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Last active March 29, 2021 00:49
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Multivariant Gaussian distribution estimation in PyMC3 using different prior
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Multivariant Gaussian distribution estimation in pymc3\n",
"\n",
"## Generate data"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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wO+uFQhEL7Jqd9cJut8Fiubos8rAsi89/fn9Ki93jceKdd95EfX0DOjuvQXV15bjpKxlS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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x103f4eac8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import pymc3 as pm\n",
"import numpy as np\n",
"import theano\n",
"import theano.tensor as T\n",
"import scipy.stats\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from matplotlib.patches import Ellipse\n",
"import scipy as sp\n",
"%matplotlib inline\n",
"\n",
"N = 500\n",
"mean = sp.stats.uniform.rvs(-5, 10, size=2)\n",
"cov_actual_sqrt = sp.stats.uniform.rvs(0, 2, size=(2, 2))\n",
"covariance = np.dot(cov_actual_sqrt.T, cov_actual_sqrt)\n",
"\n",
"prec = np.linalg.inv(covariance)\n",
"\n",
"var, U = np.linalg.eig(covariance)\n",
"angle = 180. / np.pi * np.arccos(np.abs(U[0, 0]))\n",
"\n",
"data = sp.stats.multivariate_normal.rvs(mean, covariance, size=N)\n",
"\n",
"fig, ax = plt.subplots(figsize=(8, 6))\n",
"\n",
"blue = sns.color_palette()[0]\n",
"\n",
"e = Ellipse(mean, 2 * np.sqrt(5.991 * var[0]), 2 * np.sqrt(5.991 * var[1]), angle=np.sign(covariance[0,1])*angle)\n",
"e.set_alpha(0.5)\n",
"e.set_facecolor('gray')\n",
"e.set_zorder(10);\n",
"ax.add_artist(e);\n",
"\n",
"ax.scatter(data[:, 0], data[:, 1], c='k', alpha=0.5, zorder=11);\n",
"\n",
"rect = plt.Rectangle((0, 0), 1, 1, fc='gray', alpha=0.5)\n",
"ax.legend([rect], ['95% true credible region'], loc=2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Fitting using GMM"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"GMM(covariance_type='full', init_params='wmc', min_covar=0.001,\n",
" n_components=1, n_init=1, n_iter=100, params='wmc', random_state=None,\n",
" thresh=None, tol=0.001, verbose=0)"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"from sklearn import mixture\n",
"g = mixture.GMM(n_components=1,covariance_type='full')\n",
"g.fit(data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using Wishart prior\n",
"Code steal from [Thomas Wiecki](https://github.com/pymc-devs/pymc3/issues/538#issuecomment-94639178)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"WARNING (theano.gof.compilelock): Overriding existing lock by dead process '72695' (I am process '73255')\n",
"WARNING:theano.gof.compilelock:Overriding existing lock by dead process '72695' (I am process '73255')\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 4000 of 4000 complete in 14.9 sec"
]
},
{
"data": {
"image/png": 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S1S6yxpLLDkzNVVRkyZ7l7v+91+s0s4uBvwbe4u5/udnzwyC7k5Eo9+7Lanbl\n3n1ZzZ7V3L3Qq9kFLwVuJhkc/HQz+zDwcne/txfr7xerW7KKGpMlfWpyemVL1v7RpMjSuCzZy8zs\nvwC/Doy1HmrPcJs7y/UdBj4J3OTun93s+ZC0ZGV1MhLl3l1Zza7cuy+r2bOcuxd61V3wj4DXA/8L\neBj4M+A9wNN7tP6+cLrIak18kVN3QelPU/PJ2P92cXWgU2T17bwyIr3wc8Dj3f3+Hq3vtSRdD3/N\nzP4ryaVKnrPRBE0akyUiItC7Iuugu3/KzP6Xu8fAzWb2qh6tu290Jr5YPSZLFyOWPjO3WGOonKeQ\nTya5aBdbU2rJkr3tNmCzWW23zN1/FvjZ7SwTakyWiIjQuyJr2cyO0rogsZk9jZXT6O4JnZas3Mop\n3DUmS/rN7GKN0aFi5/7+kRIAp2ZVZMme9mbgVjP7e5LZBQFw95fvVgDVWCIiAr0rsn4O+ChwhZl9\nHdhPMnXuhs7mQo9pancLbE94UczlVzwu0g+aUcTicp2LDg51Hhso5SkXc8wu1lJMJrLj3gy8F7gv\nrQBqyRIREehdkXUY+F7gKiAHfNvdt/JtbtsXekxTu1tgURcjlj42v1QnhhUtWQBjQ0VmF/ZcA7NI\nt4q7/0aaATQmS0REoHdF1m+7+8eAb21zuW1f6DFN7WIq3yquckGOgEBFlvSVuVZr1VpF1onpZZpR\nRC7UBYllT/obM/sd4ONA50Sfu39+twKoIUtERKB3RdZ3zOwdwJeB5faD7v6ejRY6mws9pul0S1ay\n2YIgoJAraOIL6SvrFlnDJWKSlq59w6UUkonsuCe0/n9i12Mx8MzdCpDP6QSGiIicY5FlZhe5+3eB\nUyTXI3lK149jkmncN1vHti70mOZFzUpTycHzwPhoJ0cpXyQKmlvKldULsin37juX7PF90wBcdHh0\nxXqOTAzDt08QFPI7tm2yus2zmhuynb3X3P2GXq7PzALgD4DHARXgP7r73Rsts2+kRKOi3g0iIue7\nc23J+gjwRHe/0cx+wd1/ZzsLn82FHtO8qNnM3CIASwuNTo48eSq16qa5snxBNuXeXeea/cGH5wAI\no2jFeoqtE+z3PTjNWOmsrs26oaxu86zmhuxm36nCsDWz7auBYZITfzngUne/7CxX+Xyg5O7XmdmT\ngTe2HlvX+EiZSRVZIiLnvXPt19Dd+/w/nMXy3Rd6/KyZfcbM+rYfU61zMeLTtWkhl9cU7tJXZhfW\nG5OVvLVtd+dAAAAgAElEQVRmFjTDoOxZNwMfJDmB+PvAnSSF0dl6GvAJAHf/MvCkzRao1HWZBBER\nOfeWrLjr9raH+57NhR7T1OhcjLjQeawQFphrLqQVSeQMc0vtIquw4vGx4aTo0jTusoctu/s7zewy\nYBp4BfA5kqndz8YoMNt1v2FmobtH6y1w19R9HA4vPMtfJyIie0WvJr6AlQXXnrRWS1YxLGh2Qekr\n7YkvxtaYXRBgTi1ZsndVzGw/4MBT3P0zZnboHNY3B3T3bdywwAKYqczx6EuuJAyyNwFGVsf3ZTU3\nZDe7cu++rGbPau5eONci6xozaw8CvqjrdgDE7n75Oa6/rzTaRVbudAtBPszTjJtEcZTJg6rsPXOL\nNQZKOQr5leOuxlozCs4s6lpZsme9EfhL4N8A/2Bm/wH42jms74vA84D3m9lTgFu3stDk5HzmjgdZ\nHt+XxdyQ3ezKvfuymj3LuXvhXIusq3qSIiNqzXZ3we4xWYXWz+qU8307nEzOI3OLNUYHi2c8PjJQ\nIAwCdReUPcvd32dm73f32MyuJTlG/fM5rPIDwLPM7Iut+zeec0gRETkvnFOR5e739SpIFnRasrrG\nZBVbt+tRnTIqsiRdURQzv1zn8P7BM34WhgEjQwV1F5Q9ycyeB9zm7neb2fOBnwD+iaT1acMufutx\n9xj4qe0uF8fxWYxSFhGRvSRb/RlSVl9rdsGuIkskbfPLdeL4zJkF28aGiswsVpMvgSJ7hJn9IvDr\nQNnMHgv8KfAhkqnc35BmNhEROT+pyNqG+jqzCwLUmyqyJH3rTXrRtm+4RK0eUak1dzOWyE57CXC9\nu98G/BjwYXe/GfgF4NmpJhMRkfNSXxRZZvZkM9vSxYjTVGlWyQc5cuHpCQU6Y7JaBZhImtpF1not\nWe3HNS5L9pjY3Zdat2/g9LWtYs6DmW9FRKT/9HIK97NiZq8mOQvZ9xebWq4vM1AYWPFYUd0FpY9s\nVmTta18ra6HKkTXGbYlkVMPM9pF0D3wC8CkAM7sE0BkwERHZdakXWcBdwAuAP0k7yGaWGssMFYZW\nPNaeUbDSqKQRSWSFdgvV2BqzCwKMDZVWPE9kj/gt4Oskx7Sb3f2Ymf1b4HXAb5ztSs1sFHgvyUWJ\nC8AvuPvfb7ZcrMYzEZHzXurdBd39A2TgTGMcxyw1lhnMr2zJGiokrQGL9aW1FhPZVXNLG7dktcdq\nzWqGQdlD3P39wHXAc939p1sPLwGvcPdzOYH388DfuPszSKZv//1zCioiIueNfmjJ2pa0rhxdqVeI\n4oh9QyMrMlxQOZDcKDU2zZbVq14r9+472+y1ZnIG/bKLx5k4MHTGzy9tFVf1eGe2T1a3eVZzQ7az\n95K7PwQ81HX/Yz1Y7RuB9tW7C8DyVhZSO5aIiPRTkbWlq4qkdeXo6coMAPmosCJDtJw0Bh6fnt4w\nW5aveq3cu+tcsp84tQhAo1pfcx1xPWk0PjY53/Ptk9VtntXckN3s/VgYmtnLgZ8jqZGC1v83uvvX\nzOwISZf2n0kxooiIZEg/FVl9ffJvqZGcwBwsrO4umLQWqLug9IPZxRqlYo5SIbfmzztjstRdUGQF\nd38H8I7Vj5vZY4A/IxmPdctW1jVxcLgz8+xW1Zv1bS/Ta0NjecqFEmGQnDxsNBuEQUgYpj6yYEP9\nWLRv1erscRwTxdGKWYx7Ya66wHBhcNt/y2qjRj2qM1QYJAhOnwvfiW0exVFn39up9aa1r9QaNYr5\ntbvxb9XZZK81auTDfKrv4Sy/P89VXxRZ7n4fSX/6vrXUKqIG1h2TtbjrmURWm1usrTvpBUCpmKNc\nzGniC5EtMLNHA38F/Dt3v3Wry93+wH0EwFKjQhzHTFemt7TceHl8zedODB6k0qiy3FgmF+ZoRE2a\nW7hsSD5XoNF1DcdSvsTBgQPUm3VOVqbIBzlqzeSzYGR0gPm5tXtDFnJF6s3Tnxn5ME+j6/cfHDxA\ntVFjvna6VXVi8CBRHHFqeWrzF75FY6VR9pX2cd/c/QAMFAbJD8Qrcg8Xh1moLVDIFQiDkGqjut7q\nOsr58hmTVxVyhdPXvwwCwiAkipLrC4ZhrnP7yNBhHl48vmLZgcIAy40KrHPR9yv2PYLlRoX5cKaT\nfag4xFJ9qXOh+AuGj1BpVJmuTDNSHGGoMMh0dYahwhC5IGRy+VRn/UPF1sne2rl9DxkqDm1pHRvt\nK225MM9QYYCAkKXG8or9B5J9qpgrbPj7knUMslRfohE1KOaKnf11qDjEQL7MyaVTQLIvjBVHmKnO\nkgtyHBk6xHdm7umsa7AwyNBIkcmppFdSKV+i2qgyVhojF4aUciWmKzNn7AdBEBLH0abbJAhCjo5c\nyIPz3+38DdczWhphqVFZ8d7sNlIcWfFeArjigqN859iD666zvd8fHDzAYH6Q5cYylUb1jPXkcwWK\nYaHznfbw0GGOd+2/h4YmmK3OUW1UO++LwcIgw8UhTixOUswVGS+PM1ebZ3mNxoUgCCjlSp3tuNa+\nMlYaox7VOxna2u+rQq7AvtIYk0snIQgo50rsL4/z0OLDEMedvx0k75N6VGe6Mtv5TCzlSxwo7+eh\nhWNnrHu0NMJQYYhjCw9TypeoNWsr/l6HhiY4sTjJcx7z9HW39Xb0RZGVBZ2WrNVFVl4TX0h/iOKY\n+aU6ExcObPi8seGSiiyRrXkdUALeZGYBMOPuL9hsoe/OP7TZU9a0XjE2uXSyc7uxjWsyrv4SV21U\nV2SrsbWLkq/+grw6Q/uLbrfuzL0yW51jtjrXub9cX2JkYOXn3UItuRpMfZ0vsGtZa3bgFcvHMVF8\nelu1CyzgjAIrybVxAdL+8j8yejr76mLj2MLDndvztfnOl+W1isZzLa56vR6AZtRgrrp+V+Z6s3bG\nfrX2Ok7/vWtdz1+sLa7Iu1xfWvGlv7vAguREea5x+st0ezvOVmc3zLCVAqv9vAfm1i+Cum20XYAz\nCiOAE4tnvse6tff75L24/nMbzfqKz4Xjq/bfE4uTndvt98VSfalTENWatTOW6RbH8aazba+3zdvv\nq3qzfvrzo7W+7oKp+z3Q/T7p/nn387vXPVed72z/td5L3a+/F1RkbdFSfe0iq5ArUMwV1ZIlqbv/\n+DxRHHN4/yZF1lCRE1NLNKOIXJ93AxJJk7s/P+0MIiKSTSqytmi9MVmQtGYtqCVLUnbrd5KzV4+5\n/MCGzzs0PsAdD8xw78PzXHHh2G5EEznvPHbie4iJCYOQQpgniiPiOO6MtTm1PEUpV2KoMEgjbtKM\nmtw39wAXj1zEQL5MPWqQC0JyYW7FsqvH7NSjBoUwOZTXm3UacZNca/xJLkiWXWpUGCkO0YiaNKIG\nzbjJSHGYerPOYmOJfJDnERcdYXJynqX6MuV8Mi5rujLDaDEZT9GMm9SjBtOVGUq5EgcH9rPcqFBt\nVhkqDFFsjSerNKqcWJqk0qwyWhxmqDDEYH5gxRijWrPeGd+TD3IEQdDpshPFEfP1BQJChguDneWW\nG8uUckmuyaVTnFie5PKxy7jw8H6mTy0RtVocAgKmKtPsK42t+J1RHLFUX2awMNB5bj7MU2vWqTQr\nLNaXGMiXKedKFMICQauL4OnMNYq5IvWoAXFMIVeg0qgyVZlmvDxGLshRjxqUcsXOutu5G1GTarPK\neGkftahGKVditjrHlUePcvLkAs2oyXR1lgPlcarNKoWwQC2qMVudZ7Q43DqRu8TDiyfYVxrlgfnv\nsn9gP4cHJyjligStecNyYY5m1CQMws42na3NMVwYIo5jalGdwfwA9ajOTHWWgJCDA/s7+2l7O9Wa\nNZYay9w9cy+jpREuGTlKOV8miiMCAg4dGuX4iVmWGxUqjSr7SqOd3z9bnSMMQppxk2qzxmhxmICA\nXJgnF4QEBFSbNeZrC8REjJf2ce/c/RwZOsxQYXDFNm/v9+11R3HEdGWWQi5PLsgxmB9YMU6srdlq\ntWi/X9rf34b3FYgG8iw3linkip08QRBQjxrUmzXK+fKKDHEcM1ebJ996Dw8XhlisL1HKFVlsLFHO\nlTvXS601W+OfgpBKo0oUR+TDHHO1BfaX9xEQsNRYphgmXVnbf6fZatJSeXjoUOe9285QjxpMVaZ5\n9MWXcfLkAjEx1WaVKI5pxk3KuTJB67Uu1peotVqpggDGiqPkwhzLjWUWakscGBgnICCKIxpxk5CA\n40uTDOTLjJVGV7zu9u3lRoWAgGKuwHxtkYF8ufXzoLOPr6XerBMGIYcPjTE5OU8UR8l7ByjmCjSj\nJsvNCiOFYepRg9nqHPP1BS4ZuYj52gLj5X0r1teIGp1tBrBQWyQm7uwDi/UlTi5PMV4eY19pjDiO\naUQNcmGOSqNCGOQo5YpEcUQURzTjJlEcU8wVqDVrDBYGWaovJ/tB1LuePiqytmi97oIAw8Uhji/1\ntolRZLtuvXuKIIBrHrF/w+c98aoJbvnGMf7h9hMqskR2wOGhQ52ioy0MwhVz6B4YOP0+LQR5CmEe\n2//IzmPdy3cvGwQBueB08VDo+qJTyBUosPL35sgx1lpXMReuWG8hV2BfbuVnQPeJxO4vOjlyFHPF\nzjjk9nNXn3gs50tcMnqUjazeNu3XBUlhuK905udS93joicEDTAwmJ5PyrUKq+wti97ZtC4OQ4dbY\npe7nFnMFirlCp5hcP3NSPHVv73K+xIXDR854zlq5RxhO7ofJ/fHyvtOvOcxxsJW53PoSOxAOrHjN\nY6VRxlrFzOGhQ+vm7C4sgyBYsS0Lnf2gyKHBidPP69oxwyCknC9TzpfZd3hszS/e7dtDhcEV+0M7\n52bK+VKnMAG4cvyKNZ+3+j0TBiEHBsY3Xf/qbdDOeHBwhMnFeQZXZYbk71pYo2gIguCM19Tej1a/\nd7r//t2v72DX/rh6ewGMlUYYK629/xXCPIcHJwjDpCALCM6YG6BtpDi85uMD+ZX7Ui7IkSPZRkdH\nLlxzmdPLllfk3Kr2vhYEQeczq/vvEubCrv2xkLynSd7Tqwss4IyCrv03aBspDq94/UEQdNbf/fdu\nv/buz8n2utdqRDlX6iu0RZ3ugmu8QYbyg9SatW31ARfppYXlOt95aJYrLhpjqLzxDGXXXLafgVKe\nr/oJok0G6IqIyPlpJ2b6Ezmf6B20RdPVZEaa4cKZZwraFfXsGoMVRXbDbfdOEcebdxUEKORDnnjl\nQabmqtz90NymzxeR7eluGRARkfNTqkWWmQVm9lYz+5KZfcbMLk8zz0YemP8uY8W1m3QvHrkIgHtb\n08qK7Lb2eKzHbqHIAvjeq5PuJv9w+4kdyySyV5jZo8xsxszO7UI3IiJy3ki7Jev5QMndrwNeC7wx\n5Txrmq3OMVOd5ZLRi9f8+RVjlwFnThkqshuiOObWe6YYHSpy8eG1+2Sv9ujL9jNUVpdBkc2Y2Qjw\nBmDjeYm7qJuViIikfSR4GvAJAHf/MvCkdOOs7f755NoHl46sPZj34pGLKIQF7py5e9OL0In0UqMZ\n8aVbH2ZuscZjHrGfcI2ZltaSz4U84aoJpuerfOorD1Ctbe16OSLnoT8mOQm45SlktzL4X0RE9ra0\nZxccBbqvStYws9Ddt3b1t5aP3v1J7py5m3KuRDOOqDSqDOTLFHKFs+4ZHwO0pjxtX9TsstFL1nxu\nPsxj41fwzVPf5re/+mb2l8+c/aZYylOrbv0ikmloxhGL9UWqzWSK2WbUJMjF/OT3vHzdWWtW+/iX\n7+O2e6YIw5AwYMX0qkHAlosASP4G7aK1XbvGcZxMrRtuPOqhvb3bJW8cx8Rx0uoTAGGYLB1FMXHr\n/6i97iAgDJLnJLP57K7V+0p7O3Rvg2Yc02zGPDi5wPxSnQB4yjVH1lzfep7x+Iv4+289zF999i4+\n+qV7ueyCEQq5kFwuPKvXnIV9fC1ZzN3eZ/OFHPVao/M+a79fkhmdkue29/E4hoFSjh/9visZGy6t\nveLzmJm9HPg5oPtM2f3An7v7ra2LEW/q2gsfw8KMJkESETnfBWm2vJjZ7wD/z93f37p/v7uvXcmI\niIjsIjO7A3iQZCLppwBfdvdnpBpKREQyIe2WrC8CzwPeb2ZPAW5NOY+IiAgA7n5V+7aZ3QM8K8U4\nIiKSIWkXWR8AnmVmX2zdvzHNMCIiIuuIQXOzi4jI1qTaXVBERERERGSvSXt2QRERERERkT1FRZaI\niIiIiEgPqcgSERERERHpIRVZIiIiIiIiPZT27IJnxcweBfw9cMjda2nn2YyZjQLvJbn4cgH4BXf/\n+3RTra910c0/AB4HVID/6O53p5tqa8wsD7wDuAwoAv/T3T+SaqhtMLNDwFeB73f3O9LOs1Vm9hrg\nh0k+U97i7u9JOdKmWvv5zYABTeAV/b7NzezJwG+5+w1mdgXwLiACvunuN6UabgOrcj8eeDPQAKrA\nS919MtWA5ygrn5lm9jVgtnX3HuB1rLEPmdkrgFcCdZLP0I/tftqt7e9rZTWzMskx9xAwB/y4u59K\nKffjgY8C7c+Wt7r7+/ot91rHTuA2+nybr5P7AbKxzUPgbSTHoAj4SZLPxHfR39t8rdxFMrDNW/k7\n37NIjv3vYoe2d+ZassxsBHgDyYEsK34e+JvWRSxvBH4/3Tibej5QcvfrgNcCb0w5z3a8GDjp7k8H\nngO8JeU8W9Y6WPwhsJR2lu0ws+uBp7b2lxuAy1OOtFU/AAy5+9OA/0HyhbNvmdmrSQ5spdZDbwR+\nxd2vB0Iz+5HUwm1gjdy/B9zk7s8kuYzHa9LK1kN9/5lpZiUAd39m699PsMY+ZGaHgf8MPBX4QeA3\nzayQQt5N9/cNsv4U8I3WceBPgF9LMfe1wO90bff39WNuVh47f5Dk2JmFbb7WMf+JZGOb/xAQt45B\nv0ZyDMrCNl8rdyb28zW+Z+3o9s5ckQX8MclBLEtfRN8I/FHrdgFYTjHLVjwN+ASAu38ZeFK6cbbl\nrzi944ckZyGy4g3AW4GH0g6yTc8GvmlmHwQ+3PqXBRVgrNUKMQb0e6v4XcALuu5f6+5faN3+OMlZ\nuX60OveL3L194fk8/f95uBVZ+Mx8HDBkZp80s79ptbY8cdU+9CzgXwC3uHvD3eeAO4HHppB3s/19\nvayPo+vvwe6/N87IDfxrM/ucmb3NzIb7NHf3sTNH0tK81f0jzexrHfOvBZ7X79vc3T9E0loCcCkw\nTQa2+arcl7VyZ2Kbs/J7VsAOb+++LbLM7OVmdquZfaPr30eBj7YO0H15UchVuW81s28AV7p71cyO\nkFS//X7mdpTTXUoAGq3m4b7n7kvuvthq8Xwf8KtpZ9oKM3sZcMLdP02f7tsbOEjyAftCkjM9f5Zu\nnC27BRgAvk1yEuTN6cbZmLt/gOSLT1v3fjJPUij2ndW53f04gJldB9wE/G5K0XopC5+ZS8Dr3f3Z\nJO/TP+XMfWgUGGHla1kghX1rC/v7Rlm7H28/d1eskfvLwKtbZ8rvBn6dM/eXfsi91rGz77f5Grn/\nP+ArwC/2+zYHcPfIzN5Jcvz5MzKwzWFF7jeRfJZ8mT7f5ut8z+r+nO759u63g0CHu7/D3R/j7o9t\n/wOuAn7CzD4LHAE+lW7KM63K3f7/a2b2GODTwGvc/Za0c25ijmRnagvdPUorzHaZ2cXAZ4B3u/tf\npp1ni24EntXatx8PvKfVbzgLTgGfbJ31uQOomNnBtENtwS8BX3R3IzlL9R4zK6acaTu635MjwExa\nQbbLzF5EMobpubvZF38HZeEz8w6SL0O4+50k79vDXT9v70NzrPzy0C/71lr7+1pZp1n590g7/wfd\n/Z/at0k+32fpw9yrjp1/QUa2+Rq5M7PNAdz9RpLvtzeTnPhr69ttDmfk/lQGtnn396zHAe8BJlbl\n6+n27tsiay3uflWrr+cNwMMkzXp9z8weTdKk/WPu3neF4Rq+CDwXwMyeAty68dP7R6sv7SeBX3L3\nd6edZ6vc/Xp3v6G1b3+dZDKAE2nn2qJbSPotY2YXAoMkX+D63TCnz0rNkHRdy6UXZ9v+0cye3rr9\nHOALGz25X5jZi0lasJ7h7velnadHsvCZeSPwO9B5n44Cn2qNqYTT+9A/AE8zs6KZjQGPAr6ZQt7V\n1trf18v6JVp/j9b/ab43PmFm7e6j3wd8jT7Mvc6x85/6fZuvkzsr2/wlZvba1t0KySQMX93GezKt\nbb46dwT8tZl9b+uxvtzma3zPegnw8Z3cxzM5u2BLTHa6Vb2OZBDsm1rjP2bc/QWbLJOmD5BU+19s\n3b8xzTDb9FpgH/BrZvZfSfaT57h7Nd1Y2xKnHWA7PJl151+Z2VdI3pM/7e5ZeA2vB95pZl8g+Sx8\nrbtnaXzQLwJvaw3IvR14f8p5NtXqQvcm4D7gA2YWA59z9/+ebrJzloXPzLcD7zCzz5N8xryM5GTI\nzd37kLvHZvZmkpMnAcmg8H4Yr3jG/r5eVjN7K/Du1nu7CvxYaqmTmdd+38xqJCeHX+nuC32Ye61j\n538B/nefb/O1cv8s8HsZ2ObvB95lZp8jOQb9DEn39S29J1PMvlbu+4E/yMA2X21HP1eCOM7CdyER\nEREREZFsyFR3QRERERERkX6nIktERERERKSHVGSJiIiIiIj0kIosERERERGRHlKRJSIiIiIi0kMq\nskRERERERHpIRZaIiIiIiEgPqcgSERERERHpIRVZIiIiIiIiPaQiS0REREREpIdUZImIiIiIiPSQ\niiwREREREZEeUpElIiIiIiLSQyqyREREREREeiifdgCR842ZvRz4eaABnAReBjwX+M+tx44DrwJO\nAA8AV7r7iday/w/4b+7+yd1PLiIie52OUSK9oZYskV1kZo8Ffgv4AXd/PPBh4G+BXwSud/cnAH8O\nfMjd54C/Bl7cWvZq4IgOXiIishN0jBLpHRVZIrvr+4BPuPtDAO7+ZuCDwF+6+1TrsXcDF5nZpcDN\nwI+3ln0Z8M5dTywiIucLHaNEekRFlsjuagBx+46ZlYBHrvG8ACi4+xeBvJl9L/BjwDt2JaWIiJyP\ndIwS6REVWSK767PA95vZ4db9nwJ+EHiRmR0EMLMbgZPuflfrOW8H/jfwz+7+4G4HFhGR84aOUSI9\nookvRHaRu3/TzF4NfNLMYuAYcAXwAuAzZhYAk8DzuhZ7N/A/gX+/23lFROT8oWOUSO8EcRxv/qxz\nYGaHgK8C3+/ud3Q9/kPArwF14J3ufvOOBhEREdmAmb0G+GGSE5BvAb4IvAuIgG+6+03ppRMRkSzZ\n0e6CZpYH/hBYWuPxNwLfDzwDeKWZTexkFhERkfWY2fXAU939OuAGkrP3bwR+xd2vB0Iz+5E0M4qI\nSHbs9JisNwBvBR5a9fjVwJ3uPufudeAW4Ok7nEVERGQ9zwa+aWYfJJm2+sPAE939C62ff5zkxKCI\niMimdqzIMrOXASfc/dMks9B0GwVmu+7PA2M7lUVERGQTB4FrgReSDPb/U1YeI3WcEhGRLdvJiS9u\nBCIzexbweOA9ZvbDrauCz5EUWm0jwMxmK4zjOA6C1fWaiIhkTD9+kJ8Cbnf3BnCHmVWAo10/13FK\nROT80JMP8R0rslp92AEws88C/6lVYAHcDjzSzPaRjNd6OvD6zdYZBAGTk/M7ETc1ExMj676maqXO\nwnyVAxPDu5zq3Gz0mrJKrykb9JqyYWJiJO0Ia7kF+Bngd83sQmAI+Fszu97dPwc8B/jMZivJ6nEq\nq/tZVnNDdrMr9+7LavYs5+6F3ZrCPQYwsx8Fhtz9ZjP7eeBTJNXize5+bJeyZMaf//FXWF6q8/Kf\n/ZeUyoW044iI7Fnu/jEz+1dm9hWS49JPAfcCN5tZgeTk4PtTjCgiIhmyK0WWuz+zdfOOrsc+Bnxs\nN35/Vi0v1QGoVhoqskREdpi7v2aNh5+x2zlERCT7dnp2QRERERERkfOKiiwREREREZEeUpGVAc1m\nnHYEERERERHZIhVZGRBFUdoRRERERERki1RkZUCkliwRkUxoNnVSTEREdnh2QTMLgbcBBkTAT7r7\nbV0//1ngPwLt62f9J3e/cyczZVEUqcgSEcmCW/75IR55ZJhiIZd2FBERSdFOT+H+Q0Ds7k8zs+uB\n1wHP7/r5tcBL3P2fdjhHpunMqIjIzjOzrwGzrbv3kByz3kVykvCb7n7TVtazsFxnv4osEZHz2o52\nF3T3DwGvbN29DJhe9ZRrgdea2RfMbK3rkwjqLigistPMrATJdR1b/34CeCPwK+5+PRCa2Y9sZV1R\nrM9sEZHz3Y5fjNjdIzN7J/AC4IWrfvznwO8Dc8AHzey57v5/N1rfxMTIzgRN0WavaWSknLnXnbW8\nW6HXlA16TXKWHgcMmdkngRzwq8AT3f0LrZ9/HHgW8KGU8omISIbseJEF4O43mtkvA18xs6vdfbn1\noze5+xyAmX0MeAKwYZE1OTm/s2F32cTEyKavaWpqMVOveyuvKWv0mrJBrykb+rRoXAJe7+5vN7Mr\nSYqqoOvn88DYltakhiwRkfPeTk988RLgqLv/JlABmiR92zGzUeBWM7saWAaeCbx9J/NkVayJL0RE\ndtodwF0A7n6nmZ0Cntj18xFgZisrGt8/xMSBod4n3GF9WvxuKqu5IbvZlXv3ZTV7VnP3wk63ZL0f\neJeZfa71u34W+DdmNuTuN7dat/6OpAD7W3f/xA7nyaRY/ftFRHbajcBjgZvM7EJgFPiUmV3v7p8D\nngN8ZisrOjW1SC5j1zfMaotpVnNDdrMr9+7LavYs5+6FHS2yWt0CX7TBz/8C+IudzLAXaAp3EZEd\n93bgHWb2eZIOfy8DTgE3m1kBuJ3kxOHmdGJMROS8tytjsuTcqLugiMjOcvcG8NI1fvSM7a5Ln9gi\nIqIiKwPUkiUispKZXQZcA3wSuNjd70k3URd9ZIuInPd29DpZ0hu65oqIyGlm9iLgI8CbgYPAl8zs\nxemmEhEROU1FVgbE2Ro/LSKy034ZuA6Yc///27v3KEnq+u7j7+ruuext2AWWmyjX+JWYCIIGNISL\nkcTl9sgAACAASURBVBBNCJBjnsQLRnzw9uCToNH4oKInnqMhUTlqVDSs4DUSwQDqCmKC6IKRqIhy\n/YJy1d2FvczuzOzcurvq+aOqe6pne6ZrmO6ZrpnP65w509V16e+vqrqqf/W7+Vbi4T8uXtyQpuix\nmIiIdLoL9wJwBWDEXbe/2d3vS80/C7gEKANXufuGTsaTV2qTJSLSoOruw2YGgLtvNbOueRylHmFF\nRKTTJVlnAZG7n0ycmfpQbYaZlYDLgJcSNyx+o5mt73A8uZG+SatNlohIg3vN7K1Aj5kdZ2b/Cty1\n2EGJiIjUdDST5e43AG9MJg8HBlOzjwEecvchdy8DtwGndDKePElnsvRUVESkwYXAM4gHsr8SGAL+\nz6JGJCIiktLx3gXdPTSzq4BzgVekZg0Au1PTw8A+nY4nL9L5KpVkiYhMcfc9xG2wuqYdVpou2SIi\nsiBduLv7+Wb2LuB/zOyYZJDiIeKMVs0aYFerbbVrFOZu0ixNlXK1/nrFit7cpTtv8WahNOWD0rT0\nJe2vpmdltrj7ofPc7gHAT4irsVeBzxO3J77H3S+cz7ZFRGR5yZTJMrNvA1cB1ydV+zIxs/OAQ939\nH4Fx4ptWrXHy/cDRZrYWGCWuKvjhVtvctm0468fnwvr1a5qmqTw5lckaGRnPVbpnSlOeKU35oDTl\nw3wzje5er+puZj3AOcCL5rPNpJ3wZ4jvRxC3GX63u28ys8vN7OykCnxrquItIrLsZW2TdSnwx8BD\nZvYpM3thxvWuBY4zs+8DNwIXAX9uZhe4ewV4O3AzcDuwwd23zC38pUsdX4iItObuZXe/BnjJPDf1\nEeByYDMQAMe7+6Zk3o3EpVuZ6IotIiKZSrLc/QfAD8xsBXG7qq+b2RCwAbjc3SdmWG8M+MtZtrsR\n2DjnqJeB9INQdeEuIjLFzF6bmgyA5wKT89je64Cn3P27Zvbu5O30Q8g5tRlet25VLqt45jFmyG/c\nkN/YFffCy2vseY27HTK3yTKz04DzgD8ifqp3NXAG8A3gzE4Et7ypd0ERkRmcnnodAduZ5YFeBucD\noZmdARwLfBFIDymSqc1wzeDgHlaVgnmEs/DyWi01r3FDfmNX3Asvr7HnOe52yNom6zHgYeJ2WW9N\nSqgws1uJGwlLm6WrCKq6oIjIFHc/v83bO7X22sxuAd4MfNjMTklqcrwMuCXzBnXJFhFZ9rKWZL0E\nGHb3p8xshZkd7e6/dPcQOL6D8S1bjdUFFy8OEZFuYWaPMEsWxt2PbOPHvQO4IulY437iNsYiIiKZ\nZM1k/QnwOuIM1QHAt8zsMnf/104FtuxpMGIRkelO6/QHuHu6A42Of56IiCxNWTNZbwROBHD3x8zs\neOAOYMZMVtId7pXA4UAv8EF3/2Zq/kXABcBTyVtvcveH5pqApSpdQ3Dwqd8Av7VosYiIdAN3fwzA\nzPqAlwOriTu+KAJHAO9bvOhERESmZM1k9QDpHgQnaV3r/DXAdnd/rZmtA+4CvpmafwJwnrv/LGuw\ny0qq9Kp6r6MHqiIidf8BrASOBjYRj7OYbQwrERGRBZA1k3U9cIuZfS2Z/nPiXgVn8zXgmuR1AZg+\niPEJwMVmdjCw0d0vzRjLstBYQzBfvVSJiHSYERfvf5y4xsQ7iAcSFhER6QqZBiN293cBnyC+sR0J\nfMLd39tinVF332Nma4gzW++ZtshXiXtwOh042cxePtfgl7J0O6woUCZLRCTlSXePgAeA57n7ZuCg\nRY5JRESkLvM4WcS9Kz1JUqyS6tp2Rmb2TOJqHZ9093+fNvvj7j6ULLcReD7w7VZBLMVBzZqlqRhM\n5X/DIMhduvMWbxZKUz4oTcvCvWb2L8DlwFfM7BCgf5FjEhERqcs6TtangLOAX6Xejoi7dp9pnQOB\n7wAXuvv3ps0bAO42s2OAsWQ7n8sSSx4HNZvNTAO17do5Wn8dBYVcpTuvg8/NRmnKB6UpH9qQaXwL\n8GJ3v8/M3g/8IfCqeQcmIiLSJllLsv4IsNogxBldDKwFLjGz9xFnyq4AVrn7BjN7F3ArMA78l7vf\nNIdtL3mqLigiMqOvA182s153/wat2wi3ZGYF4nuUASFxdfYJ4PPJ9D3ufuF8P0dERJaHrJmsh5lj\n7wvufhFw0Szzrwaunss2l5P0AMShMlkiImlXAK8EPmZmNwFfdvdb57nNs4DI3U82s1OBDxHf997t\n7pvM7HIzO9vd1YuhiIi0lDWTtRO4z8x+SFzyBIC7v74jUUljSZZ6FxQRqXP3jcBGM1sB/AnwUTPb\n390Pm8c2bzCz2jAjhwGDwEvdfVPy3o3AGaireBERySBrJuum5E8WSEMX7kGmTiBFRJYNM/tt4K+A\nvwCeAD423226e2hmVwHnJts9IzV7GNgny3bW7bsql52V5DFmyG/ckN/YFffCy2vseY27HTJlstz9\nC2Z2OPBc4GbgUHd/pJOBLXdqkyUi0pyZ3Q1UgC8BL3H3Le3atrufn7QZ/jGwIjVrDbAryzYGd+5h\nVSlf1+28drCS17ghv7Er7oWX19jzHHc7ZCoiMbO/BL5JPPDjfsAPzew1bYlAmlJ1QRGRGb3K3Z/v\n7pe1K4NlZueZ2cXJ5DhQBX6StM8CeBmwqenKIiIi02Sth/Yu4MXAsLtvJR7T6uLZV5H5aKguqEyW\niEidu9/dgc1eCxxnZt8nbn/1N8CFwD+Y2e1AT7KMiIhIS1nbZFXdfdjMAHD3rWYWzraCmZWAK4HD\ngV7gg+7+zdT8s4BLgDJwlbtvmHv4S1e6JItImSwRkU5Khij5yyazTlvgUEREZAnIWpJ1r5m9Fegx\ns+PM7F+Bu1qs8xpgu7ufQlzN4pO1GUkG7DLgpcQ3sDea2fq5Br+kRa0XERERERGR7pO1JOtC4L3A\nGHHp1C3A37VY52vANcnrAnGJVc0xwEPuPgRgZrcBpxAPMClAqJIsEZGmzOwwYANxTYlTgS8Dr3f3\nRxcxLBERkbqsvQvuIW6DlbkdlruPApjZGuLM1ntSsweA3anpzF3jLsWuIJulac/QRGoqYN+1/RR7\nehYuqHlaLscp75SmfFiKaZqnzwIfBi4FtgD/BnyR+GGdiIjIosuUyUraX02vwLbF3Q9tsd4zgf8A\nPunu/56aNUSc0arJ3DVuHruCnM1M3VvuGhytv46CgM1bttG/Ih8/tPLaZedslKZ8UJryoQ2Zxv3d\n/WYz+yd3j4ANSZV2ERGRrpC1JKvedsvMeoBzgBfNto6ZHQh8B7jQ3b83bfb9wNFmthYYJX76+OE5\nxL3kTe9dsDI52Thii4jI8jVmZoeSPPwzs5OBidlXERERWThZ22TVuXsZuMbM3tNi0YuBtcAlZvY+\n4pvhFcAqd99gZm8nHtg4ADa0czDJpWD6OFmVyuQiRiMi0lXeDnwLOMrM7gL2Bf7X4oY0Rf0WiYhI\n1uqCr01NBsBzgVl/9bv7RcBFs8zfCGzM8vnLUUMmKyhQVSZLRAQAd/+xmb0QeDZQBB5w93ldJJsN\nOwLcB3weCIF73P3C+XyGiIgsH1lLsk5PvY6A7TQfT0TapKFzwVp1QRGRZczMrmKGgiIzw91fP4/N\n14YdeW1Slf3nxEOVvNvdN5nZ5WZ2trvfMI/PEBGRZSJrm6zzOx2INAqrU2M9R0FAtazmBiKy7N3a\nwW2nhx0pAhXgeHfflLx3I3AGoEyWiIi0lLW64CM0f3oYAJG7H9nWqISwWklNBVQr5RmXFRFZDtz9\nC7XXZnYc8BLizNDN7v7APLfdbNiRj6QWyTzUiIiISNbqgl8m7gXws8RtsV4N/D7wzg7FtexVUpmq\nKFAmS0Skxsz+DngzcalSEfimmX3I3a+a53bTw45cbWb/nJqdeaiRdetW5nJsszzGDPmNG/Ibu+Je\neHmNPa9xt0PWTNbL3f2E1PRnzewN7v5kqxXN7ETgUnc/fdr7FwEXAE8lb73J3R/KGM+SVylPlWRF\nqOMLEZGUNwMvcPfdAGb2AeB24GlnsmYYduRnZnaKu/8AeBlwS5ZtDQ6Osrqn0HrBLpLX8djyGjfk\nN3bFvfDyGnue426HzF24m9kZ7v7d5PXZxFUnWq3zTuA8YKTJ7BOA89z9Z1ljWE6q1XQmK6BaVkmW\niEhiB43jYo3Q/D4zF82GHflb4F+S8SHvB66d52eIiMgykTWT9QbgS2Z2UDJ9P/DXGdb7JXAu8KUm\n804ALjazg4GN7n5pxliWhWollckKAkJVFxQRqXkQuM3MvkTcJusvgJ1m9vcA7v7Ps63czCzDjpw2\njzhFRGSZytq74J3Ac81sf2Dc3TM9MXT368zssBlmfxX4FDAEXG9mL3f3b2fZ7nIQTivJUiZLRKTu\nV8nf2mS6Vr1vxeKEIyIi0ihr74KHARuIB2k8xcy+Abze3R+dx2d/3N2Hku1vBJ4PtMxkLcUGdM3S\n1N9bnJoIAvp7C7lKe55izUppygelaelz939Y7BhERERmk7W64GeBDwP/BGwF/g34InBKxvWD9ISZ\nDQB3m9kxwBhxN7yfy7KhPDagm81MjQKHhkfrryMKDA8N5SbteW3oOBulKR+UpnyYb6bRzP4WeD9T\nXarXhhMpzryWiIjIwsmaydrf3W82s39y9wjYYGZvncPnRABm9kpglbtvMLN3EQ8sOQ78l7vfNJfA\nl7qwUq2/joKAsKzeBUVEEm8DjnP3xxc7EBERkWayZrLGzOxQpjJLJ9PYs9OM3P0x4MXJ66+m3r8a\nuHpO0S4jYdjYJiuqVmdZWkRkWbkPaDmEiIiIyGLJmsl6G/At4CgzuwvYl7g3J+mQsBrWX6t3QRGR\nBp8grnL+I+LeBQFw99cvXkgiIiJTsmayDgReCDwbKAIPuLvqr3VQtVplqilbQJjq0l1EZJn7BPBl\n4LF2btTMTgQudffTzewo4PNACNzj7he287NERGRpy5rJ+md33wjc28lgZEpcPTA+PFFQICwrkyUi\nkhh39w+0c4Nm9k7gPKYGNb4MeLe7bzKzy83sbHe/oZ2fKSIiS1fWTNavzOxK4A7i3gABcPcvdiQq\nSTq+SB0elWSJiNT8p5l9FLgRqNeqcPcfzGObvwTOBb6UTJ/g7puS1zcCZwDKZImISCazZrLM7Bnu\n/htgB3HdtZNSsyPibtxnla5+Me39s4BLgDJwlbtvmGPsS1oYho3T6vhCRKTm+cn/41PvRcTDgTwt\n7n5dMiZkTXrokWGmuosXERFpqVVJ1jeB4939fDP7O3f/6Fw23qT6Re39EnFVjBOIS8ZuN7Mb3H3b\nXLa/lKU7vmg2LSKyXE1/aNch6YvuGmBX1hXXrVuZywGk8xgz5DduyG/sinvh5TX2vMbdDq0yWekn\nea8G5pTJYu/qFzXHAA+5+xCAmd1GPLDx1+e4/SVrquQqAgKiskqyRESgPozIO4HVxPepInCYux/e\nxo+508xOSaogvgy4JeuKg4OjrO4ptDGUzsvroNd5jRvyG7viXnh5jT3PcbdDq7tAlHodzLjUDNz9\nOlLd66YMALtT06qKMU1YiR+iBsnDVJVkiYjUbQCuJ35Q+CngIeLaEe30DuADZnY70ANc2+bti4jI\nEpa14wtozHDN1xBxRqsmc1WMpVjs2CxNhUK8uwtBRDWKc8NZ0/7kzlE+/fWf86Zzf5dD9l/dzlAz\nWy7HKe+UpnxYimmapzF3v8rMDgcGgTcA3yfu2v1pc/fHgBcnrx8CTns624midt4uRUQkj1plsp5r\nZg8nr5+Reh0AkbsfmfFzppeC3Q8cbWZrgVHiqoIfzrKhPBY7zmamotTyRFwAWChEVKtQGS9nTvvN\ndzzOnQ88xTXfdV710me3Nd4s8lo8PBulKR+UpnxoQ6Zx3Mz2BRw4yd1vMbMD5h+ZiIhIe7SqLvhs\n4PTkL/36tOR/VhGAmb3SzC5w9wrwduBm4HZgg7tvmVvoS1utemChdoTm0CZr6849ANz54DY9URWR\npegy4N+JO2d6rZndC/x0cUOKDe8YZXB4AoBqGO51Da5UQ8LUe2EYsWskXn5ozyTlyt5VwyfLVSYm\n974HlCshI2PlpnFEUUSlGjI6Xmn4vEo1ZHyyQrlSJYoidu+ZrMcbb7PasI3JcpVKNWTXyEQ9LVEU\nsXXnKCNjZaqpnnDLlSrlSpVdIxOUKyGVasjuPZPsGZ+KcXyywmgyXamGhGEcZ23ZyRnudeVKtb6d\nahgvG0UR4xMVtuzY07DNarj3PhybqPDL3+ymMkvV+zCKGBqdZHi0PioAlWpIuVJlaHSSodT700VR\nxOh486FWmp0H5UqVahJLFEWEYet7daUa8uTOUcYmKkRRVP+rrRtFEU88NVLfFwCj4+X6fp5uIjm2\nzeaHUcRjW4ephiG/2TZSP0fT686mdv6FYbxfypWQ3SMTTJarDecRwM6hccqVxu9FbX56n5YrVYZH\nJ+v/wzBq2K+1z7vnkR08unWIpwZHefzJYSYmq/x628isxz6driy/myrVkLHkYfhkOT7vwyTNQ6OT\nhFG013e2tszYRKU+L0y+Y2njkxUe2TJEpRryyJahhn1d+46FYUS5EjZ8t+YrDCOeGozPr8Hhifq+\nT58fO3aP88iWIcqVKqPj8fd/ZKzMA48N1vdvpTp1XaqdB3M1Pllp+j2uiaKIweHGa9L07+70c7pc\niY/Zj+7byuNPDjddrhrG52m7zFqSlVSdmJdp1S++mnp/I7BxvttfqqLkoBeKAZQhqmTPZG3ZMQrA\nzqEJHt06zBEHD7RYQ0QkP9z9GjO71t0jMzuB+CHgzxc7LoCx4XEmqvGNPE+27BpnaHis9YJdZmDN\nijnFvX1396RxYMtIR/b5b7aPtF4ooy3JQ9u0gTW7u/5cST982LwjTsPQeLXr4057cnC0/v9XWztz\nrjxdtdjSfuJP7fXeXL+fC2Xzjj3186KZo4/Yvy2fk6/uj5aRWiarWCrGb1Szl0ht3Tl18t/5oHrF\nF5Glw8z+1MyOTDJY5wBXE/di2zX3s3AO12sREVmauuamJI2ipHi1WOsGuEkVkmZGxsoMj5Z5zrPW\n0lsqKJMlIkuGmb0DeD/Qb2bPA74C3EDclftHFjO2tGiWai4iIrI8zKV3QVlItZKsYgGoEmSsLbg1\nqSp42EFrWNnfw50PbmPz9j0csv+qDgUqIrJgzgNe5O6jZnYp8A1332BmAXDfIsdW95xnruOAg9cQ\nRVAqxg/KwjCiUJjqAyqKIoKgsU+oiXKVvp4iYTTV1qSYNMyNoohqGFEqFpJ2VXG7jIFVvZQrVSrV\niBV9pabbrlRDCkHQ8PnpedUw4tBD1vKrR3fQ31skCKhvb3S8Qn9fkUKyvTCK24LsGplg7eo+ekuF\n+mcNj07W11nZX6JULDA4PE5vqcCqFb1ArU1JRH9vEYK4V6zJcsjYZIVV/SV6arU3mgiTNjqrV/TU\n03nAAQM8/sR2CIqUikF9/0zfTqUaEhASEc/v7y01zBubqLBmZW/Tz50sVxkvV+kvVuntW9EYUxix\nZecoB6xdQakYNOz3iXKVnmKBQiFgdLxMT6lQPx+CIGCftSvZvWu0npaxiSor+0tUqmF9uXT7oD1J\nG5la+mufXzuuYRRBBKMTFVb2lZoe77Ta+VbbBwCFQsDEZNxWq7Y/do1MMLCql0IQMFGusv9+q9m9\ne5QgSUczI2NlwihiYGV8fpaK8XkSRhHVJscnbrsTEQRTae4pFRmfrFAsBPSUioyOlwmjxvTX9sHO\n4XH2G+gnAvaMjFANI4qFiGLPSlb29zCyaztH/NahPPnkEEEAk5WQvp4i5UpIsRjUz++xiQqlYqHh\nvSiK+M22PRy470p6SlPHJYL6MrX9OTEZ79OengLjExVW9k+LNYrYtmuM9fusmDpuYUih0LzMo1Ke\npNTTu1cHSOVKtX4N6O0p1r/7M2l2vZlNrW1m7TjFx6FAEJaJCgVKxRJBECTtDRuvc5C0/SxXOfJZ\n+7J9+0jcfnKySqEQ1M+5ZsIwIowiioVgr3jDMOLJwVHWremjr6eYHOOAsYk41lIxoCe5HsXxB/Xj\nlbbl8QfZ94BD6etf2fD+xGSVyUqV3lmuQXOlTFaXqlUXLJWKQDVzdcFa/emD91vFMw9YzZ0PbuPO\nB7cpkyUiS0Hk7rX60KcDnwZIqg62vY5eknn7NHAsMA5c4O4Pz7ZOZWKMe37wPXp7QgqFiImJvW/Y\npVJIpTLt5h/QcqCUFf0VwiigWg32Xn+eevpKlCcq9PSElMuzbzsoRERh8gNoWty9vVUmJ5v/SAmC\niCia85CbdcVSSHVaumtxN9PXV226/9Nqx6JQjAir2WPrX9PPxMgYURQQBBH3P4109fSVqEyWKRSj\nhnSVSiGVaoGeUutjMev2MxzLuSoUI4qlnr32eavPanrOpwXQU4p/sNeXS86t/v4K4+Pz/7n601t+\nlDnuZufqAzNst2Xa5qlYDCmUeqlWyrOeo4VCRBgFBLT+njV8h2d5b77n0M9q388ASsXO7qeaoBDR\n11ttOGf2TtvUM7lm15VX/s15bYlF1QW7VXLTqrXJKsyxJOugfVdy7NH7UywEqjIoIktFxczWmtmh\nwPOJe6jFzJ5F84Hv5+scoM/dXwxcTIYBj0c3308AlMuFGX/gN/2hkSGLODZeYmKi2NEfKll+UDX8\nWJkW90wZLGBeGSxgrx9CrbTKYMHUsZhLBgtgfHi8np75pCuKgr3SVakUIMp2LGbT7gwWzLyfWn1W\ny3M2SW/Dcsm51Y4M1kxminsux7TTGYdqNds5GoYBRNlin56Zmum9tp1DUef3U/2jwmCvc6ZZ2mrm\nel2Zi46WZLV6CmhmFwEXALUuSd6UDAC57NVKsnp6ax1fZFuv1rPgQfutZFV/D8951lrufXSQnUPj\n7DvQ34lQRUQWyqXAXcT3rg3uvsXM/gL4EPCBDnzeycBNAO5+h5m9oNUKK/tDqLavukldsUBvsUwY\nzq0Uq9jXS3Vi5q7H95KhRI1CUK/SvtfqTZ6Gz1VQKk71qFsswNPoAhqgb2WRycm4d95iMaLa5Edq\noRDFP07nqHfVCib3zL/XtEJPiUKpSGVicsZ9On35sJzteUInSrI6KoBCMHU8Cr09hJPlTCWSmc7b\nZqvN8XwtrVhJZWzvnvXmo1AqEVaSsVGT4zuX45yOrVqeoFAsNnznG75PbVTs76fUt4KJ3YNt2d5s\naS7291MdH2/L50w33xL22XS6umD9KaCZnUj8FPCc1PwTgPPc/WcdjiN3ohAoQKkUH6JCxhNg685R\nVvWXWJPUWf6dI/fj3kcHefDXuzjptw/qVLgiIh3n7tea2Q+B/d39F8nbo8Ab3P3WDnzkALA7NV0x\ns4K7z/irf/2+EQMHH8QRzz2pA+F0Tl4Hvc5r3JDf2BX3wstr7HmNu106nclq9RTwBOBiMzsY2Oju\nl3Y4nvxInsj09MWZpSBs/TSqUg3ZtmuMww9eU28weNQh+wDw8OYhZbJEJPfcfTOwOTXdyfEWh4A1\nqelZM1gA/X0l9hlYwfr1a2ZbrCvlMWbIb9yQ39gV98LLa+x5jbsdOp3JavUU8KvAp4hvZNeb2cvd\n/duzbXApHqzZ0rRu3WpgG1Bkn3166e3tm3HZJ54cphpGHHHI2vo2B9aupFgIeGLbngXdd8vtOOWV\n0pQPSzFNOXE78KfAtWZ2EnB3lpV2D43l7ultXp845zVuyG/sinvh5TX2PMfdDp3OZLV6Cvhxdx8C\nMLONxA2ZZ81k5fFgzWamEzAKgSJUkjra1aDI5l8/yao162bc1v2/jDu4WLeqp2Gbhx6wml/9eheb\nt+xu2p1lu+X1SzUbpSkflKZ8yFGm8TrgDDO7PZk+P8tKAZ2p3y8iIvnR6UzWjE8BzWwAuNvMjgHG\ngJcAn+twPLkRRXFmqK8/PkRhocjkxOismawtO6d6Fkw78pABHts6zBNPjXDkIQMdilhEZGlx9wh4\ny2LHISIi+dPpYo3rgInkKeBHgbeZ2SvN7IKkBOtdwK3A94F73P2mDseTG1FyaPqSAebCoMj4ntmf\nZm/ZEY+RddB+jZmso5KM1cObd++1joiItNkcBv0UEZGlqaMlWTM8BXwwNf9q4OpOxpBXtUxWb/9U\nJmt09/ZZ19m6c5RiIWD92sYR6Y9MdX4hIiKdFSiTJSKy7OVoAIVlJioSRFV6euKxIapBibHBHTMv\nHkVs3THK+rUrKBUbD+uB61awqr+kTJaIiIiIyAJQJqsLVSYniCgQENYHI64WepgYmnnAt+HRMnvG\nKxw8raogxE9VjzhkgKd2jTE0OodBKUVEZO5UkiUisuwpk9WFhoe2EwZFgiCsd3xRLvZSGZq5JOqO\n+54E4LADm/fadeTBcbusR1SaJSLSUepdUERElMnqQiODcSarEET0r4gHI64U+qiMNO/4Ynyywsb/\nfpT+3iKnH/+MpsuoXZaIyMIICspkiYgsdx3t+MLMAuDTwLHAOHCBuz+cmn8WcAlQBq5y9w2djCcv\nxnbvoFrooVCI6E16F5ws9sNQ80zWf/7k1wyNlvmz3z+cNSt7my5zpHoYFBGZlZmdC7zC3V+dTJ8I\nfJz4HvVdd/9Alu30r17buSBFRCQXOl2SdQ7Q5+4vBi4GLqvNMLNSMv1S4DTgjWa2vsPx5MLY7kHK\nhT56eiIKhYDVA32M9axm5RPbCcOwYdk942VuuuNxVvWXOPP3njXjNlev6OHAdSv45eYhHnxiV6eT\nICKSK2b2MeCD0FDX7zPAX7n7HwAnmtmxrbZz9AtPZv0hR3YoShERyYtOD0Z8MnATgLvfYWYvSM07\nBngoGS8LM7sNOAX4ejs+OAxDBrc9weT4GL39Kyj19C96W+RKucLIzq30r96H8uQ4/avWUAjXsmPb\nLibLVSphieFde9h89+MQ7EepL2DXyASr9+ln69AqxqMD+O9vX89vnXQmYRQxMVll0y+2MDFR4eyT\nDycII8bHykDc2+D4aJm+FT0Ukqorp/7OwVy/6WEu/cqdnHbcIZx54rPoLRUpFgMKbdw5fXsmwl8W\nnAAACAtJREFUGUniWCqUpu4URRFRarp3ZKKhc5faWR0EwdSy6RWShdJnf7d1v93qOEXRVIKapg9Y\ns7Kn69LVhW4nHtvxTQBmtgbodfdHk/nfIX4o+PPZNnLQM49i27bZxzQUEZGlr9OZrAEgXT+tYmYF\ndw+bzBsG9mnXB//oin9k/x8/1K7NtdV48n8PML1T9tuOfDXVwvMBuH93ke9+8nbWA4dT4K5n/BHc\nA7+458cN6xxPgSdue5yrbnu85WcfS4HB1T3cetdmbr1r87zTIiLd7/TnP4PzzrTFDqMrmNnrgbcR\nZ0eD5P/57n6NmZ2aWnQASDdiHQaOWLBARUQk1zqdyRoC0t3d1TJYtXkDqXlrgFb12IL165v3njfd\n2e+9NGuMXeX3FzsAEZElzN2vBK7MsOjTuUfBHO5T3UZxL7y8xq64F15eY89r3O3Q6TZZtwMvBzCz\nk4C7U/PuB442s7Vm1ktcVfC/OxyPiIhIS+4+DEyY2RFJJ05nApsWOSwREcmJTpdkXQecYWa3J9Pn\nm9krgVXuvsHM3g7cTFxlY4O7b+lwPCIiIlm9Gfg34geSN7v7j1ssLyIiAkCQbjQtIiIiIiIi86PB\niEVERERERNpImSwREREREZE2UiZLRERERESkjZTJEhERERERaaNO9y7YNmZ2LvAKd391Mn0i8HGg\nDHzX3T+wmPHNVdIl8KeBY4nHJ77A3R9e3KievuR4XOrup5vZUcDngRC4x90vXNTg5sjMSsTj6BwO\n9AIfBO4j32kqAFcARpyGNwMT5DhNNWZ2APAT4KVAlZynycx+ytRA7Y8AHyL/afp/wJ8R33M+STy8\nx+fJcZrS8nI9z3pumdkbgDcS318/6O4bFz7abPeVZrGaWT/wZeAA4vHO/trddyxS3McB3wIeTGZf\nngx83VVxz+W+102xzxD3E+Rjn2e+L3dT7DPE3UsO9nkSf8vfDO2KOxclWWb2MeIvTpB6+zPAX7n7\nHwAnmtmxixLc03cO0OfuLwYuBi5b5HieNjN7J/EXri956zLg3e5+KlAws7MXLbin5zXAdnc/Bfhj\n4h+FeU/TWUDk7icDlxD/uMp7mmo32M8Ao8lbuU6TmfUBuPtLkr//Tf7TdCrwouRadzpwFDlPUxNd\nfz3Pem6Z2YHA/wVeRHz9+0cz61mEeFveV2aJ9S3AL5Jr+JeIr3mLFfcJwEdT+/2aboybjPe9Low9\nHffLkriPJx/7PNN9uQtjbxZ3Ls7zLL8Z2hl3LjJZxE8931KbMLM1QK+7P5q89R3iHGmenAzcBODu\ndwAvWNxw5uWXwLmp6RPcvTZo543k79h8jakvTxGoAMfnOU3ufgPxUxmAw4BBcp6mxEeAy4HNxA9h\n8p6mY4FVZvYdM/vP5Il43tN0JnCPmV0PfCP5y3uapsvD9TzLuXUG8HvAbe5ecfch4CHgeYsQb6v7\nykyxHkvqeLDw59decQN/YmbfN7MrzGx1l8ad5b7Xjfs8HXeBuOThBOBPu32fZ7wvd90+nxb34Unc\nudjntP7N0Nb93VWZLDN7vZndbWa/SP0/wd2vmbboAHFRXc0wsM/CRdoWA0xV2wCoJEWwuePu1xFf\nkGvSJY65OzbuPurue5LM/DXAe8h5mgDcPTSzq4BPEA+wmus0mdnrgKfc/btMpSX9Hcpdmoifrn3Y\n3c8kfrD0FXJ+nID9iW/Ar2AqTXk/TtPl4Xqe5dwaANbQmJYRFuH4ZLivzBZr+v3asguiSdx3AO9M\nnpQ/DLyfvc+Xbog7y32v6/Z5k7jfC/wP8I5u3+eQ6b7cdfscGuL+OPG15A66fJ9n/M3Q1v3dVTcB\nd7/S3X/X3Z+X+v/TJosO0Zi4NcCuhYmybYaI464puHu4WMG0WTodeTw2mNkzgVuAL7j71SyBNAG4\n+/nAs4ENwIrUrDym6XzgDDP7HvFTpi8C61Pz85imB4lvWLj7Q8AO4MDU/DymaQfwneSp4IPEbZbS\nP9rzmKbp8nA9z3pudev9tdk1uFmsgzQej8WO/3p3/1ntNXAc8Q+1ros7432v6/Z5k7hzs88h0325\n6/Y57BX3zTnY51l/M7Rtf3dVJisrdx8GJszsiKTB8ZnAphardZvbgZcDmNlJwN2LG05b3WlmpySv\nX0bOjk1SH/c7wN+7+xeSt3+W8zSdZ2YXJ5PjxI09f5K0l4EcpsndT3X30939dOAu4DzgxjwfJ+Kb\nwEcBzOwQ4gv9zXk+TsBtxPXaa2laBfxXztM0XR6u51nPrR8DJ5tZr5ntAzwHuGcR4p2u2X1lplh/\nSHI8kv+LeX7dZGa16qN/CPyULox7Dve9rop9hrjzss+z3pe7KvYmcYfAf5jZC5P3unKfz+E3Q9vi\nzk3vgk28mbhotUCcg/7xIsczV9cR56hvT6bPX8xg2uwdwBVJQ8H7gWsXOZ65uhhYC1xiZu8DIuBv\ngX/JcZquBT5vZt8n/t7/DfAAsCHHaWom7+fe54ArzewHxOfd64hLHHJ7nDzulekPzOx/iKtovAV4\nlBynqYk8XM8znVvuHpnZJ4gzxwFxo/DJRYo5ba/v9kyxmtnlwBfMbBNxb22vWrSo498qnzKzSWAr\n8EZ3H+nCuDPd97pwnzeL+yLgYznY55nuy124z5vF/Tjw6Rzs8+k6el0JoijqYOwiIiIiIiLLSy6r\nC4qIiIiIiHQrZbJERERERETaSJksERERERGRNlImS0REREREpI2UyRIREREREWkjZbJERERERETa\nSJksERERERGRNvr/EDaxzuzQoyEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10cebefd0>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"S = np.matrix([[1, .5],\n",
" [.5, 1]])\n",
"L = scipy.linalg.cholesky(S)\n",
"nu = 5\n",
"\n",
"with pm.Model() as model:\n",
" mu = pm.Normal('mu', mu=0, sd=1, shape=2)\n",
" c = T.sqrt(pm.ChiSquared('c', nu - np.arange(2, 4), shape=2))\n",
" z = pm.Normal('z', 0, 1)\n",
" A = T.stacklists([[c[0], 0], \n",
" [z, c[1]]])\n",
"\n",
" # L * A * A.T * L.T ~ Wishart(L*L.T, nu)\n",
" wishart = pm.Deterministic('wishart', T.dot(T.dot(T.dot(L, A), A.T), L.T))\n",
" cov = pm.Deterministic('cov', T.nlinalg.matrix_inverse(wishart))\n",
" lp = pm.MvNormal('likelihood', mu=mu, tau=wishart, observed=data)\n",
"\n",
" start = pm.find_MAP()\n",
" step = pm.NUTS(scaling=start)\n",
" trace1 = pm.sample(4000, step)\n",
"\n",
"pm.traceplot(trace1, vars=['mu','cov']);\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Using LKJ prior\n",
"\n",
"Code steal from [Austin Rochford](http://austinrochford.com/posts/2015-09-16-mvn-pymc3-lkj.html)\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" [-----------------100%-----------------] 4000 of 4000 complete in 6.1 sec"
]
},
{
"data": {
"image/png": 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roWAVCRj+WkJVW5DYLJEIxlsZmhBCCA94mWBVKaV2A/8GvFNr/c/r7uBAOr35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\nmZmZmZmZNZCTLDMzMzMzswb6/yW56u8LMxBWAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11594eeb8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with pm.Model() as model:\n",
" sigma = pm.Lognormal('sigma', np.zeros(2), np.ones(2), shape=2)\n",
" \n",
" nu = pm.Uniform('nu', 0, 5)\n",
" C_triu = pm.LKJCorr('C_triu', nu, 2) \n",
" \n",
" C = pm.Deterministic('C', T.fill_diagonal(C_triu[np.zeros((2, 2), dtype=np.int64)], 1.))\n",
" \n",
" sigma_diag = pm.Deterministic('sigma_mat', T.nlinalg.diag(sigma))\n",
" cov = pm.Deterministic('cov', T.nlinalg.matrix_dot(sigma_diag, C, sigma_diag))\n",
" tau = pm.Deterministic('tau', T.nlinalg.matrix_inverse(cov))\n",
" \n",
" mu = pm.MvNormal('mu', 0, tau, shape=2)\n",
" \n",
" x_ = pm.MvNormal('x', mu, tau, observed=data)\n",
" \n",
"n_samples = 4000\n",
"n_burn = 2000\n",
"n_thin = 2\n",
"\n",
"with model:\n",
" step = pm.Metropolis()\n",
" trace2 = pm.sample(n_samples, step)\n",
" \n",
"pm.traceplot(trace2, vars=['mu','cov']);\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Show result"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean [ 4.91518801 -2.46321866]\n",
"Mean from GMM [[ 4.93281652 -2.46133614]]\n",
"Mean from Wishart Prior [ 4.89856663 -2.46438004]\n",
"Mean from LKJ Prior [ 4.89421438 -2.45729213]\n",
"Covariance Matrix\n",
"[[ 4.61318204 1.86921658]\n",
" [ 1.86921658 1.7017805 ]]\n",
"Covariance Matrix from GMM\n",
"[[[ 4.34937923 1.59778999]\n",
" [ 1.59778999 1.52559885]]]\n",
"Covariance Matrix from Wishart Prior\n",
"[[ 4.40210136 1.58589339]\n",
" [ 1.58589339 1.5406136 ]]\n",
"Covariance Matrix from LKJ Prior\n",
"[[ 4.96512434 1.62885662]\n",
" [ 1.62885662 1.60896414]]\n"
]
}
],
"source": [
"print (\"Mean \", mean)\n",
"print (\"Mean from GMM\", g.means_)\n",
"print (\"Mean from Wishart Prior\",np.mean(trace1['mu'], axis=0))\n",
"print (\"Mean from LKJ Prior\",np.mean(trace2['mu'], axis=0))\n",
"\n",
"post_cov1 = trace1['cov'].mean(axis=0)\n",
"post_cov2 = trace2['cov'].mean(axis=0)\n",
"\n",
"print (\"Covariance Matrix\")\n",
"print (covariance)\n",
"print (\"Covariance Matrix from GMM\")\n",
"print(g.covars_)\n",
"print (\"Covariance Matrix from Wishart Prior\")\n",
"print(post_cov1)\n",
"print (\"Covariance Matrix from LKJ Prior\")\n",
"print(post_cov2)"
]
}
],
"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": "3.4.3+"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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