu`, with different probabilities.\n", "\n", "So the posterior predictive distribution is a mixture of Poissons with different weights.\n", "\n", "The simplest way to generate the posterior predictive distribution is to\n", "\n", "1. Draw a random `mu` from the posterior distribution.\n", "\n", "2. Draw a random number of goals from `Poisson(mu)`.\n", "\n", "3. Repeat.\n", "\n", "Here's a function that draws a sample from a posterior `Suite` (the grid approximation, not `GammaSuite`)." ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "def sample_suite(suite, size):\n", " \"\"\"Draw a random sample from a Suite\n", " \n", " suite: Suite object\n", " size: sample size\n", " \"\"\"\n", " xs, ps = zip(*suite.items())\n", " return np.random.choice(xs, size, replace=True, p=ps)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's a sample of `mu` drawn from the posterior distribution (after one game)." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.54585" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "size = 10000\n", "sample_post = sample_suite(posterior, size)\n", "np.mean(sample_post)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the posterior distribution looks like." ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_post, label='posterior sample')\n", "cdf_rates()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now for each value of `mu` in the posterior sample we draw one sample from `Poisson(mu)`" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.5493" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pred = np.random.poisson(sample_post)\n", "np.mean(sample_post_pred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the posterior predictive distribution looks like." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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JxIkTueGGG3jqqac2mGf9+vXsuOOOzJ07N28f2267bea6NtUmX/0V20QEhx9+OPfdd98G886dO7cgp0q3adOGli1bMm/ePCZNmsStt95aXscDDzzAnnvuWWnbQw45hOeee44///nPDB06lFGjRnHwwQdz9dVXM3PmTHbaaSeGDx++wfUWW2+9NQBbbLFF+eOy56WlyZ2IK3ufykQEw4YN46qrrqrdymfgLQ+zRmzFihW89NJLANx333307duXvfbai2XLlrF48WIA7r77bg499FDWrl3Lhx9+yHe+8x1++9vflgdEixYt+PjjjwHYfvvt6dChQ/k374jgtddeq7KOgw46iIkTJwIwYcIE+vbtW636H3/8cVavXs1nn33Ggw8+WL4VlevAAw/kr3/9a/n6fPrpp7z11lvstddevP322yxZsqR8/fPp378/N998MwBffvklH3300QbrnM+QIUP49a9/zYcffkjXrsnJIkceeSTXX399eTi/+uqrG7Vbvnw53/jGNzj99NM59dRTmTNnDh999BHbbrstO+ywA++99x6PPPLIRu2qMmPGDN5++23Wr1/PpEmTNnp/+/fvz5QpU3j//eRyudWrV7N8eY1GWq82b3mY1ZH6OCOtc+fO3HXXXZxxxhl06tSJkSNH0rx5c+68804GDx5MaWkpPXv25Mwzz2T16tUMGjSIdevWERH85je/AZIPytNPP53rrruOKVOmMGHCBEaOHMmYMWP44osvGDJkCPvuu+8m67juuus45ZRTGDduHK1bt+bOO++sVv19+/Zl6NChLF68mBNOOIHi4mKWLVu2wTytW7dm/PjxHH/88eUH/seMGcMee+zBbbfdxne/+11atWpF3759ef311zdaxu9+9ztGjBjB7bffTlFRETfffDO9e/emT58+7LPPPhx11FH8+Mc/3qDNcccdx7nnnsvFF19cPu3iiy/mpz/9Kd26dSMiaN++PQ8//PAG7Z555hnGjRtHs2bN2G677fjDH/5Ahw4d6NGjB3vvvTe77bZb3oCsSu/evRk9ejTz588vP3ieq0uXLowZM4YjjjiC9evX06xZM2688UZ23XXXSnqsvSZzD/Pi4uLwzaASPlV383jjjTfo3LlzvS1/2bJlHH300Xk/MBuD8ePHM2vWLG644Yb6LqVBy71+pbby/c1Kmh0RxVn78m4rMzPLzLutzBqp9u3bN9qtDkiuARk+fHh9l9Hg9evXj379+tV3GRvxlodZLTSV3b7W9NX136rDw6yGmjdvzgcffOAAsQav7H4ezZs3r7M+vdvKrIbatm1LSUkJq1atqu9SzKpUdifBuuLwMKuhZs2a1dld2cwaG++2MjOzzBweZmaWmcPDzMwyc3iYmVlmDg8zM8vM4WFmZpk5PMzMLDOHh5mZZebwMDOzzBweZmaWmcPDzMwyc3iYmVlmDg8zM8vM4WFmZpk5PMzMLDOHh5mZZebwMDOzzHwnwc3ogqnz67zPq47tWud9mplVxVseZmaWmcPDzMwyK2h4SBogaZGkxZJG53n9PEkLJc2T9KSkXXNeGybpb+nPsELWaWZm2RQsPCQVATcCRwFdgOMldakw26tAcUR0A6YAv07bfh24FDgA6AVcKmmnQtVqZmbZFHLLoxewOCKWRsS/gYnAoNwZIuLpiPg0ffoy0DZ9fCTweESsjoh/AY8DAwpYq5mZZVDI8GgDvJPzvCSdVplTgUeytJU0QtIsSbNWrVpVy3LNzKy6ChkeyjMt8s4onQQUA+OytI2I2yKiOCKKW7duXeNCzcwsm0KGRwnQLud5W2BlxZkkHQZcCAyMiM+ztDUzs/pRyIsEZwKdJHUA/g4MAU7InUFSD+BWYEBEvJ/z0l+A/805SH4EcEEBa7Ua8EWPZl9dBQuPiCiVdDZJEBQBd0TEAklXALMiYhrJbqrtgPslAayIiIERsVrSL0kCCOCKiFhdqFrNzCybgg5PEhHTgekVpl2S8/iwTbS9A7ijcNWZmVlN+QpzMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLrKDhIWmApEWSFksanef1QyTNkVQq6bgKr30paW76M62QdZqZWTZbFqpjSUXAjcDhQAkwU9K0iFiYM9sKYDhwfp4uPouI7oWqz8zMaq5g4QH0AhZHxFIASROBQUB5eETEsvS19QWsw8zM6lghd1u1Ad7JeV6STquu5pJmSXpZ0vfzzSBpRDrPrFWrVtWmVjMzy6CQ4aE80yJD+10iohg4AfitpI4bdRZxW0QUR0Rx69ata1qnmZllVMjwKAHa5TxvC6ysbuOIWJn+uxR4BuhRl8WZmVnNFTI8ZgKdJHWQtBUwBKjWWVOSdpK0dfq4FdCHnGMlZmZWvwoWHhFRCpwN/AV4A5gcEQskXSFpIICknpJKgMHArZIWpM07A7MkvQY8DYytcJaWmZnVo0KebUVETAemV5h2Sc7jmSS7syq2exHoWsjazMys5nyFuZmZZebwMDOzzBweZmaWmcPDzMwyc3iYmVlmDg8zM8tsk+EhaXzO42EFr8bMzBqFqrY89s15fG4hCzEzs8ajqvDIMpChmZl9RVR1hXlbSdeRjJBb9rhcRJxTsMrMUhdMnV+n/V11rAcvMKutqsJjVM7jWYUsxMzMGo9NhkdE3LW5CjEzs8Zjk+EhaZNDqEfEwLotx8zMGoOqdlv1JrmV7H3AK+S/O6CZmX3FVBUe/x9wOHA8ye1g/wzcFxELNtnKzMyatE2eqhsRX0bEoxExDDgQWAw8I+knm6U6MzNrkKq8GVR6O9jvkmx9tAeuA6YWtiwzM2vIqjpgfhewD/AIcHlEvL5ZqjIzswatqi2PocAnwB7AuZLKrjgXEBGxfSGLMzOzhqmq6zw86q6ZmW2kqt1WzYEzgd2BecAdEVG6OQozM7OGq6oti7uAYmA+8B3gmoJXZGZmDV5Vxzy6RERXAEm3AzMKX5KZmTV0VW15fFH2wLurzMysTFVbHvtK+ih9LOBr6XOfbWVm9hVW1dlWRZurEDMzazx8Kq6ZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCyzgoaHpAGSFklaLGl0ntcPkTRHUqmk4yq8NkzS39KfYYWs08zMsilYeEgqAm4EjgK6AMdL6lJhthXAcODeCm2/DlwKHAD0Ai6VtFOhajUzs2wKueXRC1gcEUsj4t/ARGBQ7gwRsSwi5gHrK7Q9Eng8IlZHxL+Ax4EBBazVzMwyKGR4tAHeyXlekk6rs7aSRkiaJWnWqlWralyomZllU8jwUJ5pkWdajdtGxG0RURwRxa1bt85UnJmZ1Vwhw6MEaJfzvC2wcjO0NTOzAitkeMwEOknqIGkrYAgwrZpt/wIcIWmn9ED5Eek0MzNrAAoWHumdB88m+dB/A5gcEQskXSFpIICknpJKgMHArZIWpG1XA78kCaCZwBXpNDMzawCqupNgrUTEdGB6hWmX5DyeSbJLKl/bO4A7ClmfmZnVjK8wNzOzzAq65dGYXDB1fp32d9WxXeu0PzOzhsRbHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm+3mYpXxPF7Pq85aHmZll5vAwM7PMHB5mZpaZw8PMzDJzeJiZWWYODzMzy8zhYWZmmTk8zMwsM4eHmZll5vAwM7PMHB5mZpaZw8PMzDJzeJiZWWYODzMzy8zhYWZmmRU0PCQNkLRI0mJJo/O8vrWkSenrr0hqn05vL+kzSXPTn1sKWaeZmWVTsJtBSSoCbgQOB0qAmZKmRcTCnNlOBf4VEbtLGgL8Cvhh+tqSiOheqPrMzKzmCrnl0QtYHBFLI+LfwERgUIV5BgF3pY+nAP0lqYA1mZlZHShkeLQB3sl5XpJOyztPRJQCHwIt09c6SHpV0rOSDs63AEkjJM2SNGvVqlV1W72ZmVWqkOGRbwsiqjnPu8AuEdEDOA+4V9L2G80YcVtEFEdEcevWrWtdsJmZVU8hw6MEaJfzvC2wsrJ5JG0J7ACsjojPI+IDgIiYDSwB9ihgrWZmlkEhw2Mm0ElSB0lbAUOAaRXmmQYMSx8fBzwVESGpdXrAHUm7AZ2ApQWs1czMMijY2VYRUSrpbOAvQBFwR0QskHQFMCsipgG3A3dLWgysJgkYgEOAKySVAl8CZ0bE6kLVamZm2RQsPAAiYjowvcK0S3IerwMG52n3APBAIWszM7Oa8xXmZmaWmcPDzMwyc3iYmVlmDg8zM8vM4WFmZpk5PMzMLDOHh5mZZebwMDOzzAp6kaCZbeiCqfPrvM+rju1a532aVcVbHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw8zMMnN4mJlZZg4PMzPLzOFhZmaZOTzMzCwzh4eZmWXm8DAzs8x8MyizJsg3nbJC85aHmZll5vAwM7PMHB5mZpaZw8PMzDJzeJiZWWYODzMzy8yn6ppZjfmU4K8ub3mYmVlmBQ0PSQMkLZK0WNLoPK9vLWlS+vorktrnvHZBOn2RpCMLWaeZmWVTsPCQVATcCBwFdAGOl9SlwmynAv+KiN2B3wC/Stt2AYYAewMDgJvS/szMrAEo5DGPXsDiiFgKIGkiMAhYmDPPIOCy9PEU4AZJSqdPjIjPgbclLU77e6mA9ZpZA1XXx1YqO66yOZbTVI4TKSIK07F0HDAgIk5Lnw8FDoiIs3PmeT2dpyR9vgQ4gCRQXo6Ie9LptwOPRMSUCssYAYxIn+4JLCrIymyoFfDPzbCczaUprU9TWhdoWuvTlNYFmtb67ApcGBG3ZWlUyC0P5ZlWMakqm6c6bUlXNtMK15akWRFRvDmXWUhNaX2a0rpA01qfprQu0DTXh4yfpYU8YF4CtMt53hZYWdk8krYEdgBWV7OtmZnVk0KGx0ygk6QOkrYiOQA+rcI804Bh6ePjgKci2Y82DRiSno3VAegEzChgrWZmlkHBdltFRKmks4G/AEXAHRGxQNIVwKyImAbcDtydHhBfTRIwpPNNJjm4Xgr8OCK+LFStGW3W3WSbQVNan6a0LtC01qcprQt4fQp3wNzMzJouX2FuZmaZOTzMzCwzh0c1VTXUSmMiqZ2kpyW9IWmBpHPru6baklQk6VVJD9d3LbUlaUdJUyS9mf6Oetd3TbUh6b/Tv7PXJd0nqXl915SFpDskvZ9el1Y27euSHpf0t/TfneqzxuqqZF3GpX9r8yT9UdKO1enL4VEN1RxqpTEpBX4WEZ2BA4EfN/L1ATgXeKO+i6gjvwMejYi9gH1pxOslqQ1wDlAcEfuQnDwzpH6rymw8yTBJuUYDT0ZEJ+DJ9HljMJ6N1+VxYJ+I6Aa8BVxQnY4cHtVTPtRKRPwbKBtqpVGKiHcjYk76+GOSD6c29VtVzUlqC3wX+H1911JbkrYHDiE5E5GI+HdErKnfqmptS+Br6bVc29DIrtmKiOdIzgbNNQi4K318F/D9zVpUDeVbl4h4LCJK06cvk1xXVyWHR/W0Ad7JeV5CI/6wzZWOZNwDeKV+K6mV3wL/A6yv70LqwG7AKuDOdDfc7yVtW99F1VRE/B24GlgBvAt8GBGP1W9VdeKbEfEuJF/GgG/Ucz115RTgkerM6PConmoNl9LYSNoOeAD4aUR8VN/11ISko4H3I2J2fddSR7YE9gNujogewCc0nl0iG0mPBQwCOgA7A9tKOql+q7J8JF1Iskt7QnXmd3hUT5MbLkVSM5LgmBARU+u7nlroAwyUtIxkd+K3Jd1TvyXVSglQEhFlW4JTSMKksToMeDsiVkXEF8BU4KB6rqkuvCfpvwDSf9+v53pqRdKsFe5OAAAEUklEQVQw4GjgxKjmxX8Oj+qpzlArjUY67P3twBsRcW1911MbEXFBRLSNiPYkv5enIqLRfrONiH8A70jaM53Unw1vY9DYrAAOlLRN+nfXn0Z8AkCO3KGVhgF/qsdaakXSAODnwMCI+LS67Rwe1ZAeTCobauUNYHJELKjfqmqlDzCU5Fv63PTnO/VdlJX7CTBB0jygO/C/9VxPjaVbUFOAOcB8ks+cRjW0h6T7SO4ltKekEkmnAmOBwyX9DTg8fd7gVbIuNwAtgMfTz4JbqtWXhycxM7OsvOVhZmaZOTzMzCwzh4eZmWXm8DAzs8wcHmZmlpnDw5oESSHpmpzn50u6rI76Hi/puLroq4rlDE5H0X26gMvYLOtiTZ/Dw5qKz4FjJbWq70JypSMyV9epwFkR8a1C1WNWVxwe1lSUklx89t8VX6j4bVvS2vTffpKelTRZ0luSxko6UdIMSfMldczp5jBJz6fzHZ22L0rvhTAzvRfCGTn9Pi3pXpIL4yrWc3za/+uSfpVOuwToC9wiaVyF+beQdFN6T4yHJU0vWx9J/dMBFOen92rYuqy/tK7XJd2WXt1dsY6xkhamtV+d7e22rzqHhzUlNwInStohQ5t9Se4F0pXkqvs9IqIXyfDuP8mZrz1wKMnQ77ekNzQ6lWSU2J5AT+B0SR3S+XsBF0bEBvdJkbQz8Cvg2yRXj/eU9P2IuAKYRTK20KgKNR6bLr8rcBrQO+2rOcn9GX4YEV1JBlUcmba5ISJ6pvfQ+BrJuEW5dXwdOAbYO72Pw5jqvmFm4PCwJiQdGfgPJDcfqq6Z6f1NPgeWAGXDhc8n+cAuMzki1kfE34ClwF7AEcDJkuaSDGnfEuiUzj8jIt7Os7yewDPpQIFlI5geUkWNfYH70+X/Ayg7JrInyaCDb6XP78rp61uSXpE0nySo9q7Q50fAOuD3ko4Fqj2mkRk4PKzp+S3JFkHuPTBKSf/W0903W+W89nnO4/U5z9eTfJMvU3EcnyAZqv8nEdE9/emQc6+KTyqpL9/w/lWprE3e6ekWyU3AcekWyf8BG9z6NQ2uXiQjK38feLQGddlXmMPDmpSIWA1MJgmQMsuA/dPHg4BmNeh6cHrsoSPJDZsWkQyUOTId3h5Je1Tjxk2vAIdKapUeTD8eeLaKNi8A/3+6/G8C/dLpbwLtJe2ePh+a9lUWFP9M79my0dlV6fQdImI68FOSXWhm1bZl1bOYNTrXkIyCXOb/gD9JmkFyv+nKtgo2ZRHJB/M3gTMjYp2k35Ps2pqTbtGsoorbkUbEu5IuINn1JGB6RFQ1nPcDJEOZv05yj+lXSI61rJP0I+B+Jbd4nQncEhGfS/o/kl1vy9LpFbUgeU+ap3VsdKKB2aZ4VF2zRkDSdhGxVlJLYAbQJz3+YVYvvOVh1jg8LGlHkuM1v3RwWH3zloeZmWXmA+ZmZpaZw8PMzDJzeJiZWWYODzMzy8zhYWZmmf0/IvPkRPO2+RcAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_pmf(sample_post_pred, label='posterior predictive sample')\n", "pmf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Posterior prediction done wrong\n", "\n", "The posterior predictive distribution represents uncertainty from two sources:\n", "\n", "1. We don't know `mu`\n", "\n", "2. Even if we knew `mu`, we would not know the score of the next game.\n", "\n", "It is tempting, but wrong, to generate a posterior prediction by taking the mean of the posterior distribution and drawing samples from `Poisson(mu)` with just a single value of `mu`.\n", "\n", "That's wrong because it eliminates one of our sources of uncertainty.\n", "\n", "Here's an example:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.5447" ] }, "execution_count": 54, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu_mean = np.mean(sample_post)\n", "sample_post_pred_wrong = np.random.poisson(mu_mean, size)\n", "np.mean(sample_post_pred_wrong)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what the samples looks like:" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_post_pred, label='posterior predictive sample')\n", "plot_cdf(sample_post_pred_wrong, label='incorrect posterior predictive')\n", "cdf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the incorrect predictive sample, low values and high values are slightly less likely.\n", "\n", "The means are about the same:" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.5493 2.5447\n" ] } ], "source": [ "print(np.mean(sample_post_pred), np.mean(sample_post_pred_wrong))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But the standard deviation of the incorrect distribution is lower." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.70662518146194 1.6034967757996894\n" ] } ], "source": [ "print(np.std(sample_post_pred), np.std(sample_post_pred_wrong))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Abusing PyMC\n", "\n", "Ok, we are almost ready to use PyMC for its intended purpose, but first we are going to abuse it a little more.\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 the prior distribution of `mu`, with known `alpha` and `beta`.\n", "\n", "We still have the values I estimated based on previous playoff finals:" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.590040427964036 5.092056864405683\n" ] } ], "source": [ "print(alpha, beta)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can draw a sample from the prior predictive distribution:" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " mu = pm.Gamma('mu', alpha, beta)\n", " trace = pm.sample_prior_predictive(1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This might not be a sensible way to use PyMC. If we just want to sample from the prior predictive distribution, we could use NumPy or SciPy just as well. We're doing this to develop and test the model incrementally.\n", "\n", "So let's see if the sample looks right." ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8996907613890608" ] }, "execution_count": 60, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior_pm = trace['mu']\n", "np.mean(sample_prior_pm)" ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8847" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior = sample_suite(prior, 2000)\n", "np.mean(sample_prior)" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_prior, label='prior')\n", "plot_cdf(sample_prior_pm, label='prior pymc')\n", "cdf_rates()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It looks pretty good (although not actually as close as I expected)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's extend the model to sample from the prior predictive distribution. This is still a silly way to do it, but it is one more step toward inference." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " mu = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu, observed=[6])\n", " trace = pm.sample_prior_predictive(2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's see how the results compare with a sample from the prior predictive distribution, generated by plain old NumPy." ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8915" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior_pred_pm = trace['goals'].flatten()\n", "np.mean(sample_prior_pred_pm)" ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.8815" ] }, "execution_count": 65, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_prior_pred = np.random.poisson(sample_prior)\n", "np.mean(sample_prior_pred)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Looks good." ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_prior_pred, label='prior pred')\n", "plot_cdf(sample_prior_pred_pm, label='prior pred pymc')\n", "cdf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using PyMC\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, `6`:" ] }, { "cell_type": "code", "execution_count": 67, "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: 100%|██████████| 6000/6000 [00:01<00:00, 3008.78draws/s]\n" ] } ], "source": [ "model = pm.Model()\n", "\n", "with model:\n", " mu = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu, observed=6)\n", " trace = pm.sample(2000, tune=1000)" ] }, { "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": 68, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.plot_posterior(trace)\n", "pdf_rate()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And we can extract a sample from the posterior of `mu`" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.5549854626152246" ] }, "execution_count": 69, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pm = trace['mu']\n", "np.mean(sample_post_pm)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And compare it to the sample we drew from the grid approximation:" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_post, label='posterior grid')\n", "plot_cdf(sample_post_pm, label='posterior pymc')\n", "cdf_rates()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, it looks pretty good.\n", "\n", "To generate a posterior predictive distribution, we can use `sample_ppc`" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 2000/2000 [00:00<00:00, 3934.46it/s]\n" ] } ], "source": [ "with model:\n", " post_pred = pm.sample_ppc(trace, samples=2000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's what it looks like:" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([1, 5, 4, ..., 3, 0, 3])" ] }, "execution_count": 72, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pred_pm = post_pred['goals']" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.5305" ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_pred_pm = post_pred['goals']\n", "np.mean(sample_post_pred_pm)" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_post_pred, label='posterior pred grid')\n", "plot_cdf(sample_post_pred_pm, label='posterior pred pm')\n", "cdf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Look's pretty good!" ] }, { "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": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0461119480613534" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample = pm.Exponential.dist(lam=1).random(size=1000)\n", "plot_cdf(sample)\n", "plt.xscale('log')\n", "plt.xlabel('Parameter of a gamma distribution')\n", "plt.ylabel('CDF')\n", "np.mean(sample)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This distribution represents radical uncertainty about the value of this distribution: it's probably between 0.1 and 10, but it could be really big or really small.\n", "\n", "Here's a PyMC model that generates `alpha` and `beta` from an exponential distribution." ] }, { "cell_type": "code", "execution_count": 76, "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": 77, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "1.0278987526570482" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "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": 78, "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": 79, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "8.037394748828094" ] }, "execution_count": 79, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_prior_mu = trace['mu']\n", "plot_cdf(sample_prior_mu, label='mu prior hierarchical')\n", "cdf_rates()\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": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_prior_mu, label='mu prior hierarchical')\n", "plot_cdf(sample_prior, label='mu prior', color='gray')\n", "plt.xlim(0, 10)\n", "cdf_rates()" ] }, { "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", "Crazy 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": 81, "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": 82, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.575" ] }, "execution_count": 82, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_prior_goals = trace['goals']\n", "plot_cdf(sample_prior_goals, label='goals prior')\n", "cdf_goals()\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": 83, "metadata": {}, "outputs": [], "source": [ "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": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.092" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_cdf(sample_prior_goals, label='goals prior')\n", "plot_cdf(sample_prior_goals_st, label='goals prior scipy')\n", "cdf_goals()\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": 85, "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: 100%|██████████| 6000/6000 [00:07<00:00, 820.71draws/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 = pm.Gamma('mu', alpha, beta)\n", " goals = pm.Poisson('goals', mu, observed=[6])\n", " trace = pm.sample(1000, tune=2000, nuts_kwargs=dict(target_accept=0.99))" ] }, { "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": 86, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "5.493679356914262" ] }, "execution_count": 86, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_post_mu = trace['mu']\n", "plot_cdf(sample_post_mu, label='mu posterior')\n", "cdf_rates()\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": 87, "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_WSH, mu_VGK, beta, alpha]\n", "Sampling 2 chains: 100%|██████████| 6000/6000 [00:06<00:00, 941.93draws/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_VGK = pm.Gamma('mu_VGK', alpha, beta)\n", " mu_WSH = pm.Gamma('mu_WSH', alpha, beta)\n", " goals_VGK = pm.Poisson('goals_VGK', mu_VGK, observed=[6])\n", " goals_WSH = pm.Poisson('goals_WSH', mu_WSH, observed=[4])\n", " trace = pm.sample(1000, tune=2000, nuts_kwargs=dict(target_accept=0.95))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can use `traceplot` to review the results and do some visual diagnostics." ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior distribitions for `mu_WSH` and `mu_VGK`." ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(4.0273559918578625, 5.458780874512413)" ] }, "execution_count": 89, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_post_mu_WSH = trace['mu_WSH']\n", "plot_cdf(sample_post_mu_WSH, label='mu_WSH posterior')\n", "\n", "sample_post_mu_VGK = trace['mu_VGK']\n", "plot_cdf(sample_post_mu_VGK, label='mu_VGK posterior')\n", "\n", "cdf_rates()\n", "np.mean(sample_post_mu_WSH), np.mean(sample_post_mu_VGK)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the basis of one game (and never having seen a previous game), here's the probability that Vegas is the better team." ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.7185" ] }, "execution_count": 90, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(sample_post_mu_VGK > sample_post_mu_WSH)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## More background\n", "\n", "But let's take advantage of more information. Here are the results from the five most recent Stanley Cup finals, ignoring games that went into overtime." ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'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],\n", " 'WSH18': [4, 3, 3]}" ] }, "execution_count": 91, "metadata": {}, "output_type": "execute_result" } ], "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],\n", " WSH18 = [4,3,3],\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's how we can get the data into the model." ] }, { "cell_type": "code", "execution_count": 92, "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_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: 100%|██████████| 6000/6000 [00:20<00:00, 297.52draws/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(1000, tune=2000, nuts_kwargs=dict(target_accept=0.95))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And here are the results." ] }, { "cell_type": "code", "execution_count": 93, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior means." ] }, { "cell_type": "code", "execution_count": 94, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.738049580241473" ] }, "execution_count": 94, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_mu_VGK = trace['mu_VGK18']\n", "np.mean(sample_post_mu_VGK)" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "2.9708625859213225" ] }, "execution_count": 95, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sample_post_mu_WSH = trace['mu_WSH18']\n", "np.mean(sample_post_mu_WSH)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "They are lower with the background information than without, and closer together. Here's the updated chance that Vegas is the better team." ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.427" ] }, "execution_count": 96, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.mean(sample_post_mu_VGK > sample_post_mu_WSH)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predictions\n", "\n", "Even if Vegas is the better team, that doesn't mean they'll win the next game.\n", "\n", "We can use `sample_ppc` to generate predictions." ] }, { "cell_type": "code", "execution_count": 97, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 1000/1000 [00:02<00:00, 357.01it/s]\n" ] } ], "source": [ "with model:\n", " post_pred = pm.sample_ppc(trace, samples=1000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here are the posterior predictive distributions of goals scored." ] }, { "cell_type": "code", "execution_count": 98, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(1000, 3)" ] }, "execution_count": 98, "metadata": {}, "output_type": "execute_result" } ], "source": [ "WSH = post_pred['WSH18']\n", "WSH.shape" ] }, { "cell_type": "code", "execution_count": 99, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "WSH = post_pred['WSH18'].flatten()\n", "VGK = post_pred['VGK18'].flatten()\n", "\n", "plot_cdf(WSH, label='WSH')\n", "plot_cdf(VGK, label='VGK')\n", "cdf_goals()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the chance that Vegas wins the next game." ] }, { "cell_type": "code", "execution_count": 100, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.39666666666666667" ] }, "execution_count": 100, "metadata": {}, "output_type": "execute_result" } ], "source": [ "win = np.mean(VGK > WSH)\n", "win" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The chance that they lose." ] }, { "cell_type": "code", "execution_count": 101, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.44766666666666666" ] }, "execution_count": 101, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lose = np.mean(WSH > VGK)\n", "lose" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And the chance of a tie." ] }, { "cell_type": "code", "execution_count": 102, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.15566666666666668" ] }, "execution_count": 102, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tie = np.mean(WSH == VGK)\n", "tie" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Overtime!\n", "\n", "In the playoffs, you play overtime periods until someone scores. No stupid shootouts!\n", "\n", "In a Poisson process with rate parameter `mu`, the time until the next event is exponential with parameter `lam = 1/mu`.\n", "\n", "So we can take a sample from the posterior distributions of `mu`:" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3.29949623, 2.62837258, 3.09365202, ..., 5.89303007, 2.55362515,\n", " 3.71164352])" ] }, "execution_count": 103, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu_VGK = trace['mu_VGK18']\n", "mu_WSH = trace['mu_WSH18']" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And generate time to score,`tts`, for each team:" ] }, { "cell_type": "code", "execution_count": 104, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.40026273454485134" ] }, "execution_count": 104, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tts_VGK = np.random.exponential(1/mu_VGK)\n", "np.mean(tts_VGK)" ] }, { "cell_type": "code", "execution_count": 105, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.3569742547883298" ] }, "execution_count": 105, "metadata": {}, "output_type": "execute_result" } ], "source": [ "tts_WSH = np.random.exponential(1/mu_WSH)\n", "np.mean(tts_WSH)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here's the chance that Vegas wins in overtime." ] }, { "cell_type": "code", "execution_count": 106, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.4855" ] }, "execution_count": 106, "metadata": {}, "output_type": "execute_result" } ], "source": [ "win_ot = np.mean(tts_VGK < tts_WSH)\n", "win_ot" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since `tts` is continuous, ties are unlikely." ] }, { "cell_type": "code", "execution_count": 107, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.47224283333333333" ] }, "execution_count": 107, "metadata": {}, "output_type": "execute_result" } ], "source": [ "total_win = win + tie * win_ot\n", "total_win" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally, we can simulate the rest of the series and compute the probability that Vegas wins the series." ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [], "source": [ "def flip(p):\n", " \"\"\"Simulate a single game.\"\"\"\n", " return np.random.random() < p" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [], "source": [ "def series(wins, losses, p_win):\n", " \"\"\"Simulate a series.\n", " \n", " wins: number of wins so far\n", " losses: number of losses so far\n", " p_win: probability that the team of interest wins a game\n", " \n", " returns: boolean, whether the team of interest wins the series\n", " \"\"\"\n", " while True:\n", " if flip(p_win):\n", " wins += 1\n", " else:\n", " losses += 1\n", "\n", " if wins==4:\n", " return True\n", "\n", " if losses==4:\n", " return False" ] }, { "cell_type": "code", "execution_count": 110, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 110, "metadata": {}, "output_type": "execute_result" } ], "source": [ "series(1, 2, total_win)" ] }, { "cell_type": "code", "execution_count": 111, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.294" ] }, "execution_count": 111, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = [series(1, 2, total_win) for i in range(1000)]\n", "np.mean(t)" ] }, { "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": "3.6.5" } }, "nbformat": 4, "nbformat_minor": 2 }