{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# LKJ Prior for fitting a Multivariate Normal Model\n", "\n", "Author: [Austin Rochford](http://www.austinrochford.com)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Outside of the [beta](https://en.wikipedia.org/wiki/Beta_distribution)-[binomial](https://en.wikipedia.org/wiki/Binomial_distribution) model, the multivariate normal model is likely the most studied Bayesian model in history. `PyMC3` supports sampling from the [LKJ distribution](http://www.sciencedirect.com/science/article/pii/S0047259X09000876). The LKJ distribution represents the distribution on correlation matrices and is conjugate to the multivariate normal distribution. This post will show how to fit a simple multivariate normal model using `pymc3` with a normal-LKJ prior.\n", "\n", "First, we generate some two-dimensional sample data." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from matplotlib.patches import Ellipse\n", "from matplotlib import pyplot as plt\n", "import numpy as np\n", "import pymc3 as pm\n", "import scipy as sp\n", "import seaborn as sns\n", "from theano import tensor as tt" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(3264602) # from random.org" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "N = 100\n", "\n", "mu_actual = sp.stats.uniform.rvs(-5, 10, size=2)\n", "\n", "cov_actual_sqrt = sp.stats.uniform.rvs(0, 2, size=(2, 2))\n", "cov_actual = np.dot(cov_actual_sqrt.T, cov_actual_sqrt)\n", "\n", "x = sp.stats.multivariate_normal.rvs(mu_actual, cov_actual, size=N)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "var, U = np.linalg.eig(cov_actual)\n", "angle = 180. / np.pi * np.arccos(np.abs(U[0, 0]))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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c2dlmGAxxcLk8codFNGDV1dW4+uoJcodBImExSkQUhkpKzmP//r1IS0tBdnY2\ntFpOyVP48Pl8MJt5IEO4YDFKRBRGWnqGbobH44HFwl/WFH68Xi/S041c8xxGWIwSEYWBlp6hRSgu\nLkZWlomn0lDYqqqqwi23zJY7DBIRi1EiIpWz2WzYtWsbDAYDcnLYAJzCW2xsHBISEuUOg0TEYpSI\nSKW8Xi927NgGh4M9QykyOBwODBkyTO4wSGQsRomIVOjEieM4evQwjEYjTCaeJ0+RobGxEWPHjpM7\nDBIZi1EiIhVxOOqxbdsW6HQ6WCyckqfI4fF4kJlphlbL83rCDYtRIiIVEAQBe/fuQnl5GbKysvgL\nmSKO3V6F2bPnyx0GSYDFKBGRwtntdmzf/gWSkpKQnc12TUpjt9tRWLgPTqcTBoMBubkTkZGRIXdY\nYSUQCMBgSER8fLzcoZAEWIwSESlUIBDAnj27YLVW8Cx5hbLb7cjPz4NOp4NGo4HT6UR+fh7mzVvA\nglREVVVVuPbaG+UOgyTCeR4iIgWy2Wz4/PNP4XY3wWw2sxBVqMLCfW2FKABoNBrodDoUFe2XObLw\notXqkJmZKXcYJBGOjBIRKUggEMDOnTtQU2OLuCJUjdPdTqcz6HvUMkLaKFNE4cfhqMfIkaPkDoMk\nxJFRIiKFsFor8fnnn8Lnc8Nkiqxp+dbpbpvNhqamJthsNuTn58Fut8sdWrcMBgMEQejwMUEQYDAk\nyBRR+HE6mzB69Fi5wyAJsRglIpKZ3+/H9u1bsGfPDpjN5ojcpKHW6e7c3Inw+/1tBakgCPD7/Rg/\nfoLMkYWHxsZGDB06IqL+MItEnKYnIpJRRUU5du3ajvT09LBuXt/TFLxap7szMjIwb94CFBUVwuls\ngMGQgPHjJyh+eYFa1Nc7cPPNt8gdBkmMxSgRkQz8fj927NiKurrasG9e35sd5waDIaggVct0d0ZG\nBmbOnCV3GGHH5XJh0KAh7KkbAfgdJiIKsbKyC/j88+UABJhMJrnDkVxvpuA53U2XqqmpxfjxuXKH\nQSHAkVEiohDx+XzYvn0rGhrqYLFETvP63kzBc7pbPGrsSnApl6sJgwYNgU6nkzsUCgEWo0REIVBS\nch779+9Beno6MjPDfzS0vd5OwXO6e+DCpQl/TU0tJk+eJncYFCKcpicikpDX68XmzRtw+PABWCwW\nxMXFyR1SyHEKPnTU2pWgPZerCUOGDOOoaAThyCgRkUTOnTuLwsK9yMzMhNFolDsc2XAKPnTU2pWg\nPY6KRh7dL1JIAAAgAElEQVQWo0REIvN4PNi69Qu43U3IycmROxxF4BR8aKi5KwEANDVxVDQScZqe\niEhEZ8+ewcqVKxAbG42MjMgdDSV5qH1JRG1tLa66arzcYVCIcWSUiEgEPp8PW7duhsvF0VCSj5qX\nRLSctjSco6IRiMUoEdEAVVZWYMeObTAaM1TxS5/Cm1qXRDQ0NPC0pQjFYpSIqJ8EQcDevbtgtVbA\nYsnm+dlE/VRdbcdVV03gaUsRisUoEVE/NDQ4sHHjeiQlJYb1mfJqFw4N4MNdIBCARqPF0KFD5Q6F\nZMI/QYiI+ujo0SNYt24NTKZMGAwGucOhLrQ2gLfZbGhqaoLNZkN+fh7sdrvcoVE7FRUVuOGGm+QO\ng2TEkVEiol5yu93YvHkjAIGblFSguwbwM2fOliUmjtR21NzcjMxME5KSkuUOhWTEkVEiol44f/4c\n8vM/Q0KCHqmpKXKHQ72gtAbwHKkNVl1djUmTrpc7DJIZi1Eiom4EAgFs3boZR44cQE5ODqKjo+UO\niXrJYDC09dtsJWcD+HA4qlNM9fUOjBlzGX+miMUoEVFXqqur8fnnn0IQAjAaM+UOh/pIaQ3glTZS\nKydBEOByuTBu3GVyh0IKwDWjRESXEAQBBw4UoqTkHMxmM1s2qZTSGsCr/ahOMdlsNkyadB1/tggA\ni1Eiog6cTic2b96AuLgYmM1mucOhAVJSA/jc3InIz89rm6qXe6RWLj6fD/HxemRl8eeLWrAYJSL6\nyunTJ3Ho0AGYzWYeSUiiU9pIrVysVituvXW+3GGQgohajNbU1ODZZ5/Fjh07EBcXhzvuuAOPPPII\nT1QgIkXzer3YsmUzPJ5mtmwiSSlppFYOTU1NyMkZjPj4eLlDIQURtRh99NFHodFo8Mknn6C2thaP\nPvookpKS8IMf/EDM2xARiaaiohw7d26D0WhEYmK63OEQhbXa2jpMmTJd7jBIYUQrRj0eDzIyMvCT\nn/wEgwYNAgDMnj0b+/dHZssKIlI2QRCwe/dOVFVVcjSUKASqq6tx1VXjOVtKQUQrRmNiYvDKK6+0\n/fvUqVPYuHEjvv3tb4t1CyIiUdTX12Hz5g1ISkriufIR5NLTjyZOvAaDBmXLHVZECAQCEARg+PAR\ncodCCiTJnyeLFi3CggULkJSUhIULF0pxCyKifjly5DA2bCiAyWTiufIRpLPTj1auzENVVZXcoUUE\nq7USN9wwWe4wSKH6VIy63W6UlJR0+j+Xy9X2uKeeegr//Oc/4Xa78fOf/1z0oImI+srr9WLdutUo\nK7uAnJwcThVGmK5OP9q7d6/MkYW/5uZmpKVlICUlVe5QSKH6NE1/8OBBLF68uNMmtW+99RZmzJgB\nABgzZgwA4KWXXsKdd96J8vJyZGf3fipEp+MvCeBiHpiPi5iTYMxJsEtzUlVVhS++2IjMzEzExMTI\nGZpstFpNh/9GmqYmZ9AfIBoN0NjYGLE56YwUr5O6ulrcdtvXERWlzvcovscGEzsXfSpGJ02ahOPH\nj3f6ucbGRqxatQpz585t+9jIkSMBALW1tX0qRpOS2PKhPeYjGHMSjDkJlpQUj8LCQhw7dgwjRw7j\naS8AYmMj8xzw1NQUeDzuoNOPEhISIjYn3RErJ1arFTNnTofRmCzK9eTE91jpiLaBqbm5GY888ggs\nFguuuuoqAMCRI0cQFRWFoUOH9ulaDocLfn9ArNBUS6fTIikpnvlohzkJxpwE0+m0iI+PwvLln8Pv\n9yMtzYjmZq/cYclKq9UgNjYabrcXgYAgdzgh97WvXY3z5zuefhQI+HHNNddEbE46I+brpLm5GTEx\neiQmpqO21ilShKHH99hgrTkRi2jFaEZGBmbNmoXf/va3+N3vfgen04mnnnoKixYt6vMmAb8/AJ+P\n3/BWzEcw5iQYc3JRVVUV9uzZhsTEFERFRbPQaCcQECIyH2lp6Zg7d36H048mTJgIo9EIl8sTkTnp\nzqWvk0s7EeTmTuzx5KiqKjsWLPh62Lwv8T1WOhpBEET7CWxsbMRLL72EjRs3AgDuuOMO/OIXv0BU\nVN9q3tpaJ7/hAKKitEhNNTAf7TAnwZiTjg4dOoBz54oxfPgQNDdzxKuVVqtBfHwMC692mJNgneWk\ntRNB+1Flv9+PefMWdFmQ2mxWjB8/ERbLoFCGLwm+xwZrzYlo1xPtSgASEhLwwgsviHlJIqJe8Xq9\n2LRpPQAB2dnZXB9KJJKuOhEUFe3HzJmzgx7f3NyMxMSUsChEKTRELUaJiORQVVWFrVs3hf1u+f5M\nlRINlNPpDPrjTqPRwOls7PTxdns1brvt66EIjcIE+xQQkaodOnQAO3ZsgcViCftC9NKm7fn5ebDb\n7XKHRmHOYDDg0hV9giDAYEgIemxVlQ2TJl3b5+V5FNlYjBKRKnm9XhQUrIbVWgGz2Rz20/LdTZUS\nSSk3dyL8fn9bQdq6ZnT8+AkdHud2u2EwJCInZ7AcYZKK8U8XIlKdSJmWb6+vU6VEYsnIyMC8eQs6\ndCIYP35C0BKRqio7p+epX1iMEpGqHDxYhHPnzsBisYT9aGh7BoMhqCDtaqqUSGwZGRmYOXNWl5/n\n9DwNBF81RKQKrbvlNRrAbDbLHU7I5eZO7LS9zqVTpVLh5inqCqfnaaC4ZpSIFK+qqgp5ecuh18cj\nOVn9xwr2R+tUqcmUBYNBD5PJ1G2fRzFx8xR1p6qqCpMnT5U7DFIxjowSkaJF6rR8Z3qaKpVKX/tM\nUuSoqqrCxImcnqeB4auHiBTp4rS8EJHT8krCzVPUmZbp+QQMHjxE7lBI5ThNT0SKY7PZkJe3HAZD\nPJKTU+QOJ+L1pc8kRY6qKjun50kULEaJSFEOHTqAnTu3wmKxIDo6Mto2KV1v+0xS5GiZnp/E6XkS\nBV9FRKQIfr8fmzdvhM/n5bR8CPVml3xv+0xSZOD0PImNxSgRya6xsQEbNqxFWlo6EhMNcocTMVp3\nybduTnI6ncjPz+uwS//SYnXy5KksQiOYIAg8e55Ex2l6IpLVhQslKChYDZMpC7GxsXKHE1F6OmKU\nLZ3oUuXl5Zg2bQZ0Op3coVAY4cgoEcmmsHA/ysrOIycnR+5QIlJPu+TZ0km9pDikoLa2BmPGjENK\nSqpIURK14MgoEYWcz+fD+vVrUF1tg8mUJXc4EaunXfJs6aROUoxou91u6HTRuOyyK0SMlKgFi1Ei\nCimHox55eSsQGxsbsacpKUVPu+TZ0knZ7HY7CgrWYPnyZSgoWNNWbPa0/KKvBEFAVVUVbr55hmix\nE7XHYpSIQubcubNYv34tzGauD1WCno4YZUsn5epu9FPsEe3KykpMmTKdbZxIMnxlEZHkBEHAvn27\nYbVWqnJ9qBTr75SiuyNG2dJJubob/TQYDEEFaX9HtOvr6zBs2Ah+z0lSLEaJSFJerxcbNqxDdLQO\nmZmZcofTZ71pfxTOuitWST7djX5Onjy1w2u2vyPaXq8Hfj9w5ZVXixk6URAWo0Qkmbq6WmzcuB6Z\nmUbExKjzNCUpd5SH84grSau70U8xRrQFQYDVasX8+ewnStJjMUpEkjhzphgHDuyHxWIJGsFRg9ZC\ncdeunQAAszkber0egDg7yiN9xJUGJjd3YrejnwMd0a6srMQNN0xR7R+RpC7cwEREohIEAbt27cCx\nY18iJydHtYVo6+YQAGhsbMSpUyfR1NQEQJwd5WLveKbI0tPms4Gor6/HoEGDkZXFY3kpNDgySkSi\n8Xg82LBhLWJjY2E0qnd0r32haDZn49SpkwCAiopyDB8+QpQd5ezhSQMlxXpen88Hv9+PCROugd8v\n9PwFRCLgyCgRiaK6uhorVy5HUlISEhLU3YeyfaGo1+sxatRoJCYmQqOBaCNQ7OFJSlRRUYF58+ap\nckaD1Isjo0Q0YCdPnsCXXx6CxTLwaXklbOq5dHOIXq/HsGHDYTKZRDsGs6c1f0ShZrVacf31NyI2\nNhZNTT65w6EIwmKUiPpNEATs2LENDkcdLBbLgK+nlE09oSgU1dbDUwl/JJB0nM5GmExZyMkZJHco\nFIFYjBJRv7jdbqxbtwYJCQakp6eLck0p2yj1RagKRbX08FTKHwkkDb/fD6ezCTffPFPuUChCsRgl\noj6rqqrC1q2bkJWVJeoRgUra1KOWQjEUlPJHAkmjoqICc+Ys4DpRkg2LUSLqkxMnjuHYsS8l6R8q\n5jGGJB4l/ZFA4qqqsmHChEmIj4+XOxSKYCxGiahXBEHA3r27YLfbkJ2dLck9uKlHmaT4I4FrUOXX\n0NCA9PRMDBkyVO5QKMKxtRMR9cjv92P9+rVoaHAgI8Mo2X2kbORN/ZebOxF+v7+tFdVA/0hof6hA\nU1MTbDYb8vPzYLfbxQybuuHxeOD1+nDttdfLHQoRR0aJqHsulwsFBauQlpaG2NhYye/HtZrK05cN\nXb0Z8eQaVHkFAgHYbDYsWPB1rhMlRWAxSkRdstvt+OKLjcjONkOn08kdjuwieWq5N38k9HbXPdeg\nyqu8vBwzZsxCdHS03KEQAeA0PRF14cyZYmzdugk5ORYWouDUcm90N+LZHk+fko/VakVu7jVITk6R\nOxSiNixGiSjI/v37cOzYEUl2zKtVbwutSNbbEU+x16BS79TX1yM7OwdDhw6TOxSiDjhNT0RtAoEA\nNm/eAL/fB6NRuo1KasSp5Z71dte92k6fCgdutxuABhMmXCN3KERBWIwSEYCWX1YFBauQlJSEhIRk\nucNRnEjtgdqXdbJ9ac3FjWqh4/f7UV1djQULvi53KESdYjFKRKitrcGmTetFP1EpnHRXaIXrxqa+\nHgPKEU9lqqiowKxZc7j2mxSLv3WIItz58+ewf/8erg/tQVeFFoCwPbe9Py2YOOKpLJWVFbj22uuR\nkJAodyhEXWIxShTBDh06gPPnzyInJ0fuUFShs0KroGBN2PbM5DpZdautrcXQoSNgsQySOxSibrEY\nJYpAgiBgy5bNaG5ugslkkjscVQvngi1S18mGA5fLhZiYWFx55dVyh0LUI7Z2IoowHo8Hq1blIRDw\nITU1Ve5wVC+ce2ayBZM6+f1+1Nc7MHXqdLlDIeoVFqNEEcThqMfKlSuQkpIEg8EgdzhhIZwLttZ1\nsiZTFgwGPUwmU1ishQ1ngiCgoqICM2feCq2Wv+JJHThNTxQhysouYPfuncjOzuYvKRGF+w5ybkhS\nl4qKCtx44xTEx8fLHQpRr7EYJYoAR48ewenTJ7hRSSIs2EgJqqurMWbMOJhMWXKHQtQnkg2PPPfc\nc1i0aJFUlyeiXhAEAdu3b0VJyTlkZZnlDoeIJOJ0OpGQkIhx4y6XOxSiPpNkZLSwsBAfffQRrrmG\nx44RycXn82H9+rWIjY1GWlqa3OFQO+HUJD+cnota+Xw+OJ1NmDfvNrlDIeoX0UdGvV4vnnnmGYwf\nP17sSxNRLzmdTuTlrYDBoA+LXd3hpPVUI5vNhqamJthsNuTn58Fut8sdWp+F03NRK0EQUFlZiZkz\nb+WhFaRaohejb7/9NsaMGYMbbrhB7EsTUS/U1NRg9eqVyMoyITY2Vu5w6BLdnWqkNuH0XNSqrKwM\nU6fO4M86qZqoxWhxcTE++ugjPPHEE2Jeloh6qazsAjZvXo9Bg3J4DrVChVOT/HB6LmpktVZiwoRJ\nSE9PlzsUogHp05pRt9sNq9Xa6eeMRiOeeeYZPPzww1yfRiSDkydP4PDhQ9wxr3BSnWokx9pNntAk\nn+rqagwfPhpDhgyVOxSiAetTMXrw4EEsXry403UpjzzyCAKBAO66664BB6XTsQcicDEPzMdFzEkw\nnU6LvXv34uTJU7BYsuUORxG0Wk2H/yrJxInXYOXKvLbpbUEQEAgEMGHCxH7Ha7fbsWrVyrZrNjU1\nYdWqlZg//2KDeilyIsVzCSUlv06643A4YDRm4qqrrhT92nyPDcacBBM7Fxrh0nPs+mnx4sU4cOBA\n29Sg1+tFIBBAXFwcVq1ahaws9j0jEpsgCPjiiy9QXV3NqToVqaqqwr59+9DQ0ICEhARcc801MBqN\n/b7eqlWrYLVag0YoTSYT5s6dK0bIXRL7uVD3mpqaAABz5szhhiUKG6IVozabDW63u+3f77//Pg4f\nPozXXnsNFoulTye+OBwu+P0BMcJSNZ1Oi6SkeOajHebkokAggPXrC6DTaZCRkQa324tAQJQfZ9XT\najWIjY2OmJx8+ul/0dTkCvq4Xq/HN77xTQCRl5PeUFtOvF4P6urqMW/ebZKdosb32GDMSbDWnIhF\ntD6jmZmZHf6dkpKC2NhYDBo0qM/X8vsD8Pn4DW/FfASL9Jx4vV6sXZuPpKQk6PUtbwiBgKCKX6hA\n6NY3qiknA6HXG9DY2NnaTUPQ84+UnPTlNaaGnPj9flRWVmH+/NsRCLT8MSrt/SL7PbYzzIl0uACC\nSGWcTidWrvwMqakpiIuLkzucPmNvSvHl5k6E3+9H60SXIAjw+/0YP36CzJHJI9xeY4IgoKKiAjNn\n3oro6Gi5wyESnWTF6EMPPYSlS5dKdXmiiFRTU4M1a/KRlWVCdHSM3OH0C3tTii8jIwPz5i2AyZQF\ng0EPk8mEefMWROxJSOH2GisrK8OUKdORkMAuBRSeJDkOlIjEV1Z2Abt370ROjkXVGxfYm1IaGRkZ\nmDlzltxhKEI4vcZae4lG6h8WFBk4TU+kAqdOncS+fXuQk5Oj6kIUaOlNeem+SfamJDGFy2uMvUQp\nUrAYJVK4gweLcPLkMZjNZrlDEQXXN5LUwuE15nA4kJaWgcsvv0LuUIgkx2l6IoUSBAE7dmxDY2N9\nWPVtbF3fWFRUCKezAQZDAsaPn8BpSBKN2l9jLpcLGo0OkyZdJ3coRCHBYpRIgQKBADZsKIBWq0Fq\navgdr8v1jSQ1tb7GvF4PGhoaMXfuAtUvySHqLU7TEymM1+vFqlWfIyYmGomJiXKHQ0Qh4vf7YbVW\nYfbsuZI1tSdSIo6MEimI0+nE2rWrYDIZVdu6iSicSXVggyAIKC+vwOzZc9lLlCIOi1EihaipqcHG\njetgsWRDp9PJHU5EC9UJUaQurc30W3uYOp1O5OfnidLTtby8HFOmTGMvUYpInAcgUoDy8lJs3rwe\ngwblsBCVWbid3kPikaqZvtVqxfjxE8NqoyJRX3BklEhmp06dxNGjh5GTkyN3KBGlq9HP7gqOmTNn\nyxw1yUmKZvrV1dUYNmwkhg4dNtDwiFSLxSiRjA4ePIDS0vNh00NULbqbbpX69B4uAVAvg8EQ9PoY\nSDN9h8OB1NR0XHHF18QKkUiVOE1PJJO9e3ehoqKUU3My6G70U8rTe7gEYODsdjsKCtZg+fJlKChY\nE9LcidlMv6mpCVqtDtdee73YYRKpDotRohATBAHbt29BbW0N0tLCr4eoGnQ3+inl6T2tRbDL5UJx\n8WkcP34M58+fxZYtmwd87UggdzHf2kzfZMqCwaCHyWTq1+Yll8sFt9uDadNuYS9RInCaniikBEHA\npk3rIQgBpKSkyB1OxOpuulXK03ucTidcLhdOnToJjUYDjUYDr9eL/fv3YcqUmzld3wMlrOcdaDN9\nt9uNxkYn5syZz0KU6CssRolCJBAIYN26NYiNjYFez2b2csrNndhhzeilo59Snd5jMBhw+PDBtkK0\nVWxsLDdI9YLU63ml5vV6UVtbh7lzF7CpPVE7/GkgCgGfz4dVq1YiPj4Oer1e7nAinljTrX2VmzsR\nzc2etn8LggBBEGA2Z6umoJKTlOt5peb3+2GzVeHWW+chKorjQETt8SeCSGIejwerV+chLS0NsbGx\ncodDX5Hj7PKMjAxMnDgRR44chtfrRUxMDLKyzIiPj1dFQSW3nka0lSoQCKC8vBzz5t2OmBierEZ0\nKRajRBJyuVxYvXolTKZMHvFHAIApU25GQ0OD6goqJZByPa9UBEFAaWkZbr11HuLi4uQOh0iRWIwS\nSaShwYGCgtXIzubxnkqhhB6foSyo2j/fhIQE3Hjj9UhISBb9PqEkx4h2fwmCgLKyMsycOZvHfBJ1\ng2tGiSRQU1ODtWtXw2KxsBBVCLnbAl1KEAIQBAStgRRLZ893xYoV7GkaQmVlZZgyZTqSk9k5g6g7\nHBklEpnVWolt277AoEE5bN0isoGMbCqhLRBwsUh0u92orKyAx+PBjh3bsHDhYowePVq0+3T2fKOi\ndCgs3I9bblHHyKKaVVSU4/rrJyt6CQGRUnBklEhEZWUXsH37FuTkRHYhKsUpOQMd2VRKW6DCwn1w\nu904ffoUnE4nfD4fmppc+PDDf4o6atnV821s5K59qVVWVuDqqyfCbM6WOxQiVWAxSiSSc+fOYs+e\nXSxEJZoO725kszd60xYoFEdNOp1OVFZWdOg1qtVq4fP5ev1ceqOr58u1i9Ky2awYN+5rGDJkqNyh\nEKkGi1EiERQXn8LBg4WwWCxyhyK7gRaNXRnoyGZPx3yGak2pwWCAx+MJOv0pJiZG1FHazp6vz+dD\nbm7Xu/blPPc9HNjtVRg2bBRGjRJvuQVRJGAxSjRAx48fxdGjR2A2m+UORRGkmg4faMPznhrdS1VE\nXyo3dyKionQIBAJtz0EQBGRlmUXtNdrZ873jjju6XMOotA1ealNbW4Ps7BxcfvkVcodCpDrcwEQ0\nAIcPH0RJyTmYTCa5Q1GM7s59HwgxGp531xYoVGtKMzIysHDhYnz44T/h8/naGt/HxsaK3mu0/fPV\najWIj4+By+Xp9LFK2eClRvX19UhNTcfVV7NXLFF/sBgl6qeiov2orCyD0WiUOxRFkeqUHKn7c0pV\nRHdm9OjReOihhyV7Lp11HcjM7P51qpQNXp1RQn/YrjQ0NCAuLh6TJl0vdyhEqsVilKgf9u7dhZoa\nO9LTlfELUUmkLBqlbHge6qMm+/tceirMWqfbW5+H0+lEfn4eFiy4DYMGdb27e6DFuFQFY1fPp/0S\nC7k0NTVBo9Fi8uSpssZBpHa6Z5999lm5g7hUc7MXgYA0jaDVpHVajfm4SAk52b59Kxoa6pGSkhr0\nObvdjm3btuDQoYO4cKEEyckp0Ov1ksaj0WgQHa2Dz+eHRP3T+0yv12PEiBEYO/YyjBgxUvIcXKo/\nOdHr9cjJGYSGhgYAAlJT0zBlys2yFzzttRZmLpcLPp8PTqcTJ04cR07OoLYcb9u2BS6Xq8N0u0aj\nQUNDA8aOHdNlTpKTU3DixPG2x7cW41Om3Nzj9683cfVX18/HgREjRg7o2gP52WlubkZzsxu33DI7\nrLpnKOE9VmmYk2CtORELR0aJekkQBHzxxSb4fJ5OT1RR8ggO9Y7Sj5rszbrO/vYXHciItpTrTZW4\nfMDtdqOhoRFz5swPq0KUSC4sRol6QRAEbNq0HoCApKSkTh/DDSAtlLy+T+16U5h1Nd3em/6i/S3G\npSwYQ7mWtze8Xi9qa+swd+4CaLVsSEMkBv4kEfVAEARs2LAOGg26/YWuxBGcUGN7IGn1pr1VV/1U\nu+svGoq4+qun/rCh5PV6UVVVhVtvnYeoKI7lEImFxShRN1oL0agoLQwGQ7ePlfIXslqEqldnpOpN\nYdZTP1W54uovOZ5PZ1oL0TlzFiAmRry1ckTEaXqiLrUvRHuzCSPUu7GVqLPRYZfLhcLCfWhsbOS0\n/QD1dl1nqNe+St12S+61vO0L0djYWNniIApXLEaJOtHXQhSQ/heyGly6vq+pqQknT55AYmIimpqa\nuKlLBHIXZl1RalwDxUKUSHosRoku0Z9CtFW4/kLurUtHhysqygAAZnNLf8tI3dRF6uT1emGzVWHu\nXBaiRFLimlGidloLUZ1OE/LemOHg0vV9MTFxGD16TIdcRtqmLlInFqJEocORUaKvtC9Ee9qsRF1r\nPzpcULAGNputw+cjbVMXqY/P52MhShRCHBklAgtRqSipLQ9Rb/h8PlitNhaiRCHEkVGKeCxEpcNN\nXTQQoT5AgYUokTxYjFJEYyEqvUjf1EX9E+rjdVmIEsmH0/QUsViIEilXKA9QYCFKJC8WoxSRWIgS\nKVuojtdlIUokP07TU8RhIUrUs1Cv17zUpQcoAOJ3YvD5fKipqcX8+bdBp4sW7bpE1DccGaWIwkJU\nfHa7HQUFa7B8+TIUFKyB3W6XOyQaoNb1mjabDU1NTbDZbMjPzwvp91bqTgwtI6JW3HnnnRwRJZIZ\ni1GKGHIWouFasCmhaCHxhXK9ZlcuPUDBZDKJtnmpdWp+/vzbWYgSKQCn6SkiyF2IhnJXcCh1V7Tw\nuE/1CtV6zZ5I0YmBa0SJlEfUkdFjx45h7NixGDduHMaOHYuxY8fizjvvFPMWRH0m99S8EkaZpKKU\nooXEZTAY2qbHW4XDyVksRImUSdSR0dOnT+Oyyy7Du+++2/ZGFhXFwVeSz8VCFLKtEQ3ngi0Um0wo\n9HJzJ3YYzQ+Hk7NYiBIpl6gjo8XFxRg+fDjS0tKQnp6O9PR0JCcni3kLol7rWIjKVxyF6ygTwOM+\nw5WU6zXlwEKUSNlEHbYsLi7GmDFjxLwkUb8opRAFxBtlkrvVTmci8bhPJX4fpBAuJ2exECVSPo1w\n6ZDNAMydOxfDhg1DSUkJGhsbcdNNN+GXv/wlEhL6VgzU1jrh8wXECku1oqK0SE01MB/t9CYngiBg\n8+YNAAKyF6Kt7Hb7gAq2SzdBtRa08+YtQGamEfHxMXC5PAgERPtxVjWtViNJTrr7Pii9IJUqJ0rm\n9Xphs1V1WYjyPTYYcxKMOQnWmhPRrteXB7vdblit1k4/l5aWhpKSEgwePBgvv/wyHA4HXnzxRfzq\nV7/Cn//85z4FpdOx4xRwMQ/Mx0W9ycnWrV8ACCAxMTFEUfUsM9OI2bP7v7u8qGg/oqKiOmyC0mg0\nOHCgELfeeiuAlmKDWrTmQuycdPd9mDVL2d0DpMqJUnk8HtTUVOP22+9ATExMp4/he2ww5iQYcxJM\n7Fz0qRg9ePAgFi9eHLQZAwDeeust7N69G3FxcdDpdACAl19+Gd/85jdRVVUFo9HY6/skJcX3Jayw\nx9BVCiAAACAASURBVHwE6yon27dvh9/vRmZmeogjkpbH04yYmOAfV7fbhdjYlpNjWv9LF4mdk+6+\nD/HxnRc8ShMJr5Pm5mZ4PC4sXnxPrzbR8j02GHMSjDmRTp+K0UmTJuH48eO9fvyIESMAAFartU/F\nqMPhgt/PoXCdToukpHjmo53uclJUVIiKilKkpaXD5fLIFKE0YmLiUFfnCNq1npoaD7fbi9jYaLjd\n3oiZfu2JVquRJCfdfR+U/pqTKidK43K54HQ2Yc6ceWhocANwd/lYvscGY06CMSfBWnMiFtE2MBUX\nF+Ouu+5CXl4eLBYLAODo0aOIiorCkCFD+nQtvz/AdRntMB/BLs3JsWNfoqSkBEZjRlj+oh0/fkKn\naxWvvjq37fkGAoKin7scG3/Ezklvvg9Kp/TXyUA4nU54PF7MmjUXgqDp9fsm32ODMSfBmBPpiFaM\nDh8+HEOHDsVvfvMbPP7446ivr8ezzz6Lu+++W1Fr9yj8FBefwunTJ2EymeQORTJq37XeuvHH7Xaj\nsrICHo8HO3Zsw8KFizF69Gi5w+s1tX8fwlljYyMCAWDWrDmdLiUjIuUSdTe91WrFCy+8gN27d0Oj\n0eC2227DY489hujovq1R4o61FtzBF+zSnJSUnMOBA4XIysqSOzTZqGGXdEHBGpw7dw6nT59q2/QT\nCASg1+vx0EMPi17M9ZSTSGnP1J4aXif95XA4EBUVg6lTp/WpEOV7bDDmJBhzEkzW3fQ9MZlMePPN\nN8W8JFGXKirKUVi4D9nZ2XKHQj1wOp2orKxoK0QBQKvVwufzhfwc+0vbMzmdTuTn56miPRMFq6+v\ng16fiBtvvEnuUIion9ingFTJbq/Czp3bWIiqhMFggMfjCdr4ExMTE/JjUQsL97UVokBLeyadToei\nov0hjYMGrra2BikpaSxEiVSOB8eTZCoqyrFx43o4HPVISkrG9Om3wGweePFYV1eHTZs2tG2UI+XL\nzZ2IHTu2wePxQKvVQhAECIKArCwzAgEBBQVrQjZl7nQ6g6ZyW0ZIQ1sU08BUV9uRlWXh0bNEYYAj\noySJiopyLFnyDkpLL6ChoQGlpRewZMk7qKgoH9B1GxsbkZeXh5ycHG5SUJGMjAwsXLgYer0eUVFR\nMBgMGDlyFPx+P2w2K2w2G5qammCz2ZCfnwe73S5ZLAaDAZculRcEQTGndVHPqqpsGDRoKAtRojDB\nYpQksXHj+qCTaqKiorBp04Z+X7O5uRlr1uQjOzubhagKjR49Gg899DCmTp2GK6+8EsOGDYPJZEJC\nQmJIp8xzcyfC7/e3FaSt7ZmUVtjY7XYUFKzB8uXLUFCwRtICXU2s1kqMHDkGV1xxpdyhEJFIOE1P\nknA46judCnU46vt1Pa/Xi9WrVyI72/zVCV9+EaKkUMvIyMDMmbPa/r18+bKQT5kPpD1TqHbhc5NV\n5yoqKnDlleMxbNhwuUMhIhGxGCVJJCUlw+EIPqkmKSm5z9fy+/1YtSoPmZkZbUfNUngwGAxBazhD\nMWV+aVHcG6EsELvbZBXKzgNKIQgCysrKcO2118NiGSR3OEQkMk7TkySmT78FPp+vw1Soz+fDtGkz\n+nSdQCCAtWvzkZqaguhodZz9Tb2nlilzILS78LnJ6iJBEFBaWoobb5zKQpQoTHFklCRhNmfj/vsf\nwObNG1Bf37Kbftq0GX3aTS8IAtavXwODwYC4uDgJoyW5qOlEo1AWiHKNGCtNIBBAaWkpbrllNlJS\nUuUOh4gkwmKUJGM2Z+N//mdRv75WEARs3rwB0dHRiI+PFzmy8GG321FUtB8eTzNiYuIUW8h1pz9T\n5nIIZYGYmzuxw5IAJY8YS8Xv96O8vBy33joPCQk8UpoonHGanhRpx45tCAT8MBjEO24s3LSuYQxl\nW6RIFsolBa0jxiZTFgwGPUwmU0RtXvJ6PaistGLevNtZiBJFAI6MkuLs3bsLTmcDUlJS5A5F0SJ9\nk0uoz5cP9ZICtYwYi83tdqOmphbz5t2GmBiuEyeKBCxGSVEOHixCdbUdaWlpcoeieJG8yUWu1keR\nWiCGisvlgtPpxLx5tyEqir+eiCIFf9pJMY4fP4rS0hIYjUa5QwkS6lG43ojkTS6RPiocjpxOJ7xe\nL269dT60Wq4gI4ok/IknRbhwoQQnTx5TbCGqxLWZamqLJLZIHhUOR3V1ddBqozBz5hwWokQRiD/1\nJLuamhrs3bsLWVlmuUPpVCj7S/bFxU0uJuj1kbXJhefLhw+7vQppaRmYOnUaj/klilCcpidZuVwu\nbNq0Djk5OXKH0iUlj8JlZGRg1qzZiI+PgcvlQSAg9PxFYYCtj8JDZWUlRo0ai3HjLpM7FCKSEYtR\nko3P58PatfnIzs5W9IhIJK/NVCo1NcunYK3He06YMAlDhgyVOxwikhmLUZKFIAgoKFiN9PR0xZ83\nz1E4ZeLOdnUKBAIoKyvDlCnTFblGnIhCj8UoyeKLLzYhPj4OsbGxcofSI47CDZwSuxFQ6Pl8PlRW\nVmL27LlsZk9EbViMUsjt378XXq8bycnJcofSa2obhVNS8SdXT1BSlovN7G9XxR+hRBQ63E1PIXXi\nxDFUVlaoqhBVG6W1olJqNwIKHafTCaezCfPnsxAlomAsRilkysou4PjxozAaORomJaUVf0ruRkDS\na+0hOnv2XMWvDyciebAYpZCoqanB7t07YTYrs5doOFFa8ceeoJGrutqO9HQje4gSUbdYjJLkWnuJ\nWiwWuUOJCEor/iL5pKhIZrVaMXToCEyYcI3coRCRwnEDE0lKLb1Ew4nSWlH1pRuBkjZeUf8IgoDy\n8nLk5l7DHqJE1CssRkkygiBg3Tp19BINJ0psRdWbbgTcda9+gUAApaVlmDqVPUSJqPdYjJJkWnqJ\nxnP3rAz+f3v3HhxVmeYP/Nu5J925kAu5gdwCCXdyIRACSLjpkISgP7FqZ5XRnSp33XGdlcVRlJmd\nQa2xBsfdddxxHYvZqalxd13rt84M4uyADD9RBAIkgogRjCAk6Xtune5Op/v0+/uDSTTpENLJ6T6n\n+3w/VRTaOXQ/efKm8+R9z/u8kdaKChh749WmTXcoHB3dyo0eokbceSd7iBJRcFiMUkicPXsaAwP9\nyMjIUDoUihBq23hF4+fxeNDV1Y3a2m385ZOIgsZilGQ32EtULS2ceB9iZNDr9QEFKXfdq5/T6YTH\n40Vt7VbejkNEE8Ld9CQrtfUSVVsD+HCz2Ww4dOh/8dZb/xeHDv2vqj9v7rqPPF/1EP0GC1EimjAW\noySb7u4u1fUSVVsD+HCKtEJ8cONVbm4e9PoU5ObmcvOSirGHKBHJhcv0JAu3240jRw5h2rRpSocy\njJbvQ4zEDUGRuPFKi8xmM4qK5mH+/IVKh0JEUYAzozRpfr8fhw//ryp7iaqtAXw4abkQp9AQQqC9\nvR1LlpSyECUi2bAYpUl7770/ISMjXZX3jGn5PkQtF+IkP0mS0NbWjjVratjMnohkxWKUJuXcuWZ4\nvQNISkpSOpRRafk+RC0X4iQvj8cDi8WKLVu08b1DROHFe0Zpwq5fv4Zr164gNzdP6VDGpNX7ENV4\nEhNFnt7eXggB1NU1qHL1g4giH4tRmhCHoxenT59U3YYlGk6rhTjJw2azIjt7KpYvX6m6+8GJKHqw\nGKWg+Xw+HDlyCAUFBUqHQkQhIISAyWTC/PkLMW9eidLhEFGUYzFKQRFC4OjRw8jKykJMDG85Joo2\nkiTBaDSiunqt6m/BIaLowGKUgnL27GnodDqeP/1nPGqUoonH44HdbsfmzVtgMLDrAhGFB6e2aNyu\nXPkCJlMH0tLSlA5FFSLthCOisfT19cHpdKGubhsLUSIKK86M0rj09HSjufkMNyx9jZpPOOKMLQXD\nbrcjLS0DNTWbuFGJiMKOM6N0S16vF0eOHEZhYaHSoaiKWk844owtBcNkMmLGjFmorl7DQpSIFMFi\nlMYkhMC77/4Rubk5/EE1glpPOBqcsXW73Wht/RyffdaCq1ev4Nix9xSNi9TF7/ejra0NFRUrsGDB\nIqXDISINYzFKYzp58kMkJiYgPj5B6VBUR60nHDmdTrjdbly+fAlOpxNerxculwtnz57m7CgBALze\nAXR0dGDjxjtQUMBbb4hIWSxG6aYuXfoMXV02bma4CbUeNarX69HR0Q6dTjdsNjsxMRHNzWcVjIzU\nwOl0oru7F/X1dyEtLV3pcIiI5N/A9NJLL+GNN96Az+fDHXfcgT179iAhgbNqkcZms+GTT87zPtFb\nCPUJRxPZiFRWVoH33vt/Q/8vhIAQAvn5BYrfz0rKstvtiI1NwJYt9bzthohUQ9Zi9Be/+AX+67/+\nC//8z/+M5ORk/MM//AP+9V//FY899picL0Mh5vF4cOzYERQWKr98N7IYq6hYjunTtXHy0+BGpMEd\n+06nEwcPHrjl7Gt2djbKysrxyScXMDDgRUJCPPLzC5CcnByW+1m5k1+dzGYzFi9egNmzS+Dz+ZUO\nh4hoiGzL9H6/H7/61a/wxBNPoLKyEosXL8ajjz6KCxcuyPUSFAZCCBw+/L/Iy8tXfOZktF3hb799\nAFarVdG4wmWs1lG3cvvtNZgxYyZKSkowZ04RkpOTw3I/K3fyq48QAm1tbVi2rBTl5crez0xENBrZ\nitHLly+ju7sbGzZsGHqsrq4O+/fvl+slKAw++OA9GAx6xMUp34L2ZsXY6dOnFY4sPCbTOkqp+1kn\nU0CT/Hw+H9rb21BTsxEzZsxSOhwiolHJVnFcv34d6enpaGpqwj/90z+hq6sLmzdvxq5du3jPaIS4\nePECnM4+ZGZmKh0KgJsXY3192rjvUa/XB+QgmNZRob6fdTRq7b2qRW63G729vait3cbje4lI1YIq\nRj0eD8xm86gf6+vrg9vtxosvvoinnnoKkiThBz/4Afx+P/bs2RNUULGx3OQPfJWHcOTDbDajtfUz\n5Oer535Mg8EAl8s1orgRMBgMiImJ/s0XFRXL8fbbX90zKoSA3+9HeXnFsM9/8L/VkJPRvmZCCBgM\nqWGNT005UUJ3dw8SEhLQ0HAXYmKGv4/w/fUrzEkg5iQQcxJI7lzoxMiu3WNobGzEjh07Rr2X8Kc/\n/Sl27tyJ3/zmN6ioqAAAvPvuu9i1axc++ugj+SIm2Xm9XrzxxhsoLCxU/D7Rr7Narfjtb3+LuLi4\noWLM5/Nh27ZtyMnJUTq8sLBarThz5gwcDgcMBgOWL1+u6s+dXzPlmUwmzJo1CytWrFA6FCKicQmq\nGB3L6dOnsWPHDhw/fnxombe1tRV1dXXDHhuP3l43JIm7PWNjY5CWlhzyfBw69AckJSWp8naKGzuz\nz6Kvrw8GgwEVFRUoLMyHx+OF3y/L0I14MTE6JCbGqyYnI79mZWXlYd9NP96c2Gw2nD17Bk5nH/R6\nA8rLI3fnv9/vR0dHByorV+K222YEfDxc7yeRhDkJxJwEYk4CDeZELrLdMzp//nzEx8ejpaUFq1at\nAnCjGNXr9cjIyAjquSTJz9YjXxPKfHz88Tn4fBLi4uJVUciMlJmZhY0bv7rvcXDZ1e8XqoxXSWrJ\nycivGQDF4horJyNbZ/X1OXHgwO9VcXBBsDweDzo77di48U4YDKljvl/w/TUQcxKIOQnEnISObIv+\nBoMB27dvxzPPPINz586hubkZP/3pT7F9+/ahe5ZIXex2O1pbLwf9ywJRNIiWnf/d3d0YGPChru4u\nGAypSodDRBQ0Wfv37N69G/v27cNDDz0EANi6dSt27twp50uQTHw+H44d+xMKCpTfsMQm6aSEaNj5\nbzKZMGPGLCxdWqp0KEREEyZrMRoXF4fdu3dj9+7dcj4thcCxY0eRlZWl+IaliZ4yRDRZk22dpSRJ\nktDRYURV1SoUFCh/UhoR0WRw/VyDWlouYmCgH0lJSUqHEjVLpRR5ysoqIEkSBvdwCiHCckrVZLnd\nblgsVtx5Zy0LUSKKCsofs0Nh1dPTjU8//QSFhYVKhwIgOpZKKTINnlLV3NwEp9MBvd6A0tLw7/wP\nRldXJxITk1Ffv4334hNR1GAxqiF+vx9Hj76L/Px8pUMZEslLpRT5lDilaiKEEDCZTJgzZx4WLVqs\ndDhERLLir9Ya8v777yEzM1NVMyqRulRKFC6SJKGtrQ0rV1azECWiqMSZUY34/PNLcLn6kJWVpXQo\nw0TiUimFj9Y7LbhcLjgcDtTWNqjiHm8iolBgMaoBfX0OnD//EaZNU+dmh0hZKpWL1gus8dJ6pwW7\n3Q6DIRV1ddsU73pBRBRK6lmvpZDw+/04cuSwKvqJ0lcFlsVigcvlgsViwcGDB2Cz2ZQOTXW02mlB\nCIH29nbMmjUHa9asYyFKRFGPxWiUO3HiONLT01R1n6iWabXAmggtdlrwer1ob2/D6tXrUFKyQOlw\niIjCghVKFLt69Qq6uzuRkpKidCj0Z1ossCZKr9cPbWwbFM2dFpxOJ7q6elBbuw05OTlKh0NEFDYs\nRqOUy+VCc/Np/lBTGa0VWJOhpU4LNpsVCQnJqK2tR2JiotLhEBGFFYvRKCSEwJ/+dAh5eerpJ0o3\naKnAmqzBTgu5uXnQ61OQm5sbdZuXBu8PnTt3PqqrV/P+UCLSJO6mj0KnT5+EXp+C2NhYpUOhEdjK\nKjjR3GnB6x2A2WzBunUbkZmZqXQ4RESKYTEaZUwmI8xmI3Jz85QOhW4imgssGh+Hw4GBAS/q6rYh\nISFB6XCIiBTFYjSKSJKEkyePq+q4TyIazmQyIT+/EBUVlVyWJyICi9GocvLkcWRmZvIHHE0YG/KH\njs/ng8lkwsqVq1BQoM4DKIiIlMANTFHCbDbBbrfxyECaMDbkDx2Hw4Gurm5s2bKVhSgR0QicGY0C\nfr8fJ058wOV5DRht5nLqVHnad43VkH/TpjtkeQ0tMplMKCiYhvXrl3PVgohoFCxGo8CJE8cxZcoU\nzf6g08rS8s3Oaq+v34rp0yd/3Csb8svrq2X5ahQUFCodDhGRanGZPsLdWJ63Ijk5WelQFKGlpeWb\nzVw2NclzlCgb8svH4ehFd3cPamsbWIgSEd0Ci9EI5vf78eGHHyA3N1fpUBSjpbPebzZz2dcnz8wl\nG/LLw2w2IT09E9/4Rh1PUyIiGgcu00ewEyc+RGamdpfnAW0tLev1+oDPVwgBg0GemUs25J8cn88H\no9GIqqrVnA0lIgoCi9EIZTabYbdbkJen7eb2NyvQonFpuaysYtg9o4Mzl2Vl8s1csiH/xDgcvfB4\nbjSx52woEVFwuEwfgW4sz7+v6eX5QVpaWtbCWe2RyGQyIiMji8vyREQTxJnRCHTy5AnNL88P0trS\nMmcu1cPr9cJkMmPVqtXIz598NwMiIq1iMRphLBYLbDYT8vLYU3QQCzQKtxtnyw+grq6Bs6FERJPE\nYjSC+P1+HD9+DAUFLETVRiu9TtVEqZybTEYUFt6GsrIKrk4QEcmA94xGkFOnTiAzM4M/AFVGS71O\n1UKJnHu9Xly/3obly6tQXs7TlIiI5MJiNEJYLBZYrSYkJ6coHQqNoKVep2oR7pz39vait7cXdXUN\nvD+UiEhmXKaPADd2zx/j2fMqpaVep2oRzpybTKY/L8uXczaUiCgEWIxGgJMnT2DKFC7Pq5WWep2q\nRThy7vV6YTabUVXF3fJERKHEZXqV6+7uhtHYweV5FdNSr1O1CHXOe3p64HD0obaWy/JERKHGmVGV\nO3r0KPLztX3KktpprdepGoQq50IIGI0dmD17LpYsWSZTtERENBYWoyp25UorJElCTEwM/H6hdDg0\nBvY6DT+5c+5yudDT04116zYiI2OKbM9LRERj4zK9Svn9fjQ3N3F2jSgMzGYz4uOTUF9/NwtRIqIw\n48yoSjU1nUV6errSYRBFNa93AGazBStWVKGwcLrS4RARaRKLURVyu924du0KbruNPxyJQqWz0464\nuATU19+F+Ph4pcMhItIsFqMq9OGHHyAvj5uWiEJBkiQYjUYsXLgYxcXzlQ6HiEjzWIyqjMVigdPZ\nh9RUvdKhUIRS6sz2SOBwOOB2u7F58xYYDOwDS0SkBtzApCJCCJw69SFyc6cqHQpFKCXObI8EN1o2\nGZGRkYna2gYWokREKsJiVEU+++xTJCUl8qQlmrBwn9keCTweDzo6OrBq1VqUly/n9xcRkcqwGFUJ\nn8+HixcvcAc9TUo4z2yPBFarFX4/sHXr3cjJyVE6HCIiGgXvGVWJU6dO8L4+mrRwnNkeCXw+H9ra\nLFi0aCmmT5+pdDhERDQGzoyqgMPRC6vVjKSkJKVDoQgX6jPbI0FPTzd6ex245557MGvWbKXDISKi\nW+DMqAocP/4+cnNzlQ6DokCozmyPBH6/H0ajEUVF81BaWoqkpCS43U6lwyIioltgMaqwa9e+hN/v\nQ2xsrNKhUJSQ+8z2SHDjXPlerF+/CenpGUqHQ0REQWAxqiAhBJqaTqOgoEDpUCaMPS1JaWazCTk5\nebj99g3cKU9EFIFkK0YbGxuxY8cO6HQ6CCGG/X306FGeKDSKjz5qQnp6mtJhTNhgT8vBVkJOpxMH\nDx5AbW09C1IKuYGBAVgsVlRVVSM/P3J/oSMi0jrZitGysjIcP3582GPf/e53kZmZyUJ0FD6fD1ev\nfoHCwkKlQ5mwsXpabtp0h8LRUTSz2WxISkpGff02nitPRBThZCtG4+LikJWVNfT/b7/9Ni5fvoxD\nhw7J9RJRpbn57LB8RSL2tKRwuzEbakFZ2XLMnDlL6XCIiEgGIWnt5PP58C//8i94+OGH2cR9FDd6\nIF6L+FZOer1+qIXQIC32tKTwsFqt8Hp9qK+/i4UoEVEUCUkx+s4778DhcOCb3/xmKJ4+4kXDrCjA\nnpYUHh6PB21t7Vi8eBlqajZyWZ6IKMoEtUzv8XhgNptH/VhOTg6Sk5MBAG+++SbuvfdeJCQkTCio\n2Njo7cXv8/lgNLaNawd9TIxu2N9qM3VqDurrt6Kp6Sz6+vpgMBhQVhbanpZqz4kSojknFosFaWnp\nuPvu/4O4uPG/XQ2+h0Tze0mwmJNAzEkg5iQQcxJI7lzoxMh11jF8fcf8SC+//DI2bNgAu92O1atX\n48CBAygqKpI12Ghw/Phx9Pb2DhXuRBSov79/6L1kxowZSodDREQhFNTMaGVlJVpaWsa85oMPPsD0\n6dMnVYj29rohSf4J/3u18vl8aGm5jIKCArjdA7e8PiZGh8TEeHg8Xvj94/6dIaoxJ4GiLSdmsxkZ\nGVOweXMd4uLi0NUV/ClKsbExSEtLjtr3kolgTgIxJ4GYk0DMSaDBnMhF9qb358+fR1lZ2aSeQ5L8\n8Pmi7wve2HgKGRlTgi4Y/H4RFUWGnJiTQJGeE4/HA6vVhpUrV6Gg4EbLs8m+D0Tre8lkMCeBmJNA\nzEkg5iR0ZC9GL126hLVr18r9tBFPkiS0t7dFdF/RaMFTo9RFCAGz2YzMzCw0NNzNo3GJiDRG9mK0\ns7OT7ZxGce5cMzIzpygdhqaMVnQC4KlRKuJ2u9HV1YWVK6uRl5evdDhERKQA2YvRgwcPyv2UEc/v\n9+PatasRfQZ9pLnZUaWpqak8NUoFBmdDs7JysHXr3YiJ4S5VIiKtkr0YpUCffPIx0tJSlQ5D9eRc\nPr/ZUaWXLl3C9OnTh13LU6PCy+12obOzG6tWrUFubq7S4RARkcJYjIaYEAJXrrQiLy9P6VBU7WYz\nmcEsn3+9mP3ssxZkZWUjJSVl6OM6nQ46nYAQYlh7Mp4aFR5CCJhMJkydmoeGhvWcDSUiIgAhOoGJ\nvtLWdp0nxozDzWYym5vPjuvfDxazFosFLpcLAwMeXLr0GVwu19A1QgjMnVvMU6MU4HK5YDQasWrV\nWlRVVbMQJSKiIZwZDbGLFz9GZmam0mGontPpDDhMIZjl85HFbH5+IRyOz2A0dmDOnKKhonPt2nUA\ngObmJjidDuj1BpSWhvbUKC0bnA3Nzy/A2rWcDSUiokAsRkOot7cHbrcbkiSxldAt6PX6gII0mOXz\nkf82JSUF8+YVo6vLDr0+JaDo3LRps7yfAAXo6+uDw+HA6tXrkJWVpXQ4RESkUixGQ6i5+Szi4mLZ\nSmgcysoqhuUp2OXz0YrZ5ORkzJxZzl3yYSZJEkwmE6ZPn4Gamk2jHh9MREQ0iMVoiPh8PtjtNly8\neEE1rYTU3Ow9OzsbtbX1E14+n2wxS/Kw2+3Q6WKwadM3YDBwUxgREd0ai9EQ+fjjc8jKypr0vZBy\nkWO3eqhlZ2dPePl8ssUsTY7H44HNZsPSpWWYPXuO0uEQEVEEYTEaItevX0NeXu6k74WUy1i71aNl\nGXsyxSxNzI0NSkZkZ+di61Ye5UlERMHj1tYQMJtNiIm5UfSVlVWoopWQWmZoKXr09PTAarVi7dr1\nqK5ew0KUiIgmhDOjIfDJJxeGlofVsnyslhlainxe7wAsFguKixdi/vwF3KBERESTwmJUZn6/Hz09\nXTAYCoceU8PyMTf40GQJIWCxWKDXG7BlSwMSExOVDomIiKIAi1GZXbr0GVJT1XcOvVpmaCkyOZ1O\n9Pb2orKyCvn5BUqHQ0REUYTFqMyuXm1V7YlLapihpcgiSRKMRiNmzJiNdes2ckmeiIhkx2JURm63\nG263W+kwiGRht9sRExOLzZu3sGcoERGFDItRGX388Tkue1PE6+/vR2dnJ5YtK8PMmbOVDoeIiKIc\ni1EZ2e1WnsFNEcvv98NsNiM7Oxf19XexVRMREYUFi1GZ9Pf3o7+/X+kwiCakp6cbHo8Xt9++HhkZ\nU5QOh4iINITFqEwuXWrBlCkZSodBFJQbPUOtmD9/IYqL53ODEhERhR2LUZmYTEZkZKQrHQbRuNw4\nxtOE9PQM1NY2ICEhQemQiIhIo1iMykCSJPT19bEYpYjQ1dUFn09CdfXt3HBHRESKYzEqg6tXryA1\nla1vSN3cbhe6urqxaNFSFBXNVTocIiIiACxGZXH16hWkpaUpHQbRqHw+H8xmM6ZNuw1r1qxHo2Fz\n/wAAGD5JREFUTEyM0iERERENYTEqA7fbhdRUvdJhEA0jhIDZbIZen4o776xDcnKy0iEREREFYDE6\nSR6PB17vgNJhEA3T3d0Fj8eLlStXY+rUqUqHQ0REdFMsRifp+vVrvF+UVMPtdsNu78SCBYtQXFzC\nVk1ERKR6LEYnqb39OlJTeb8oKcvr9aKtrQ0FBdPQ0LCOpycREVHEYDE6SS6XC8nJSUqHQRolhIDR\naERBQR5qa7ciPj5R6ZCIiIiCwmJ0EiRJgtvtApA5qeex2WxoajoDp9MJvV6PsrIK9n+kW7LbbQB0\nWLduA2bPno6uLid8Pr/SYREREQWFxegkdHV1TfrkGpvNhoMHDyA2NhY6nQ5OpxMHDx5AbW09pk7N\nkSlSiiYOhwNOpxNLl5ZhxoyZiItjqyYiIopc/Ck2CWazCQbD5Fo6NTWdGSpEAUCn0yE2NhbNzWfl\nCJGiSH9/P9rb25Gbm4/6+rswY8ZMpUMiIiKaNM6MTkJnpw3JySmTeg6n0xmw4/nGDGnfpJ6Xoock\nSTAajcjPL0R9/V2Ii+O3LRERRQ/+VJsEj8eDxMTJLdPr9fqAglQIAb2e7aK0TpIkmM0WpKam4c47\n65CSMrlffIiIiNSIy/STMDDgmfRzlJVVQJIkCCEA3ChEJUlCaWn5pJ+bIpPf74fJZERfnxM1NRuw\nYcMmFqJERBS1ODM6QUIIeDyTL0azs7NRW1uP5uYmOJ0O6PUGlJaWcze9BgkhYLFYkJCQiDVrajBl\nyuS6NBAREUUCFqMT5PP5IIQ8bXSys7OxadNmWZ6LIo8QAlarBbGxcVi5cjVycthFgYiItIPF6AR5\nPP2IjWX6aOKEELDbbRAiBhUVK5GXl690SERERGHHamqCPJ4BHrlIE2a32+H3+7F0aRmmTZuudDhE\nRESKYTE6Qf39brbYoaB1dXXD4/FgyZJSzJw5U+lwiIiIFMdqaoJcLifi4+OVDoMiRHd3D/r73Viw\nYDHmzCkK6C1LRESkVSxGJ8jt7ufMaISy2WxoajoDp9MJvV6PsrKKkHUvcDh60dfnREnJAsybV8Ii\nlIiIaARWUxMUHx8Hv1+e3fQUPjabDQcPHhg6gtXpdOLgwQOora2XtSDt63Ogt9eBuXNLsGDBQhah\nREREN8Gm9xOUlJQMn8+rdBgUpKamM0OFKHDj6NXY2Fg0N5+V5fldLhf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "blue = sns.color_palette()[0]\n", "\n", "e = Ellipse(mu_actual, 2 * np.sqrt(5.991 * var[0]), 2 * np.sqrt(5.991 * var[1]), angle=-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(x[:, 0], x[:, 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": [ "The sampling distribution for our model is $x_i \\sim N(\\mu, \\Lambda)$, where $\\Lambda$ is the [precision matrix](https://en.wikipedia.org/wiki/Precision_(statistics)) of the distribution. The precision matrix is the inverse of the covariance matrix. The support of the LKJ distribution is the set of [correlation matrices](https://en.wikipedia.org/wiki/Correlation_and_dependence#Correlation_matrices), not covariance matrices. We will use the separation strategy from [Barnard et al.](http://www3.stat.sinica.edu.tw/statistica/oldpdf/A10n416.pdf) to combine an LKJ prior on the correlation matrix with a prior on the standard deviations of each dimension to produce a prior on the covariance matrix.\n", "\n", "Let $\\sigma$ be the vector of standard deviations of each component of our normal distribution, and $\\mathbf{C}$ be the correlation matrix. The relationship\n", "\n", "$$\\Sigma = \\operatorname{diag}(\\sigma)\\ \\mathbf{C} \\operatorname{diag}(\\sigma)$$\n", "\n", "shows that priors on $\\sigma$ and $\\mathbf{C}$ will induce a prior on $\\Sigma$. Following Barnard et al., we place a standard [lognormal](https://en.wikipedia.org/wiki/Log-normal_distribution) prior each the elements $\\sigma$, and an LKJ prior on the correlation matric $\\mathbf{C}$. The LKJ distribution requires a shape parameter $\\nu > 0$. If $\\mathbf{C} \\sim LKJ(\\nu)$, then $f(\\mathbf{C}) \\propto |\\mathbf{C}|^{\\nu - 1}$ (here $|\\cdot|$ is the determinant).\n", "\n", "We can now begin to build this model in `pymc3`. As you can see, we are passing summary statistics to `testval` which will be used as the starting point when we do inference further below. When summary statistics are available, it is always a good idea to use them in this manner." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [], "source": [ "init_sigma = np.std(x, axis=0)\n", "init_corr = np.corrcoef(x, rowvar=0)[0, 1]\n", "with pm.Model() as model:\n", " sigma = pm.Lognormal('sigma', np.zeros(2), np.ones(2), shape=2, testval=init_sigma)\n", " \n", " nu = pm.Uniform('nu', 0, 5)\n", " C_triu = pm.LKJCorr('C_triu', nu, 2, testval=init_corr) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a slight complication in `pymc3`'s handling of the `LKJCorr` distribution; `pymc3` represents the support of this distribution as a one-dimensional vector of the upper triangular elements of the full covariance matrix. " ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "scrolled": true }, "outputs": [ { "data": { "text/plain": [ "(1,)" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "C_triu.tag.test_value.shape" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to build a the full correlation matric $\\mathbf{C}$, we first build a $2 \\times 2$ tensor whose values are all `C_triu` and then set the diagonal entries to one. (Recall that a correlation matrix must be symmetric and positive definite with all diagonal entries equal to one.) We can then proceed to build the covariance matrix $\\Sigma$ and the precision matrix $\\Lambda$." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with model:\n", " C = pm.Deterministic('C', tt.fill_diagonal(C_triu[np.zeros((2, 2), dtype=np.int64)], 1.))\n", " \n", " sigma_diag = pm.Deterministic('sigma_mat', tt.nlinalg.diag(sigma))\n", " cov = pm.Deterministic('cov', tt.nlinalg.matrix_dot(sigma_diag, C, sigma_diag))" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[ 0.54737873, 0.88092866],\n", " [ 0.88092866, 1.98234664]])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cov.tag.test_value" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While defining `C` in terms of `C_triu` was simple in this case because our sampling distribution is two-dimensional, the example from this [StackOverflow question](http://stackoverflow.com/questions/29759789/modified-bpmf-in-pymc3-using-lkjcorr-priors-positivedefiniteerror-using-nuts) shows how to generalize this transformation to arbitrarily many dimensions.\n", "\n", "Finally, we define the prior on $\\mu$ and the sampling distribution." ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with model:\n", " mu = pm.MvNormal('mu', 0, cov, shape=2, testval=np.mean(x, axis=0))\n", " \n", " x_ = pm.MvNormal('x', mu, cov, observed=x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We are now ready to fit this model using `pymc3`." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n_samples = 4000" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|██████████| 4000/4000 [00:05<00:00, 718.12it/s]\n" ] } ], "source": [ "with model:\n", " trace_ = pm.sample(n_samples, pm.Metropolis())" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "trace = trace_[50:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We see that the posterior estimate of $\\mu$ is reasonably accurate." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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7koYBTp1QmBYstNtNmNahTW5vCPXuzAHIUUVWHOkkm6ko3wJzh+GoBc74MYhE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JmSVWw+McYYY4wxxhhjjDHbZPGX3THGGGOMMcYYY4wx28WbT4wxxhhjjDHGGGPMbHjziTHGGGOM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\nQkqlUjgeE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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['mu']);" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([-1.41866859, -4.8018335 ])" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "mu_actual" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The estimates of the standard deviations are certainly biased." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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K0mXkNUs4iver0qEQREFV+Rbj49g3fkC1Hj2rBydwyTq13j8lzMFAPBmIPcZl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hKuW301c81zCmyZIB+UCiXnN3yBxdaFbN//JK7QADt6P2FX3x7WVp7IhjnrWGJtQKmYFo6+guOE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\nZZ555hny05/+lPT29hKz2UzMZ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "pm.traceplot(trace, varnames=['sigma']);" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.75945843, 1.50000803])" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "trace['sigma'].mean(axis=0)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([ 0.3522422 , 1.58192855])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sqrt(var)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "However, the 95% posterior credible region is visually quite close to the true credible region, so we can be fairly satisfied with our model." ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [], "source": [ "post_cov = trace['cov'].mean(axis=0)\n", "\n", "post_sigma, post_U = np.linalg.eig(post_cov)\n", "post_angle = 180. / np.pi * np.arccos(np.abs(post_U[0, 0]))" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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U1FRz/PhxVCoV77+/iNtuu4n77hvPmjVfusuOHz+RTZs2ce21IwgNDWXkyFF8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\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(8, 6))\n", "\n", "blue = sns.color_palette()[0]\n", "\n", "e = Ellipse(mu_actual, 2 * np.sqrt(5.991 * post_sigma[0]), 2 * np.sqrt(5.991 * post_sigma[1]), angle=-post_angle)\n", "e.set_alpha(0.5)\n", "e.set_facecolor(blue)\n", "e.set_zorder(9);\n", "ax.add_artist(e);\n", "\n", "e = Ellipse(mu_actual, 2 * np.sqrt(5.991 * var[0]), 2 * np.sqrt(5.991 * var[1]), angle=-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(x[:, 0], x[:, 1], c='k', alpha=0.5, zorder=11);\n", "\n", "rect = plt.Rectangle((0, 0), 1, 1, fc='gray', alpha=0.5)\n", "post_rect = plt.Rectangle((0, 0), 1, 1, fc=blue, alpha=0.5)\n", "ax.legend([rect, post_rect],\n", " ['95% true credible region',\n", " '95% posterior credible region'],\n", " loc=2);" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" }, "latex_envs": { "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 0 } }, "nbformat": 4, "nbformat_minor": 0 }