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hierarchical_partial_pooling.ipynb
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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "# Hierarchical Partial Pooling"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Suppose you are tasked with estimating baseball batting skills for several players. One such performance metric is batting average. Since players play a different number of games and bat in different positions in the order, each player has a different number of at-bats. However, you want to estimate the skill of all players, including those with a relatively small number of batting opportunities.\n\nSo, suppose a player came to bat only 4 times, and never hit the ball. Are they a bad player?\n\nAs a disclaimer, the author of this notebook assumes little to non-existant knowledge about baseball and its rules. The number of times at bat in his entire life is around \"4\".\n\n\n## Data\n\nWe will use the [baseball data for 18 players from Efron and Morris](http://www.swarthmore.edu/NatSci/peverso1/Sports%20Data/JamesSteinData/Efron-Morris%20Baseball/EfronMorrisBB.txt) (1975).\n\n\n## Approach\n\nWe will use PyMC3 to estimate the batting average for each player. Having estimated the averages across all players in the datasets, we can use this information to inform an estimate of an additional player, for which there is little data (*i.e.* 4 at-bats).\n\nIn the absence of a Bayesian hierarchical model, there are two approaches for this problem:\n\n(1) independently compute batting average for each player (no pooling)\n(2) compute an overall average, under the assumption that everyone has the same underlying average (complete pooling)\n\nOf course, neither approach is realistic. Clearly, all players aren't equally skilled hitters, so the global average is implausible. At the same time, professional baseball players are similar in many ways, so their averages aren't entirely independent either. \n\nIt may be possible to cluster groups of \"similar\" players, and estimate group averages, but using a hierarchical modeling approach is a natural way of sharing information that does not involve identifying *ad hoc* clusters.\n\nThe idea of hierarchical partial pooling is to model the global performance, and use that estimate to parameterize a population of players that accounts for differences among the players' performances. This tradeoff between global and individual performance will be automatically tuned by the model. Also, uncertainty due to different number of at bats for each player (*i.e.* informatino) will be automatically accounted for, by shrinking those estimates closer to the global mean.\n\nFor far more in-depth discussion please refer to Stan [tutorial](http://mc-stan.org/documentation/case-studies/pool-binary-trials.html) on the subject. The model and parameter values were taken from that example.\n"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "%matplotlib inline\nimport pymc3 as pm\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport pandas as pd",
"execution_count": 2,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now we can load the dataset using pandas:"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "data = pd.read_table( '../../../pymc3/examples/data/efron-morris-75-data.tsv', sep=\"\\t\")\nat_bats, hits = data[['At-Bats', 'Hits']].values.T",
"execution_count": 7,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now let's develop a generative model for these data.\n\nWe will assume that there exists a hidden factor (`phi`) related to the expected performance for all players (not limited to our 18). Since the population mean is an unknown value between 0 and 1, it must be bounded from below and above. Also, we assume that nothing is known about global average. Hence, a natural choice for a prior distribution is the uniform distribution.\n\nNext, we introduce a hyperparameter `kappa` to account for the variance in the population batting averages, for which we will use a bounded Pareto distribution. This will ensure that the estimated value falls within reasonable bounds. These hyperparameters will be, in turn, used to parameterize a beta distribution, which is ideal for modeling quantities on the unit interval. The beta distribution is typically parameterized via a scale and shape parameter, it may also be parametrized in terms of its mean $\\mu \\in [0,1]$ and sample size (a proxy for variance) $\\nu = \\alpha + \\beta (\\nu > 0)$.\n\nThe final step is to specify a sampling distribution for the data (hit or miss) for every player, using a Binomial distribution. This is where the data are brought to bear on the model."
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "N = len(hits)\n\nBoundedKappa = pm.Bound( pm.Pareto, lower=1.0 )\n\nwith pm.Model() as baseball_model:\n \n phi = pm.Uniform('phi', lower=0.0, upper=1.0)\n kappa = BoundedKappa('kappa', alpha=1.000001, m=1.5)\n thetas = pm.Beta('thetas', alpha=phi*kappa, beta=(1.0-phi)*kappa, shape=N)\n y = pm.Binomial('y', n=at_bats, p=thetas, observed=hits)",
"execution_count": 8,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Recall our original question was with regard to the true batting average for a player with only 4 at bats and no hits. We can add this as an additional variable in the model"
},
{
"metadata": {
"trusted": true,
"collapsed": true
},
"cell_type": "code",
"source": "with baseball_model:\n \n theta_new = pm.Beta('theta_new', alpha=phi*kappa, beta=(1.0-phi)*kappa)\n y_new = pm.Binomial('y_new', n=4, p=theta_new, observed=0)",
"execution_count": 9,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "We can now fit the model using MCMC:"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "with baseball_model:\n trace = pm.sample(2000, init=None)",
"execution_count": 20,
"outputs": [
{
"output_type": "stream",
"text": "Assigned NUTS to phi_interval_\nAssigned NUTS to kappa_lowerbound_\nAssigned NUTS to thetas_logodds_\nAssigned NUTS to theta_new_logodds_\n100%|██████████| 2000/2000 [00:26<00:00, 76.47it/s] \n",
"name": "stderr"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Now we can plot the posteriors distribution of the parameters. First, the population hyperparameters:"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "pm.traceplot(trace[-1000:], varnames=['phi', 'kappa']);",
"execution_count": 21,
"outputs": [
{
"output_type": "display_data",
"data": {
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oUI3H1IKuussdHdWF8olU7zkVevvk9Q7oj8LU8uWwdKn93NseU26QWith6u9/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\n+bR1WGm+z3qLLUIQMw1SFP8F4Hrg6KQrIVJrDzwAJ50UlhNOSLo2IsV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QvhCR+lJgSjoU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\n+Id1rlqlx3L8+Oh8NDToMYiH/A4dGu1Hfb22e+pUfUjh72EQ9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eB4E/AN4G1AL/BD4Frn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\nrkJggg==\n",
"text/plain": "<matplotlib.figure.Figure at 0x11c6c8940>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Hence, the population mean batting average is in the 0.22-0.31 range, with an expected value of around 0.26.\n\nNext, the estimates for all 18 players in the dataset:"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "player_names = data.apply(lambda x: x.FirstName + ' ' + x.LastName, axis=1)\npm.forestplot(trace[-1000:], varnames=['thetas'], ylabels=player_names)",
"execution_count": 26,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": "<matplotlib.gridspec.GridSpec at 0x11ec769b0>"
},
"metadata": {},
"execution_count": 26
},
{
"output_type": "display_data",
"data": {
"image/png": 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mOG0A7GZmyds4niQMlz2eKHuc8Ht7IhHbB8BRwCHAy8ApwKnFBGFmNwK/J8xh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\nTkSuQmCC\n",
"text/plain": "<matplotlib.figure.Figure at 0x11ef0ad30>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Finally, let's get the estimate for our 0-for-4 player:"
},
{
"metadata": {
"trusted": true,
"collapsed": false
},
"cell_type": "code",
"source": "pm.traceplot(trace[-1000:], varnames=['theta_new']);",
"execution_count": 23,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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ANzvnKs0rZXQDxYQpP0hob6/P0K3OzMpnFGb1as2Bs/XWsNlm2eW+zdSrMPXB\nB5oHy7neKaz2RLrKY+qZZ3Qc0ZPHEr2xnYbP2HKvuW8rcRjr4sXw1lsaEtgXhKlKA4kOBMZm8kzd\n7Jy7Jfx0xiARWRcVvTobImgYdcOkSfCTn+jnoINqbU3PoaFBE8Tfc0/PmSXJMIw+yd7Ak8CFwHsi\ncquIfEZEBtTYrm7lgw9qbUFplCJMQf2KEB4L5as+ixfD22/Dq6/mLq93Ycpf13q1ry/SVR5TL7+s\nIY89kd78/AmPrdz70O8bC1N9LRy0UmFqDlXykhKRy0TkQBHZUkT2B24F2oCJRXY1jB7B229rsvMj\nj4Tvf7/W1vQ8TjgBdtxRvaYMwzDqEefcDOfc/wO2AI4AFgJ/BN4XkUonhulRrFwJ//539ZLbdiXF\nBg1emKrFYGDt2tLDP0yYqj5p56fehSlvV73a1xfpSlGhmp6czsEdd8D8+TBvnnoNpjF5Mtx4Y3Xq\n7Mm89x7cemvucaR5TBW7J/36hgZ9ubN8eX6ZJkwVZhxwqYgMr4INw4Eb0OmVbwQWAPs65+pksk/D\nqJy2Np19b9114W9/s2TnldDYqF5Td9yhcdaGYRj1ilMecs6dCRwKvAGcWmOzirJmTfG3+hMnwmuv\npa/3sw/VIMUXoIOpJ55IHgQ89RSsWJH97rdJCyXxy2sxyL/lFv29qzY9fSDYXaQJeKEwtWwZvPhi\n7vo1a7retkL0tQFsV/L6653PcxW2n2p6TPlnUiFhqq1Nn9fvvVdamW1t+nx88UV45BF4+OH0befO\n7dyzpLcI5C+8kP+7mSZMFWtL/pqus44+W+68M7/MvnJfVzpMvg4YDbwlIktEZH74Kacg59xY59xw\n59xA59wWzrkvOOfeqNAuw6grfvITePJJuOkm2GCDWlvTcxk7Frbd1rymDMOob0RkcxH5vog8g4b2\nrQS+WWOzCvL++/rm99FH07fxneLZs9O38WF8tRpwzJypA8qFC3OXr12rYVnTp2eXFRscVeIxNWtW\nYU+Dcih1UGweU91HmPx80iR4Lphr85139B6qZSireUxVh7Y2FbiffLJz5STN0FYNfDvsVyBL9Ntv\n69/5JY7IY6G+O0TWap2TWj3PkrzhOitM9e+fvy4O0X38cXjggfJs7UlUmvz8B1W1wjB6IdOmwSWX\n6Mxy++5ba2t6Nv36qdfU6afD889rQnTDMIx6QUS+ApwEHADMBK4HPu2ce7OWdpXC/PnQ1ARLC6Rr\n9wOVASnb7RByAAAgAElEQVQZs5YsgSlT9P9aDRT8TLdp4lBS/o9iwlSpgyfnVPiaMwdGjy5tn2pg\nyc+rTymhfH6bd97RWYN32km/r1oFQ4Z0vY1J9DXPikpZvFiTh48enewxWWg2tbvvhvXWK61PHz47\nqnnvec/UQsLUkiX6d9Cg0sr0x9wTk5G3tSULOl2Nv77V8JjybS1ptvZYAHvzzew+tTjurqYiYco5\n9+dqG2IYvYmVKzWv1IgRKqgYnefkk+Hii9Vr6qabam2NYRhGDheg6Qi+7Zx7ptbGlMOiRTrbTyGv\nXt+xbmpKXh+KQbUSQLxtaW/7k3KBpNnqB2ilDvJrJQqYx1T1KSWUz+PD+aqd3LoSeoPHVHe0zWee\nUS/Rjo7kcLhC9/CSJfopRZhKyz3UWXxbS7J95UoVLPzzutS2UGwyiGpS7edQe3vnBJqFC2Ho0PLL\nqESYWrhQxcJYMPRi48CB+fWk/bbcfLNGk3QFLS3wz3/CgQd2TfmFqLgJishWInKRiFwnIhtnln1S\nRHaunnmG0TP5/vf1zel11/VORbsW9O8P554L//gHvPRSra0xDMPIYQvn3P/raaIUZDvNhX6rinlM\nhdRqYOw78KtWJS+vxGOqXGGqu/DCWTU9pl54QcPR+hotLfDGG9nBYTnJz72nQz14mtSLx1RHR+nJ\n+2O64z4qJoxUS2QMw+Oq+Uz05zbJY+r22zXMtFhbjok9prqjPVfrWnf2et13n4bHlYs/Z2nCVLjc\n/8bed5963cX4a1qOMNWV+N97HxLanVQkTInIx4EXgYOAzwHrZlaNBC6ujmmG0TOZNAmuugp+8Qud\nTc6oHqeeCsOHa+4uwzCMesG5nuuHUorlvqOa5jFVK5Yvz3qt+I57OcJU2oCx3FC+YkJXV1FNj6nn\nn699Au9a8PrrMHVqNkSmHGHKCwCeWj4F6mVa+f/8R705KqGzSbUXLOh8XdU6f778xsbqtYu33spO\nQFEolM8LIc5pWpFiuaZqEcpXTY+pztqwqILp1pI8pkK8Xc3NuaF8SWF9/jkShvLFz+tyBLiOjuzz\nrBKKHVtXUqnH1P8BFznnRgPhY/kBwLLpGH2WxYvhy1+Gww6Dr32t1tb0PgYMgB/8QKeqnTmz1tYY\nhmH0HgqJMF6wKGXg0p2D84cfziah9vaHs++F9pTjMVXurHy+nIULdTas7qLWOab+9S94993ql9ud\n+AGk/1tOKF8sTHUFr7yioWfFiJMkV0pn958zp3p1+/uplKTys2bB/fcXnxW0uz2mqilMTZmSFRz6\n9dM63nknfzvfLjs6dMKKxx4rXG53CtJp57+1tTJPu85cr84IMMVC+dra9HdkwIDiOaaSQvni8+Rc\nvgiX1q5efVW9wMoRakP8MfUkYWp3IEkPnw9sVLk5ICLnikiHiPyyM+UYRi349rc118af/1wfrt29\nkdNPh003Na8pwzB6PyLyDRF5Q0RWi8hUEdm7wLbHiciTmdmSV4jI0yJycql1FRo8rVxZeJuuyqdS\njLDDX47HVLVn5avkmBcu7F7vlqRjbmnRgb9PllwObW3a33nxRT2OxYurY2d3E4uU/u/8+epJ5bcp\n5LlQyfVva4MZM4oLe7Nmleb90NkcU86p58hNN1XWHqpBfB69J0sp9vhnVKliYVd7TIXCVFeENzc0\nqPDw2GPZY/eEHlNQeDzS2gqTJ+cuq0Uo3/Tplc2E2Jlz2xkBppRZ+RobSxem+vXL9YJLel7Hdqa1\ndb9dsXuhvT35PvD7VxqS2xkqFaaWAZsmLN8DmFupMZkO15nAs5WWYRi14vbbYcIE+PWvYdiwWlvT\ne2lu1lxT118PL79ca2sMwzC6BhE5EbgcuBDYE+0b3SMiG6bssgj4Meq5vhtwDXCNiHyilPoKdfC9\nF1IpA/Aw11NX56gIO87e/jVrcgcLSd5RXZ1jauVKePrp9O07OjTfyIwZpZVfar2lbBvu471LKrlO\nYRLmp56Ce+7pmYnVkzwTPG+8oX/DdlAt4WLJEvX8nj698HZtbbli65o1+eIrdD4Xzd//Dvfeq/8X\nmqGzGJ1JoB0/gyrJpVaM7vKY6opQvrj8tBkE/fdSkprXOiegp6UlfUbVcsoph84ce7EcU+3tet5L\nEaZaWzVMPkxon/QbFbfNtHJ9OcWO7+9/z4rvsT1J9XUHlT4+bgJ+JiIbAQ5ARPYBfgFMqKRAEVk3\ns+8ZQCceiYbR/SxeDF/9Khx5JHzxi7W2pvdz5pmaa+pHP6q1JYZhGIqI9BORQ0XkqyIyOLNss0z/\nphLGAX9wzl3rnHsFOAtYBZyetLFzbrJz7jbn3Ezn3BvOuSuA54BRpVRWbWHqoYc030x34Fyu/eHA\nvTtD+TwzZmgIVtpAy3vJxGGHpdIVyc/LxQ9eGhuzAlfSG3bvlTW3wtfWy5Z1rWdZHMKXhD+upqZk\nWyqZacy3rSSRKbYvbEe33gq33ZZuQ6WD7XC/Sj1m2to6l+sq9vDxgkp4bP/4hz5bOht+1p0eUwsX\nZkOOq0X4zEsTEHy7LSRMVfpc6Ox+8f7OlSeElPqMXrNGvcqSQkwrFV7a20tLfl6Ox1RTU7LHVNJk\nC+F+SXhhKmzLjz2mDhQxSd6Y/phqIVpWKkydC7wOzEMTn78ETAGmA5dUWOaVwB3OuQcr3N8wasZ3\nvqMPv6uvthC+7mDAALjwQk2wWeittGEYRncgIlsCzwO3of0Zn9bgHPSlXbnl9UcnlHnAL8skWL8f\n2K/EMsYAOwCPlLJ92kDj/fezAkopHVVfTqWiSynl33FHbv6MOP9G2mAhXlbMY6rUUIa4HD8wSBqQ\ntLRkQ2eSpnwvh2omPy8Xf44bGrLnK2mg5JdNm6bXqKMjP/QoZOXK3DxBd92l+3YVSQPkGC+CDBpU\nWJiqpN5i91TsMZVGPSQ/v+++7P+hSFUq8XmMxYe2Nv289x7Mm1e+fW+9lR6WvHy5erFVy0vkkcxT\n19/jfpKGSklqp4WueVNT9lgKjUuS2m4p45jw2r7zjoqlnRHKOzo6J2amsWSJ2vfKK/nrirXPDz6A\nJ57If66F36vhMeXD/kIBMenlSVxOWrlJHr/vvJP73PX7JomWPU6Ycs61OOdOQzs8n0bf3u3qnBvr\nnCv7lhaRzwMfRQUvw+hR3HEHXHcd/OpXsNlmtbam73DKKbDDDnD++bW2xDAMg1+jL+fWB0I/mVuB\nMRWUtyHQCMRpj98nOZUCACIyRESWi8ha4A7gW6W+8EvrhM6bp4Ocddctz2OqqwbKra0qer30Um6d\nHR3ZQWDSYKEcjym/vNJ8Nd6OYl4dnQl7KpdKcm0VIvTGiIW8tjZ49tncNrVmjc78N3Wqvrlfu1Zn\nxIu5/XYVoyC7f1fmPErLMRXiPZbShClPOecxLGfx4uRExT63VSmJoTsbylcNwhDA55/XfFXlkPYM\nShLxyhHJPVOmZK9lvP+dd8Ldd+cnwy+nvhAvJnZWfE6r37ncvGehV92gQZr2wreZUoWpco4xPD9T\npujxlpOTKEloK3X/l14qXdgtdF8Xu1emTdNnVJg/b/FiDV32FBKmGhuhf389rtDOmTNVJA23bWjI\nbStJdvtrvNtu+rfYsfvjSxKw/G9T0m9QTwzlAyDjKn67c+6GjJt52YjIcOBXwMnOuRqk2TKMyglD\n+E45pdbW9C369YOLL9YObHeFixiGYaQwCvixcy6WMt4Eqpl1UMikUEhhOZrvcy/gPGC8iBxYSsG+\nA7x0ae4As6NDZwsqNVdKvE2hzn9bW/lhXr68hQtzbWxv17fTvtzYnqQBWEeHdvZjAalawlRSKF+4\nbWc9rMsZSBZKcltOmb6cMJTPH4c/X7Nn6+Bx7tzc8lpasjPMTZ+e7I2QZJ9IbgLySlmxQttbONAs\nRZjy7WPgwMo9ppYsyT3WcJ977tEZ5UIefVSFEk+x/DuVJj93Ln/Wu7R22dpa2gyBkM1bVoq3lye2\nPRa3yxVRCl2XYjmmvHef9/wMr3s5HlvlClOrVqk4G4sJSR5GoSfZv/6VXTdggF7DUkL5wvNYjqgZ\nCkO+jELJuH37TbvPQo+pNWsKz674bJCJuiuFKU94XA89lJ0JUaRw8nMv2ofnCDTUe8qU3P0aGtKT\nn/vfNX8vDR2qf9OO3S+Pc42F+OuR1D7De6C76Vd8k3xE5OpC651zXymjuJGoy/tTIv99FDYCB4rI\nN4EBGff1HMaNG8dQf2UyjB07lrFjx5ZRtWF0Dj8L3x/+YCF8teCzn4VLL4XzztMfC7sGhtG3mDhx\nIhMnTsxZtqzYfOFdQ2PmEzMcFYvKZSHQDmwSLd+YfC+q/5LpL3k/lOdEZBfUG31y2j7XXTeOQYOG\n0tQEV1yhYsL++4/lN7/R/lRHh3aawzf0+fUm/w/ayW1qSt7PD75mzy590pCkGYe8x9SAAdp5LyZM\nhcv8gC7sPvr1xUIw4u09fmBQTJgq5jHlj2XIkNLsKETSefADj9BzqdBgfsYMfdv/qU8lh/LFb9q9\noOTp3z9f9CvUPrx9Iup9s+OOMGJEun3F8J5X8+fDhz6k/5cqTA0YoAPHSnNM3X03bLghfOITufWm\nEefEWbUqtx34+zK2oVi5q1apwOb7S7Nnlz4b2ssva0ja0UerV86bb8I22yRv29ys98/y5bptKaTd\nR0mhRcW8q5LKK1SXJ/SYmj5dz8/Ysbn1PfSQ/i1lyFmuMOXDDefPh803T7e3UI4p3y7KDeULZzZ9\n/vmsZ45fl5ScOxQq0zyeHnhAxeCkZ2xYnrd30iS950o5v8VE4ULr40ky4udxUkh3eK6bm9PFG59j\nyv92Frovfd1J57ejQ587ra3Z3xP/vIzvB2+vX75okQp8SW3QlxUes+9PLV2aDftbd93u7U9VJEwB\nH46+9wd2BQZToPOTwv3o7DEhfwVeBn6WJEoBjB8/nhGd+XUyjE7yr3/pLHzXXmuz8NWKhgb48Y+1\nk3T//dkOn2EYfYOkF1IzZsxg5MiR3W3KvcB3AP9izmWSnv8vcFe5hTnnWkXkKTQM8HaAzMu7McAV\nZRTVAAwotMEXvzierbfW/tSuu+bnQvEhcmlTS+fbnvu2u5jHFJQXApImDLS3ZzvsYXnVCuWbPFmF\nhV12Sd/e4/dLCuULty02aPVJruMBWrWSn/vzHwpwYUhkjA83C8N2knJM+bpij4LGxuy5LyWPl7fP\newrMm1dcmGpp0fa38cb56+K6Q1uLCVPNzXo8hcJbwoGic/mCwKJFyduWwpw5WUEE9Fw3N+eXV+h+\na2/XNvWRj6josc46pXtFhF5mb7+t1+2ll2CDDbIeHCH9++vfDz6ATWJ5PYWw3Xh7IVmYSmv78WDd\nt+VScolBrrjqvTKdSw61LIVyhSl/zPF+5QpTYWhcucKUc/DCC7DzziqKLF6sXn2HHZbd9t574dhj\nVUDzpHlMhW0n7T7zz3Dncp+bq1aph1qaANoZj6lZs3LLiYWp2Ds0ri/2oCzVY8qzZInew8uX672Y\nFsrX0KD3kz/Xgwfn2vLWW+qBtf/+sOWWWZvmztXPkUfmliuSFaZC+31/6oknsi8rtttuBh/7WPf1\npyoSppxzR8fLRKQf8Hs0EXo5Za2M9xGRlcAi55xNBm/UJYsWwVlnqSBy8sm1tqZvc+SRsO++cO65\nMGZM9+bsMAzDyPA94B4ReQloBm4Atkc9nyp15f4l8LeMQDUNnaVvEPryDhG5FpjjnPth5vsP0DxX\ns1Ex6kjgZHQ2v5JIStDrO9iFQqliLwUfxgPpA/n29uyApbVVByOTJqnwsOWW6TYmlffKK/rmfqON\n1NYkj6nly7ODj1KFqVCw8Z38JGFqaTSXtB/IJA3UwgFKZ3+vKhGmkgaiIaUIJqF3w6uvZkUIf9yh\nSBKHCsXnvpAwFedIWX/94rY99pgO4JK8LWLhI7S10AB2xQrNseYFWl9GmqjV0gL//CeMGpXs9bJq\nFTz+ePoxJF2XcBDt62huVvtbW7Nl+32nTNEB/ZFHZkOBwjDYF16AD39YZziOSWoD99yT/f/tt/O9\nM2L8dU3zOlywQAfHW2yRXq+3N25XhepN85gqVZjyniKtrdl23d6uoZVdwZo1Kjput122LsgXk5Ls\n98viZ6KIXp+kBNcdHer5OGuWej6GxO3Ol+89DcPwaS8WL1migv3Chbn38qJFKlqmUcw7zvPwwyo0\nlyNMdXTo837o0MKhg6FX4sKF8MYbsN9+udtA+jMqnqUzrKOtLStmJx0X5IbqrrtuevJzEa1r6VL1\nmhw0KPd3zItMS5fqb2dSPrKw3MbGrPi3dm2+iJ4mxHUHlXpM5eGcaxORy4CH0c5Up4rrvEWG0XV8\n61t6M1sIX+0Rgcsug49/XD3YLNeXYRjdjXNujojsAXwe2B2dsfjPwPXOuSLZYVLL/LuIbAhcjIb0\nPQMc5pzz7+6HA2F3dx10RsDhaAL2V4CTnHM3V1J/W5u+Lfdijn8LH/P009qhz9qd21lP88iYPj37\nVnbtWrj1Vv3/1VfLF6Z8InT/ZjktIe099+h671lVTNhJ8wCYM0d/e4YN023iPIeFhKlyQvmK0VmP\nqXLyJf3739lcRO3tKmx44uMNB5nhwKatLX+g2Nqq4VJNTbkijt8+pJTz5UVC7+UU4m0pV5havlyv\ndVi/D68JiQXNefPyjwkKi1Kvv557biGbQDlk1SodeP/nP9oevVeSF5B9cuWVK/OFKX/8S5aoOBUz\nc6beg2nnO0xGnyY8+3OQlt/G59QKhan43IceU5Mn5+aii72nvDdaLBQ4BzfeCHvvnVt2Wjtfvlyv\nbeiR1pkk0Ousk77OeyKBCi8NDenJ1zvjMRVex9mzsyLnwoVZ8Sgpf1p8vyRdyyVL1PaFC7P3/9tv\na7s89NDc34bbb08/nrRjCZPVNzSk33OepUv1BQfkh2CGxMfivRH33jub66lY7qxQqI5tCT2mkuqL\n8duNHq22hM8jkaxNXpwPhanYzviY7wp8tn2IYRhm3tqa/U2cOVNzaPlj6+4E6FUTpjJsjYb1dQrn\n3CFVsMUwuoRbbtHkmddfn/yDbnQ/o0Zpvqlzz4Xjj9c3D4ZhGN1JZlbiCVUu8yrgqpR1h0TfLwAu\nqFbdPqdNsVC+eBpuL0z165ed3j2JcOrq8P+ksKCQQh3lxkatd84czSG06aa5NnvRwg84i3lMpc2q\n570nxo5NtqdUYaorXmy1t8PNN8Mhh6gHWVxvJR5THR25CbJXr072IohDM8PZqIYMyfXs8X8/+EA9\nOCDXyylMhlzI3jRWrMgXpkrxmIrxCbAHD8495lCY8vtOnapClC8/LSF5GP4U8u67KoyE9wOoR8q7\n7+Yumz1bvUniY2tvzybshlyPpbitxiKyZ8kSFS923DFbZhpp63zbj9eHYkxMIY+peIKE8Ho9/3w2\n1C7OG+TLjD3O0q73smXat3/33fRjKIYv+2MfKzwz5+Qg+Y3PtVZsVsBtttH2EYq+ScJU6NWY1N79\ncm9rLLKEx+GZOTP3+5NPZgXg8H4I2/fs2dn/V67MCixpHmzhsYTCiPeqjW2cO1efcz7/WnhOQy/f\nNCEsJskr79VX1bMwDEn1XmlJYeOg9/F66+Xn+0rDb+dF5PDZ4T2mQAVEv70/F0nC1JAh+olz1fl9\nVq/WulpacvP8+Wdxc7Nerx7hMSUiP48XoXmnjgGu76xRhlGvzJ8PX/saHHdcaUn5jO7j//5P4+F/\n/nOdrc8wDKMrEZFjSt3WOXd78a3qi7CT269f7iCmEP5NflNTVpiaNUu9PrbaKr/8mNmz1dPkiCOy\nnfSQQoNEP7PRokX61nns2PScQcWOobFRBx1hSE8hu0NCYSamlHCkmDvu0JD1UGjydsasWaPlvvpq\nsjAVUmxWvtdf14F66NXi60jCX5swsbkvb8CAXGHKL/cDIcjOduXLiu1btUq9iYYPV08UPzC89Vb1\ndFhvvey2jz2mIlGYbi5NdIP0AeyqVbps3XVzxbn+/ZNnGpszJ+uFEofXFePhh2H77fOXb7BBrjDV\n3KxheknHEYuIYXuNB7J+2aBBsNNOudcinE0vvA5+MJu0Ls2ekFA0iwnbxsSJWc/JMEdRXD7khpgl\neUwl2VnoWbb55nq+C3l9eRuSvMq8beGMlUmE5a5YoV5u3s40e7fcUu+TxYvT84p50STJQzD8P9zG\nP++SjsPvE0/m8Npr2fVNTdm2trzAdB9pQnAosvnfmvD50dqa6/njmTtXhdRjj80vN3yZUqow1d6u\n98G8ebnnY9my/GvS2Jh7L8R1hB5TpQpT/lzPmaNJ47faSpd5z7tQmIqfpWvX6jlatkyfhRtumC9M\neTvWrFHhasGC5N8pL0w9/3xhu6tNpR5T+0XfO4AFwA+AP3bKIsOoU5yDL39Z///d7yyEr97Yemv4\n7nc1rO+MM/I70oZhGFXmX8U3ATQ9QZkpcGtPOLBsaEgXpuLl3gvDz5DX0qJhewCbbZZ9M5uUe8Z7\nKqxerWLWRz6Sv03YwQ8HVuEyz9NPF85zkoYXIpYt0855KHjEA+ukAU6pHlOlClMrVuhgKUw+HJfl\nSQu7KdVjKlz/5JNZkTHEC1PxtY9zQsXCVHjNkwZDjz2WW1ZoX1OTCo6LFulgdPFi/d33uXn8zHLh\nIPrVV3X90KEq1niBo1AS7fi7b2/9++cmJ06a2t3/Hw8Yw/pC8S2JsH1/6ENqsz/Gl17SsgYMyJ1g\nALLHFgt64TlPEqZ8aE+cbDttJrJ4u2KiW7y+UDhmfO79MYYiGeg1XrgwG24cCqWxx1QpwlSY2HyT\nTbLREGn7em66SQX08PkQ2hAKE0mE5T70ULKIGNsrkr3v0uyLn4uh2BHmw4s9puLnUanPJy+ceEHU\ne/yVIgTHy9vast5AocBaSNiJ20dYZpowVUhsjD3DQO//N9/MfhdJ9jIL8bPyQbL9Q4Zkj9Fv5//6\nfI9r12pdXpDyXqBpoXz+nvFh7THhM3qDDQoLU5CfP7GrqSi63Tn38ehzkHPuBOfcVc65MuZWMYye\nw+9/D3feCddcU/oMI0b3cu652gE999xaW2IYRm/HOddQ4qfHiVKQG1Li3/zHA/A4vAZ0gPzGG9lO\ncejpEc7aFr99jzvR4cC7pUU/zuW+wQ3FgeZm9TYJl73ySroQUGymKv+GOg6rCr0BwsFhiB+ExMLU\n/Pn5+5dK0gAh3n/RouI5asoJ5fPnMn7r7q9dfM18Dimfg6i1NVcMCQWAJNEuFD3iMNAwLM+LMAsX\n5rcj51QsGD1av991l7aZf/87m9MsFi/8fuFfjx+09euXLkylDejfeUcHzeH6UHyDfOEiPOb99tPZ\nhgcOhN12y+aX8YPUpDp9MnQRPWfhefZlx20gHEB7wjDFODfQFluoh1VamUl2eQol9Y63bW1NPtZ+\n/bQtPf643k9ps4CGeZjSQuPmzs3muwI9D7GnZlroISR7B6V5TN1yS+724fHG90OakBYKU2mhfN5j\nKq7n0UdzQ+vCchsb88tJElaTZrtsaFCRw3uuJQmgMYVC+bztTz2VXR/f56UQekyVKrrFy/0919am\nnoUhsTCV9JIkTZgaODD/JQvk3x8tLbrOP3tCASu+PqHA1NhYWJjyAne8n8c/b5O8lrsSm7/KMErg\n5ZfVG+frX8+ddtOoLwYPhp/+FG64oXByUcMwDENJe6NfzGPqxRc1n0fagNQP5MN8I1On6uDo3ntz\n9zvmGDjqqGxHfYMNNIHu++/r93/+Uz/Ll+cOUEJxYJdd1MNk//1z8wymhZXEnh+33ZZ98+5cduaj\nWFgIw4puu61waF/oMbRypYZmhInSCw3cCg2k/ODFn8MFC9Sr6t57s95paQNxz+rV2VCctO389YhD\nqbyHSr8o7sJ7OSSF8sW5w+LzNnx4rs2FhCmPc/meQ/37a13hgCpOJl6OMOU9Fwp5TMUeWGEZkyfn\n1hcPPAsJU/37aziOZ9QozR1WyAvQe0z166fnoFAon/du9LnZQlpbVch74onc5c7BAQfAnnvmDszT\nPEeKeUwVGtivXZs8uPZlLF6cOwNoXF54LdKE2jgs1YsASYJYEkmen76uWPBbu1afac8/r3ng0ohn\newvt9cJUmD8ryRsnbGeFRMNQmErzYoo9F5Pq2nhjfVbOmZMexpl0PHFd3oMPcpPsFwoPTCOcBTQt\nf9l++yUv92yxhbbB2IMT1M6lS9NnniwkTA0YkPxciO+P99/PTrQB+hvnt0vLMeXXx79xoR2hMDVz\npv5+TJmS3S7OadVdVCRMiciTIjKtlE+1DTaM7qalBb7wBXUZv+yyWltjFOPUU+GjH4Vvf7v8hJWG\nYRiVIiJjROROEZktIq9l/j+01nYVIx6QesJOb5IwlZT3JaShQTu3LS1Z76MFC3Tg4vfdfHNNsLzO\nOio8hMIUwIMP5pYZD05C233HftAgTXruCQc3IXGnfdWqXA8wES1r5crc3xI/+xeouOPFsxj/pj0t\nrG/gwPzBUuyRVgzn1APi/vuzdvjcQ/5cTpyYFVfCcn3S+gMP1CTN8fpwUBezZk3+wMd7XPjzveGG\n2eTnDQ2wxx654lRrq4qJPmwqDodqa8v1mEgSplas0EH+kCEqSIIOtsJkwUkk5flKO9/e469fv9xB\nYyiYFBIRlyzJ/R63u/h7OMiN781Bg9RjP2nAGdbt86L5+8+TlmMqyWNqxQoVpcJZ1SD3PPkJDiDZ\n6yKuK+l7KAwleaslCVP+Xm9ry7+v0oSpQvdaUtm77Za/LilaIkmY9nX552ZIU5MKpWnnC7QNp3kv\nhc9ifwyxDWkeUzGhR1FSm0oSptKux7Bheg/PnZt+zkMKiWCh7bvuqn8LCVNpObQKhfL5+uLjSfJ6\n8u3c51v09fhz5nNfxXWEHnPh7wZkczCG9cT2e9ra9Nk5dmz2pUvoMZXUDpLC3CHZY+rddzWPoZ/J\nE/S8DBwIO+yQX0ZXUqnH1EPAjmjS86mZD5llDwP3BJ+CiMhZIvKsiCzLfKaIyOEV2mUYVef887VT\ndxq9MpEAACAASURBVMMN+W6cRv3R2Ai//a3mm7jyylpbYxhGX0BEvg7cDSwHfg1cAXwA3CUi36il\nbcVoakruDBfzmIpD3GIaG7PeHnHSbr/sgANgxIjssr331uS+ab+1YY4PX4cnHMwUyuviZ29K6rS3\ntelxOZcVplatyh2Yxced9rbcD2zTvBqScrqUmn8q9PaYN0//Txqgv/qq/j9rVu4AbdUqXfeRj+iA\nMvQuit++J4VyrF6t7Sa0d/BgrXPZMj1vgwfrdn6gKZIvPm2xRfYaxtc8zuXl7YjL8Pv6AWY8u1US\nSTmmig2m+/XLFYpK9ZiK1yflAwoJhZo00bhQ+25vV9GjXz8dxIYhoKG3RLh9Uo6pNCEgTZhK297f\nOytX6r0Sn9877siKX0liUaHr6O9XL3yH9UGuV1Gh4wjx5zZJgAmXHX+8tvE1a9Rz0nsqhjYkCVNt\nbcllh/TrV9hjyie+9seW9AxKm4kvJDw/SQLbQw9pCGzYZpOezf6cDRyo5SR5KW2/fWEvLv/98cdz\nc0b5BPhhvqk4nDCt3EKhfP78xtciPg+hMNXenru9v2f8PZt0TP7cxCGUsVdcnGMqJOn6JYXyhfU3\nNmr7jHnxxWxIdSGBG+DTn856aHUXlQpT6wFXOuf2ds6dnfl8DPgt8CHn3AX+U0JZ7wDnACMznweB\n20Rk5wptM4yqMWkS/OIXcOml6oVj9AwOOEDDLn/4w9w3AIZhGF3ED4FxzrmxzrkrMp8vAOMy6+qW\nvfdOngksDNEpR5jaZRf929CgSZvXWy/71tsvB30TGw/aNthAPV923DGb8PlfQYr5t9/Wzvbw4fo9\nyWMqrGOzzfLt8yERcWgZwDPPaD4dL0yts07ulNkNDfmhP2mhfL7Tn5agOCl0ptzE6M89l83/FA9k\n16zJ9TgKy164UMv3b8OTvCu8R0c46A9pasq1cd111YalS/WaDxqkXgJPP50tPy5r/fWz1zAe8MY5\ntbzH1MCB+QOuddbJF6bSRB1QIcQLesU8pjxxIus0YSpJDPHncsyY/HLjwaEPVU0SNdL2CenoyIof\nm26q59G3Wd9GwrbY3p4N+yuFePDrywyFg5D2dhWtbr9dP0lhZ0lJ6T1hWK7Hn5eODr0/vdjs6wtt\nTbuuxTymktpPKEp4j9Dly1VImTVLlz/1VDaPWNKsfKUIU0lJtQvlmComTKUdayjcJD3P167V6xre\niwMHajhpUl1+Zr60vF6lTBgQsuWW+pxuaFA7+vXTdCqxWBIea9y2i+WYiq9FfC5jjym/vb8OIYWE\nqZjYo7OQx1TSfRH+fqQJV+uvn3utRozQ8/joo7l1erbeOtf2WlCpMPU54JqE5X8FPltOQc65fzvn\n7nbOvZb5nA+sAPat0DbDqAqvv64hfEceCePG1doao1wuvVQ7x1//eu0esIZh9BnWQz2mYu4FEiSQ\n+mHAgMJvaTs6kpOfp82S5D1anNOB8RFH5A4c/QA4SRjyNDRkPY7ipLf77psd4IQDnSSPqXD9UUdp\nJ93nzNhoo6zAFeOPMw7li8UYSPeYimfHK8VjKg4BSyPpNy0WyMLv4cDP52Vqbs5ei/DcxWEhScIA\n6AAttGOddbIeLOuumytCeSEl6e27v0Y+BM/z8sv6NynXyVFH6QsoT3NzdrtC3kSe1avhkUdyRaS0\nkJ+QUBAKB5axB1JchvcAaW7Ozw8V2+uTiyfNSJlkR4z3mOrfP3u+vWjk22KY2Nx7TPnQ02LEHlM+\nz5OfFTGmo0MnDgJtH1On5m/jRcmkc5/k9RGyenVuGy0mEnqKeUyVKkzFnn2vvpr1HqtUmAo90WJ7\nk2bliwWgSkL50ma2g1xvuP7989tsKEy1tCSHjDpXWJiK2XHHbHhuU5PaN2hQ7m9JuP+kSdoWW1uz\nbSYM5UvzmIqvc1LOsSSPKZHca7R0aeeEqbQcU6Gt8fbheY7blD+OUPDfbjvYfffsb1bopbXzzhrS\nfeCBuiwpyX13UKkw1UKycLRvZl1FiEiDiHweGARY6mKjZqxapW66G2wAEyaU1tEx6oshQ+CqqzT2\n+8Yba22NYRi9nNuB4xKWHwvc2c22lE3Yafcd8WKhfGn4jn7aYOiAA7TzW0iYAh3EJ709bm5OHjwm\nCVNhZ33gQM0Rs9FGKp5ttFG6l4j3mGpuzg0/Crf34kChxLe+LCg/lO+hh5LLjbfzpNmRtI/3aopt\nhdI9pvr1y5a5++7ZBMEtLblCUUjSYMe3g3jWO49f5vOG+Vwt4fGI5HtMgQ5uR41Kth80pKVSYSop\n/BGyMxOG+KTCsddVbK9nww1zvQwL2RHjc0z165e9dj53WlI+qHDWzZEj08v1xMLU/Pma0L+pKWtz\nKECWkuuzkOdHkjAVPhdaWnIH3+F91hmPqSTxKGzTocdUUt1+m7ieOBwsif7984XmQsnPCx2H3zdt\nBk5fbqH7JPSGS7pPfV0DBuS+SIjtSxOmko4jtN/f+2mJuDs69Jn2/PNarvcALpT83AuKaYKOx4e5\nJoXyhffRpEn5Xp7lCFPh9U06vpg4lC/OwZfk+efbbPj9qKM0ZO+jH9Xvw4ZpLqtaCVMFHF0LcgXw\nBxHZE5gGOFSUOhO4tNzCROQjqBDVjOZnOM4590qFthlGp3AOvvpVfesxdWpyPgOjZ3DMMfDZz2oi\n9E9+svBMNoZhGJ3gJeA8ETmY7Iu1fYEDgMtF5Gy/oXPuiu43rzDhIMF7whRLfp6G77inbZuUbyqN\n44/XumfPhhkzdFlTU3ZgVCyULxwU+PUf+pB6cXkb49wf4fZePPLnwosRjY3wuc9pfpy0UD5fd6U5\npgrRGWHKe0yFYY6VClN+2113hZde0mNsbdXzFPad/GBvwABNgv7ss9l122+vv81DhuQP4rbdVst8\n6y21Y6utsl5um2+uxzBvXm4oXzhA8/nL9tknf3Y5UJGr2sJUoaTxSeF5SQPRYsJFsRxTbW16Hry9\nr7yiYlc8g6Hf3m+3ww654Z9J+Jw/sZ2bbabrXnxRhSIvnBQSTzbYQK+Bv7+eeSZ/myQBO86fFAoW\nnQ3lK+Qx5a+5F4eGDMktJ0nUCMv1Ca/98nXXzQoku+yi9xCoGBfn0ysUypdE6MUUPsNCQo+ppMTu\ncd2QPzulPzZfV/g8LNVjKi1UzbPFFno+fNlpIa4e/wwIjy++Tv73JL7OxUL5wjYQJ7BP8nJLszVt\ncobw3t5/fxW1085PKEwNGJAVSUeNyv7OhucxFPB9XcU8ErubivxAnHM/Ac5AO1xXA38E9ge+kllX\nLq8AewD7AL8DrhWRnSqxzTA6y5VXqpfUn/6kbwGNns0VV+iPx3e/W2tLDMPoxXwZWALskvn/y8Cu\nwNLM/+Myn++UU6iIfENE3hCR1SIyVUT2LrDtGSIyWUQWZz73Fdo+JOz4+oFHPEuSf0tfDN/Rjwd+\nBx+cFYRKpakpP+l0GEpSiTAVMnw4nHCCCh4hbW25sy75AYgflIShhMU8ptLyrRTLMVUq3qZYIDv4\n4NxyQwFm+fLcAX84eIk9vNK8FEKPKf997Vpd1tysA55jj80tE1RQChHJvjSKB7x77aWi0jHH6Pf9\n9svu39AABx0Eo0drbpT+/TUUJZxh0LPNNvnLNthABZu0kKkkQvtCAaxYKJ8nyWMqiXBWyWJ2hHgR\nYu3afHHrsceSc25676okmpv15d7nPgdHH61/w/Mbto04JPiII/RaFfKY2nZbFXf8oD+8l9ZfHz71\nKRW5ksIdYzvD4/GEHkExaR4qSR5T22yjXp5+nT//YU4eyA+HCz2m9tpLz5f3vNl6a/VW8eXtsUd2\nvyFDtKwk7yPfhgoJU6Fo4mf/TPOYCsstRGOjhpduuGHhUL64fE+5oXxhHX7mTn+d08QeX45vl/H1\n9/aEHmDxvVRO8vN45sZQuPLfw/L32Sf7f+ytm9QevddS0rUr5DG13nrZ7/G9HQtT9UalHlM4524A\nbqiGEc65NuD1zNcZIvIx4NvA19L2GTduHEMjGX3s2LGMHTu2GiYZfZSHHtJ8UmefrfmljJ7PppvC\n+PFw2mnasTrhhFpbZBhGtZg4cSITJ07MWbYsyS2gi3HObV18q/IQkROBy4GvoN7p44B7RGQH59zC\nhF0OQvtlU4A1wA+Ae0VkF+fcu4Xq2mSTrOeQ95gqlmMqjTRhyg8uKsF37r0dvkNdbFa++G1xEv37\nq+AReii0tOTW4wd5fuDlO/f9+yd7oYQ2hB5TAwZkB9+VeEz5N/DhdscfrwniY4Fso41ykyjHZRcL\n5Wtv17o23lgH0R0ducJGv37qJeOXJXkTFZrBK4k0T4w0ry3IFXG23TZ9u5iNNsqdwj3NY2rw4Gwi\n/ko8pvbcUxPA+/2LeXvsuWfxGaCThKlBg/T4Z83S+pM8MrbdVo/v9cyIq7VVP0nnd9tt1YvH389J\nucZCYSoMsfU0NOR7lcTrfZiUF2GGDdPQw6amrHgaDsIh/xqF1yLM+VRIvEm713wYYnjcXlDwz8i0\ndhknEI+vk59tr61N/4/bwiGH6LF42x59VL39Q3uTckwl4QWWgQP12RALsBtskCuiprXLnXZSAbe9\nPSvEpIXyxW0uyUs0ZMUKfYYWC+VraFCRMg5Xi/Eea0keU6DP6vXXzxWmQrHRhyJDVozywpRvx/4Y\n/KytBxygoayQ9Rb9xCc0r1rsMRU+q9I8psLtC4XFh/eEc7nnNi3EHXqxMCUiQ4DjgW2A8c65JSKy\nBzC/WAeoBBqAgvNDjB8/nhHhHMOG0UmefVbjbA8+WGfiM3oPp56quabOPDM7HblhGD2fpBdSM2bM\nYGQpyVLqn3HAH5xz1wKIyFnAkcDpwM/jjZ1zXwy/i8gZwGeAMcCEQhVtuaV2yJ96Kjt4CgfY1cwx\nVQm+TN/5Dmdo8yQJU8U8ptLo6Mj1mPKDvCSPqWK5akJhqn//3MSzacLU4MG5uWtCu5I8rfr1y9++\nmJdJOKhOEqZ8XU1NmnD+vffyham99tIP5IoDhQaQpQhT22xT+ixxlbL77jrg9qRdx+2208F5aB8U\nFqbCssLBaDGPqW22ydZViLB9+7p9e/WDcz/wPfJIePBBFX4+9jGYPj2/vFB02morPYYkz7OYeAAc\n51VrbEwPdfXrvQDgRR1vS9L97ImvVTjID8WhUkL5wvU77JD1rkt6jvl7Ou1ZEgtTsUdnmKvIrxs2\nLOt5FYbTbbKJzp758MN6j6XlmOrfP1/8iz2mlizJ5hnzeCGmmDC1/vpaR5qHJeSG8oWEdsV5rlas\n0DC1QYNUyImJ6wjrL3b+/UQKscfU3Xdr/qR4Bsndd1eR/Z57tL2K5ApTgwfrTJ6DBhW2y3sX++ff\nllvmtt2BA1X4XLo0X3xOaqfxzK4hscdUWE+hUOBeKUxlckLdD6wCNkdn41sCnAgMA04to6yfAJOA\nd4DBwEnoW79PVmKbYVTCG2/A4YdrroN//rN4fL/RsxCBq6/W5H4nnaQ/9IWmkjYMwygHERHgBGA0\nsDFRqgTn3PFlltcfGAn8NCjDicj9wH4lFrMO0B9YXMrGodjS2pof5hELU2lCVZrHVGfwHXTfkd5x\nRw0TamzMeqMUC+Url9Bjyr/5D3NMQeG+QlLy8/B3J0nUCkNRCglTMUnbxjPtFfIySZqVL8yFAyqw\njBmjYs7cudmQSj8YHTYsK/aEg67jj88dkBYSCLfdVvtju+1W3GuoUvyAvLEx14MtzWOqmFcepAtT\nO+2Uf57jNhkO5ksVT8Mca2HenaRZA4cM0VDIUCwCtau5Wb1IQpFyv1KfLgn2xt9DezbaSJPNx9t7\nIdyLCt6WtPMO2WPxOY1iEbO5WQW6QjmukpJiJ3mFhTnxkoSp0aO1zb/7rh5DPKNeHO7qhSl/fH4W\ntJhttoH339dy33orO2tinGOqqSnZKy30mOroyD4nPV7YKCZMNTbqPZz0fPUkeUzFouTw4fDCC9nv\nzz2nf1etyl6D7baD114rbE+hdb4+H46eFFY7cWJ+XiWftL+hQZ8HoTdbQ4N6l7a363O2sTErZIEK\nUyecADffrNehuVnr9+/LwrYgoh5waaGVIU1NhX+/koSpMWP0HBQa39S7MFWpSeNRd/FtUXdxz7+B\nlFsslU2Aa9E8U/ejHbFPOucerNA2wyiLBQvgsMP0x/Cuu+ovEZxRHdZbD66/Hh5/HC65pNbWGIbR\ny/gVcB2wNbACWBZ9ymVDoBF4P1r+PlAkA81/+T9gLtq3KkoYLtfQoL+NPrytqal8j6lC4Vfl4ssM\nc4yss076YKlaHW5/TnxCaD/wSgtd8YSilh88rF6dO2DwoXyrVulkK5AvHsTEibqLEc/M5fHX05MW\nyhfbsfHGue0krmvXXeEzn8n3LApFpkLXZscd9SVhV4lSoCJNnPsqbNvxuU3zuosTcHtCT8Pdd88X\nnuJB9V57Zb2kSn0pmhSqCrnJt+PZt2Jxd+ONs7OXVXqvhuG5m22Wf2zhuUsaLK9enRvK19SUPLti\nmjDlvZvi8+YFpnI9puJ6jjkmNy9QkjC16aZZYWPlysLnMgzlKzSzIuSORZ57Tr2efN1hjqkhQ5L3\nD70805JnL1uW63GXhP89SAox84Sz8nkGDcoKZqNHqzCVJsb4kNqttsp6jVX6DPfib0ND+kQESUI+\nZMW0fv2yno6Njflhz7vumhUK/TaQngsqxAvI8TmM22mcvyqpXB/+6oWpjTfOTg6RRr0LU5X6DOwN\nfC3z9i5cPhcoK4uAc+6MCm0wjE6zYoUmH1y2TF1KazU9ptE9HHAAXHSRfsaMSX9TZRiGUSZfBI53\nzt3VxfUIUFSWEJEfAJ8DDnLOFQimyRLmTWlpUWHqySd1WTnClH9zW81ZUL1t8Sy5aUKB376c8L0j\njlCR6JFHsvuGg8dNNskPUUsLNws9Yzo6tK8xZ07uQN6/8X7mGfWIGDYse379oGWLLeDtt7P7pAlT\n8Ux3Hn/88QA9FtTC8+QHV0nClLcbKvcsL+eadAXhNQw91NKEqTTvg4YGbTOTJuUOfv9/e2ceJkdV\n7uH3my3bkGTCZMgGZCMrZCWQAAFJ2EFZlCWCKFF2RFB2VBRQAZXtIsr1IotIBBW9IKthk31JIHAh\nRIVI2JIYCMHsIXPuH18fu7qmenqZ7q6ame99nnq6u/p09alzqk+f86tv+fTT9DGisvCFF4M9e2pc\nqfr6lsG0cxF2FWutjz1bbqmiwfDhuvgeNqz4BWrPnmnLEEhfO9tsk34/qq5bbKHfPXiwihIbN6qo\n1rVrpqWKJ3wd+vMcP14Dcofxv8t8hKkoVz1PWGTKNq74+q1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Etiphfa4HxgBHlfCYRifg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"text/plain": "<matplotlib.figure.Figure at 0x11ec348d0>"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Notice that, despite the fact our additional player did not get any hits, the estimate of his average is not zero -- zero is not even a highly-probably value. This is because we are assuming that the player is drawn from a *population* of players with a distribution specified by our estimated hyperparemeters. However, the estimated mean for this player is toward the low end of the means for the players in our dataset, indicating that the 4 at-bats contributed some information toward the estimate."
}
],
"metadata": {
"kernelspec": {
"name": "conda-env-dev-py",
"display_name": "Python [conda env:dev]",
"language": "python"
},
"language_info": {
"mimetype": "text/x-python",
"codemirror_mode": {
"version": 3,
"name": "ipython"
},
"file_extension": ".py",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.5.2"
},
"anaconda-cloud": {},
"latex_envs": {
"eqNumInitial": 0,
"eqLabelWithNumbers": true,
"current_citInitial": 1,
"cite_by": "apalike",
"bibliofile": "biblio.bib"
},
"gist": {
"id": "08078792809cc29b522253957464d5b7",
"data": {
"description": "hierarchical_partial_pooling.ipynb",
"public": true
}
},
"_draft": {
"nbviewer_url": "https://gist.github.com/08078792809cc29b522253957464d5b7"
}
},
"nbformat": 4,
"nbformat_minor": 1
}
@usptact
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usptact commented Nov 30, 2016

Approach section -- "i.e. informatino" should read "i.e. information".

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