diff --git a/training_bayesian/2_mcmc.ipynb b/training_bayesian/2_mcmc.ipynb new file mode 100644 index 0000000..267d46d --- /dev/null +++ b/training_bayesian/2_mcmc.ipynb @@ -0,0 +1,1388 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2 Markov Chain Monte Carlo\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "# https://docs.pymc.io/notebooks/GLM-logistic.html" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "import pandas as pd\n", + "import numpy as np\n", + "import seaborn as sns\n", + "import matplotlib.pyplot as plt\n", + "import pymc3 as pm\n", + "from sklearn import preprocessing\n", + "from scipy import stats\n", + "from scipy import special\n", + "\n", + "# Use a theano shared variable to be able to exchange the data the model runs on\n", + "from theano import shared" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1 Recap\n", + "---\n", + "\n", + "\\begin{equation}\n", + "P(\\boldsymbol{\\theta}\\ |\\ D) = \\frac{P(D\\ |\\ \\boldsymbol{\\theta})\\cdot P(\\boldsymbol{\\theta})}{P(D)}\n", + "\\end{equation}\n", + "\n", + "---\n", + "### Example\n", + "As an introductory example, we observe two weights, 65kg, and 75kg.\n", + "\n", + "We would like to learn something about the distribution of the weights.\n", + "\n", + "![](images/weights.png)\n", + "\n", + "---\n", + "How do we model this?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.1 The data" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "weights = np.array([65, 75])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.2 Parameter space" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "# lets creat a grid of our two parameters\n", + "mu = np.linspace(60, 90)\n", + "sigma = np.linspace(0, 10)[::-1]\n", + "\n", + "mm, ss = np.meshgrid(mu, sigma) # just broadcasted parameters" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.3 Likelihood\n", + "$$ \\prod_{i=0}^N{P(x|\\theta)} $$\n", + "$$ P(x|\\theta) \\sim NB(\\theta) $$" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 22, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "likelihood = stats.norm(mm, ss).pdf(weights[0]) * stats.norm(mm, ss).pdf(weights[1])\n", + "aspect = mm.max() / ss.max() / 3\n", + "extent = [mm.min(), mm.max(), ss.min(), ss.max()]\n", + "# extent = left right bottom top\n", + "plt.imshow(likelihood, cmap='Reds', aspect=aspect, extent=extent) \n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.4 Prior" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 24, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAQ8AAAEMCAYAAADauzOQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAFmpJREFUeJzt3XuMXVd1x/Hfmhm/xgl5EIMgOATaNBRFkIdbXlWEEv4AWpFSUSlIVKFqZakSJaBWbfinoX9UKhV9/VGBXB5BgJJSFxVEJSANSVVaNW0SEnBwKCmB4GASG+LYscfzuqt/3BsxZ+3te87dc+85dzzfTzQanzPnsebkzppz16y9j7m7AGBUM10HAGBjInkAKELyAFCE5AGgCMkDQBGSB4AiE0seZvYJM3vKzA6sWXehmd1pZt8dfL5gUucHMFmTvPO4TdKbw7pbJN3l7pdJumuwDGADskk2iZnZpZK+5O5XDJa/I+mN7n7YzF4k6R53v3xiAQCYmLmWz/dCdz8sSYME8oIzbWhmeyXtlaSdO3dec/krfqGlEFFnfL9v1n+gcYViU3SU5KiTOWzFD77/uI4ePTrSmdpOHo25+z5J+yTpmj1X+3/c+/WOI8JzcnerXvBj7N4Lx0iPWneeSSUPy6yp2yf+lKfHyJ23wTYtZI83vOZXRt6n7b+2PDl4u6LB56daPj+AMWk7eXxR0k2Df98k6Qstnx/AmEzsbYuZ3S7pjZIuMrNDkm6V9OeSPmdmvyPpcUm/OanzY7qUvK0pP1nNuTJvA+reMjV5e7HZTCx5uPs7z/Cl6yd1TgDtocMUQBGSB4AiJA8ARaa2zwPTo6upKnNF1mRNSWy5fWp7KXLn2dxFVO48ABQheQAoQvIAUISaB6bIeGordQ1p42r4imfZbBUQ7jwAFCF5AChC8gBQhJoHNpYx9JzkaiIWVnkyN0eTA4eDtDGLT4e48wBQhOQBoAjJA0ARkgeAIhRM0Zm60meT0mhbM5Rli6ybri2sijsPAEVIHgCKkDwAFKHmgXY0aO5qdYb1mnPHprF8w9fwoXFN6iTJeTdQHYU7DwBFSB4AipA8ABQheQAoQsEU0ytTZG1SVG1rJrHNjjsPAEVIHgCKkDwAFKHmgYlo1vA1mVnBSvapa97KzSUW12y22dS58wBQhOQBoAjJA0ARah4Y2aQGsI3tqCUzrBfMdN7WoDYP349Nyazs3HkAKNJJ8jCz95vZw2Z2wMxuN7PtXcQBoFzrycPMLpb0Xkl73P0KSbOSbmw7DgDr09XbljlJO8xsTtK8pB91FAeAQq0nD3d/QtKHJT0u6bCkZ9z9q3E7M9trZveZ2X1HjhxtO0yMmWc+6vep/0+efuTOVXfe5LjJBplzbXJdvG25QNINkl4m6cWSdprZu+J27r7P3fe4+55duy5qO0wANbp42/ImSY+5+xF3X5b0eUmv7yAOAOvQRfJ4XNJrzWze+n+wvl7SwQ7iALAOrTeJufu9ZrZf0gOSViR9Q9K+tuNA95LaQkEdoaTykNvH4rnH0YiV+36mpMFrHDrpMHX3WyXd2sW5AYwHHaYAipA8ABRhYBw2lok9ea5uap/6fWyTTQfEnQeAIiQPAEVIHgCKkDwAFKFgikScuarwIHFFukmy7EOXm+xzpnPVC8XNSTSNqb3Zx9rAnQeAIiQPAEVIHgCKUPPA9MrUXtIaR31dJMpVGYpqESE+T3apf8pcXRyNY+kAdx4AipA8ABQheQAoQs0DY1E0GG0M/STZI9Qc1zM9G3FQmzcYKDettYi2cOcBoAjJA0ARkgeAIiQPAEUomGIimg1gG75Nfo/6Gddrz5Wd1Tz+Hg1NY7mHyCUr48xiZzfuPAAUIXkAKELyAFCEmgdqlc1Gvv7jlk8GVBJMnPwnblBSwcgVSuJhN25lhDsPAEVIHgCKkDwAFKHmgVY0qkw0mTTZe2GLXF2h5myN6gzVbXJHTI4yoUmTpxV3HgCKkDwAFCF5AChC8gBQhIIpxqNBsbP2ECVHyA6MG85y+9jwbdJBcPUzrjeZCb1k1vbcE/2sg+JsJ3ceZna+me03s0fM7KCZva6LOACU6+rO428lfdnd32FmWyXNdxQHgEKtJw8ze56kayW9W5LcfUnSUttxAFifLu48Xi7piKRPmtmrJd0v6WZ3P7l2IzPbK2mvJO2+ZHfrQWLMGkzak9QIGu2TOZV6mbVrv57WB2biqS3WIuqb0dJ90vMMnz5oY+mi5jEn6WpJH3H3qySdlHRL3Mjd97n7Hnffs2vXRW3HCKBGF8njkKRD7n7vYHm/+skEwAbSevJw9x9L+qGZXT5Ydb2kb7cdB4D16eqvLb8v6bODv7R8T9JvdxQHgEKdJA93f1DSni7OjfUrmwm9yejX+n1ig1SuOFrbJJbZIh5lplFhNh63Po6NXCCNaE8HUITkAaAIyQNAEQbGbXK5QVZFxxnDPk1mRk9qKSVPjMtUHpJxZU1qK0WD0UZvEysZPNcG7jwAFCF5AChC8gBQhJoHJqJJDSStX4SZ0UsG051hXYNgKnphkNtsg52S2kSunhTrJBt4xnXuPAAUIXkAKELyAFCE5AGgCAVTJIoKjjWzgOWPOfw8+YFx1aJqz3MD44a3n1nmd+aMxXXDi7mS5HGfMcy4vpFw5wGgSG3yMLNb2wgEwMbS5G3LrWY2L+lCSQ9IusPdn55sWACmXZPk4ZJOS/qK+nON/qeZ3ejuD000MkyvksF0DZ7sljSJNRkYlxmwlquDrJWdCT1IKiBJTSQTb9hm41YzmmmSPB5x9+feuuw3s9skfVTSdROLCsDUa1IwPWpm1zy34O7/K2nX5EICsBE0ufN4r6Q7zOx+Sd+S9CpJj000KgBTrzZ5uPtDZnalpDdJukLS3ZJun3Rg2FjqBqxluzxiz0aD3opYz1j11dptorSnIw0wPnU+/xS6mZptMnWSmuXcmmntBWnUJObui5L+ZfABADSJAShD8gBQhOQBoAgD4zCysmFzzeYWWytX+OyFAulqL1MwzRY315wl1+QWfo1aOPdMtvg5vEks9z0ns4uNqRYav6dY8J0E7jwAFCF5AChC8gBQhJoHajWpV9Q97a1kYp9cY1ZsCss2idXUPLJfD6tsploz6GUay+KkQjNJLSU3e3pcMfoT5KYFdx4AipA8ABQheQAoQs1jk8n2OIx+lNyBR1tWZiBcWM7VM5rUPHLr1soOjAvMq7WHGU+fGTdjw+OP35+UTkRU8pS5bP9IB7US7jwAFOkseZjZrJl9w8y+1FUMAMp1eedxs6SDHZ4fwDp0kjzM7CWSflXSx7o4P4D166pg+jeS/kjSuWfawMz2StorSbsv2d1SWMhqUGStmzmsyUzoTQa9rfRWqsu+kmwTj5Oc1zOD3ELxMxZVZzPH9FBETZraGhRmN7LWvzsz+zVJT7n7/cO2c/d97r7H3ffs2nVRS9EBaKqL1PgGSW8zs+9LukPSdWb2mQ7iALAOrScPd/+Au7/E3S+VdKOkr7n7u9qOA8D60CS2yTWbpGf0fZKJcnJPma+ZCT1Xz4jrVnrLyTa1TWKZ35lzM9XvaaUXah6WNonNxoF9sW6Se0pe0limocu5tdMym3qnycPd75F0T5cxAChzdpeDAUwMyQNAEZIHgCIUTDGy7KMja5rEciNMk0dHhqaw2BDWX1ctkC6XFEwzzVvei7OPh4JpLy2Yzln1x8cVl3Ozp9WUSKejFtoIdx4AipA8ABQheQAoQs0Dibr6RX6nsE8yE3qu5jG8KWw10yQWaxxLq0vJNrnmsrVyDV8+UzMwLrNPrK3Mxe/Z6gcDptcld7WnsxDCnQeAIiQPAEVIHgCKUPNAA+ufCT03MC4d5FZdXuql9YxY41hcXUy2yfV+rDU7k77sez685hF7OiRpZaYa71yogTSZcT3Kzower7fV10BiP4k12GdU3HkAKELyAFCE5AGgCMkDQBEKphhZfiaxWCCtf3RkOhN6/aC3WCBdWD2dOW51v1gMnZtJC5m92Wp8sw2axOZ6W6rHmKkeI3udYjNdzcxiTSWPrWyhsYw7DwBFSB4AipA8ABSh5nEWSyeeabxjdbF2MFd6rl6YPT33FLfYJBYbwE6vpPWMUysL1W0yNY/cYLm1ZnM1j9DENhNqHHOZxrJYW4k1nC0zmRnjY42jbnIgSR7KF9MyTI47DwBFSB4AipA8ABSh5rHJNHva2/Dl3MC4uoFwTSYzjgPhcvWMhZVTleVYA5GkxVDziHWFLbPV/gwpV/Oo/l7dkql5bJ3ZWllOJzNK6zzxKXNxoFyjHprc4LkOKiHceQAoQvIAUITkAaAIyQNAEQqmm1yTAmoskOae/hYLpLFYmJvRPCmQhqawXDH0ZCiYPrP4bLJNXcF0a6ZgGgu6sQAZi6OStH12e3WbUADOzf7u2hKWS4fCdY87DwBFSB4AipA8ABSh5oGM0Z9qVjcQLjexTxzAFif2eXY5rWccO32isnx86WSyzcJKdcKgWI/J1TyWQ80jTv6zdTZT85ir1jxiDSTXGNcLg+WSJ+s1eMpcMpu61GhG9XFr/c7DzHab2d1mdtDMHjazm9uOAcD6dXHnsSLpD9z9ATM7V9L9Znanu3+7g1gAFGr9zsPdD7v7A4N/n5B0UNLFbccBYH06rXmY2aWSrpJ0b+ZreyXtlaTdl+xuNa7Nrm7yn9wkQ3FgWXy/v5x5+lsc+HZquVq/OL6Y1jOePn28snwss82p5Wp9Je3zSCcDWu7FCZBjzSOtk+ycm68sL81Vv8dcb0u8Tk2ubZwMqETuuOt9ilxnf20xs3Mk/ZOk97n78fh1d9/n7nvcfc+uXRe1HyCAoTpJHma2Rf3E8Vl3/3wXMQBYny7+2mKSPi7poLv/VdvnBzAeXdx5vEHSb0m6zsweHHy8tYM4AKxD6wVTd/+6pmcCaGRnBRu+TW4wVywELvvwWcKkdCBcOuit2hAmST89XW0cO3rqVLLNs0thYFyId/ts+rJf7lXjj0+M2zG3Ldln55adleVzVs8Jx0wb4+JguZ6HgXKZJrH0KXPpJnFVG0+Qoz0dQBGSB4AiJA8ARRgYdxYpeUJckz3iNrG+0V8XJv/pDX8anFQ/sU9sCJOkp06eHLosSadP10wGtDU3MK76PW2Zqf5ePWfLjmSf87adW1mOA/t2Zmoe8bpsnW3wNL4GAxPbqHFE3HkAKELyAFCE5AGgCDWPs1jx5LpJX0cczJXWPOIgsPg0uNOr1Ql6JOlUTc3jSKaHI9Y4njmWThgUax69UM/Yti2d2Gd1dXjN49ytaZ/HedurNY/ztp5XWc73eVRrQ8lkQJl60rR2RXHnAaAIyQNAEZIHgCIkDwBFKJhuMiUNR7HJKtckFguBsVgYB8FJ0rNL1YJonBn9JwtpwfT4M/UF01ML1eJsk4Jp3GbLlupMYhfsSJvEnh9mbl8IBeBcY1wsLMfrNtfgaXxu6e/8ZEb1FmZT584DQBGSB4AiJA8ARah5oFbdbOpSbrb02CSWqXksx5pHdZunn11I9jlxvFpnePp4WvM4eap6nF6vGu+O7WnNI9q2rTp47un5+WSbWLOJA+NyEyCthuuUNIU1mD29sPVv7LjzAFCE5AGgCMkDQBGSB4AiFEw3uWYzV1U1axJrMJPYUrUgemyx2tx16mRaMD1+IozEPZHOJNY7Hs4VCqYn5tPRrjNhFO38fHUU7bHz01HBz4b4T69UtylpEusV/P/oCnceAIqQPAAUIXkAKELNY7NpMsN6nEmswWxXcV2cSSz/xLhqjeBkeNLbwkJaZzi5EBrAYn1Dkp4J+8VwV9L4T26rHndhIcRyOlOzWa5+j4uhxhHrPlKmxpFcy9H//0hpI1kbk49x5wGgCMkDQBGSB4Ai1DwwslzfQS8UFlbDe/nc+/+lXvX9/+JKmIF9ufp1SVpcCsdZSI+rhbDfaog38ytzZTHUaJaqyyvLmfhXV8NydZv4FD0pnVgpHXSYQ58HgLMIyQNAEZIHgCIkDwBFKJhucrlSXP386k2OGxvLMkXWOCt7Ly5nBuCFImuu4StZF0+9kvmOwj7x3LlYYvx1xdAzrduoOrnzMLM3m9l3zOxRM7ulixgArE/rycPMZiX9naS3SHqlpHea2SvbjgPA+nRx5/HLkh519++5+5KkOyTd0EEcANahi5rHxZJ+uGb5kKTXxI3MbK+kvYPFxR1zOw+0EFtTF0k62nUQa0xbPNL0xTRSPE/VLEvSfesKZ+quz+Wj7tBF8sgN+EuqSO6+T9I+STKz+9x9z6QDa4p46k1bTMQznJmNnAu7eNtySNLuNcsvkfSjDuIAsA5dJI//kXSZmb3MzLZKulHSFzuIA8A6tP62xd1XzOw9kr4iaVbSJ9z94Zrd9k0+spEQT71pi4l4hhs5Hss17wBAHdrTARQheQAoMnXJw8zON7P9ZvaImR00s9eZ2YVmdqeZfXfw+YKO4/mgmT1hZg8OPt7aYjyXrznvg2Z23Mze19U1GhJPl9fo/Wb2sJkdMLPbzWz7oEB/7+D6/MOgWN9lPLeZ2WNrrs+VbcUziOnmQTwPm9n7ButGew25+1R9SPqUpN8d/HurpPMl/YWkWwbrbpH0oY7j+aCkP5yCazUr6ceSXtrlNTpDPJ1cI/WbEB+TtGOw/DlJ7x58vnGw7qOSfq/jeG6T9I6OXjdXSDogaV79P5r8q6TLRn0NTdWdh5k9T9K1kj4uSe6+5O7H1G9f/9Rgs09J+vWO45kW10v6P3f/gTq6RkPi6dKcpB1mNqf+D8hhSddJ2j/4etvXJ8bTdV/TL0r6L3c/5e4rkv5N0ts14mtoqpKHpJdLOiLpk2b2DTP7mJntlPRCdz8sSYPPL+g4Hkl6j5l908w+0ebbqOBGSbcP/t3VNTpTPFIH18jdn5D0YUmPq580npF0v6Rjgx8Uqd+oeHFX8bj7Vwdf/rPB9flrM9t2xoOM3wFJ15rZ881sXtJb1W/cHOk1NG3JY07S1ZI+4u5XSTqp/u3TtMXzEUk/J+lK9V8Qf9l2YIP37G+T9I9tnzsnE08n12iQpG6Q9DJJL5a0U/0R3FErPQq5eMzsXZI+IOkVkn5J0oWS/riNeCTJ3Q9K+pCkOyV9WdJDkjIzSQ83bcnjkKRD7n7vYHm/+j+8T5rZiyRp8Dk3Tqm1eNz9SXdf9f5j0v5e/ZHCbXuLpAfc/cnBclfXKBtPh9foTZIec/cj7r4s6fOSXi/p/MHbBqndIRHZeNz9sPctSvqkWn4NufvH3f1qd79W0k8lfVcjvoamKnm4+48l/dDMnhvhd72kb6vfvn7TYN1Nkr7QZTzPXeCBt6t/G9i2d6r6FqGTa3SmeDq8Ro9Leq2ZzZuZ6WevobslvWOwTZvXJxfPwTU/pKZ+baHV15CZvWDw+RJJv6H+/7vRXkNdVHtrKsFXqj/a+ZuS/lnSBZKeL+ku9bPjXZIu7DieT0v61mDdFyW9qOVrNC/pJ5LOW7Ouy2uUi6ezayTpTyU9ov4P5KclbVO/fvXfkh5V/63Vto7j+drg+hyQ9BlJ57T8Gvp39ZPqQ5KuL3kN0Z4OoMhUvW0BsHGQPAAUIXkAKELyAFCE5AGgCMkDQBGSB4AiJA+MlZnd81xH7mDg1TQ9bwdjRPLAuP28+h2KkvQq9bsocRYieWBszOylkp7w/mA4qZ88vtlhSJggkgfG6UpVk8U1InmctUgeGKdXS9ouSWZ2mfrzWPC25SxF8sA4XSlpxswekvQnkg7qZ0O8cZZhVC3GxswelXSVu5/oOhZMHnceGAszO1dSj8SxeXDnAaAIdx4AipA8ABQheQAoQvIAUITkAaAIyQNAEZIHgCL/D2C8LBJS+4C1AAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "prior = stats.norm(80, 3).pdf(mm) * stats.cauchy(0, 2).pdf(ss)\n", + "\n", + "plt.imshow(prior, cmap='Greens', aspect=aspect, extent=extent)\n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.5 Posterior" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, '$\\\\sigma$')" + ] + }, + "execution_count": 31, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "unnormalized_posterior = prior * likelihood\n", + "posterior = unnormalized_posterior / np.nan_to_num(unnormalized_posterior).sum()\n", + "plt.imshow(posterior, cmap='Blues', aspect=aspect, extent=extent)\n", + "plt.xlabel(r'$\\mu$')\n", + "plt.ylabel(r'$\\sigma$')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.6 We can do the same with pymc3" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([65, 75])" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "weights" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Sequential sampling (1 chains in 1 job)\n", + "CompoundStep\n", + ">Metropolis: [sigma]\n", + ">Metropolis: [mu]\n", + "100%|██████████| 10500/10500 [00:01<00:00, 5297.18it/s]\n", + "Only one chain was sampled, this makes it impossible to run some convergence checks\n" + ] + } + ], + "source": [ + "with pm.Model():\n", + " mu = pm.Normal('mu', mu=80, sd=3)\n", + " sigma = pm.HalfCauchy('sigma', 2)\n", + "\n", + " observed = pm.Normal('observed', mu=mu, sd=sigma, observed=weights)\n", + " trace = pm.sample(draws=10000, chains=1, step=pm.Metropolis())" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n", + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace);" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(0, 10.0)" + ] + }, + "execution_count": 50, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(2, sharex=True, sharey=True, figsize = (8, 8))\n", + "axes[0].imshow(posterior, cmap='Blues', extent=extent, aspect=4)\n", + "axes[1].scatter(trace['mu'], trace['sigma'], alpha=0.01)\n", + "plt.xlim(0, mm.max())\n", + "plt.ylim(0, ss.max())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 1.7 Conclusions\n", + "\n", + "- Posterior is proportional to likelihood multiplied with prior.\n", + "- We 'showed' (with plots) that samples obtained with `pymc3` are from this distribution.\n", + "- `pymc3` can be used to approximate any posterior, even if we can not validate this with plots or math." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2 Intermezzo: Logistic regression \n", + "\n", + "Let's do a Baysian Logistic regression. What is the chance I'll make \\$50k?\n", + "\n", + "First we load and preprocess some data. We use **age, education and working hours** as features $X$ and we try to predict:\n", + "\n", + "$$ y = \\begin{cases}\n", + " 1, & \\text{if income > \\$50K} \\\\\n", + " 0, & \\text{otherwise}\n", + " \\end{cases}$$" + ] + }, + { + "cell_type": "code", + "execution_count": 259, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
\n", + "\n", + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
ageeduchoursmore_than_50kage_squared
039134001521
150131302500
23894001444
35374002809
537144001369
\n", + "
" + ], + "text/plain": [ + " age educ hours more_than_50k age_squared\n", + "0 39 13 40 0 1521\n", + "1 50 13 13 0 2500\n", + "2 38 9 40 0 1444\n", + "3 53 7 40 0 2809\n", + "5 37 14 40 0 1369" + ] + }, + "execution_count": 259, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "data = pd.read_csv(\"https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data\", header=None, names=['age', 'workclass', 'fnlwgt',\n", + " 'education-categorical', 'educ',\n", + " 'marital-status', 'occupation',\n", + " 'relationship', 'race', 'sex',\n", + " 'captial-gain', 'capital-loss',\n", + " 'hours', 'native-country',\n", + " 'income'])\n", + "data = data[data['native-country'] == ' United-States']\n", + "data = data[~pd.isnull(data['income'])]\n", + "data = data.assign(more_than_50k=(data['income'] == ' >50K') * 1)\n", + "education_map = dict(zip(list(map(lambda x: x.strip(), data['education-categorical'].unique())), data['educ'].unique()))\n", + "data = data[['age', 'educ', 'hours', 'more_than_50k']]\n", + "data = data.assign(age_squared=data['age']**2)\n", + "\n", + "data.head()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Make a correlation table for the features and the labels" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 35, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 8))\n", + "corr = data.corr()\n", + "mask = np.zeros_like(corr, dtype=np.bool)\n", + "# indices for upper triangle of matrix\n", + "idx = np.triu_indices_from(corr)\n", + "mask[idx] = True\n", + "sns.heatmap(corr, mask=mask, vmax=.3, cmap=sns.color_palette('Reds'))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.1 Model\n", + "Now we need to think of a model that can explain this data. It's often easiest to start with the labels. The labels are $y \\in {0, 1}$. \n", + "\n", + "## Exercise\n", + "* What is a distribution that can generate these labels?\n", + "* What is/ are the parameter(s) of this distribution?" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise answers\n", + "\n", + "A Bernoulli distribution represents binary outxomes. The Bernoulli has a parameter $p$, where \n", + "\n", + "$p = P(x=1)$\n", + "\n", + "* What is the formulation of our model?\n", + "\n", + "Hint: we need a link function $\\frac{1}{1 + e^{-z}}$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$ y \\sim Bernoulli(p) $$\n", + "$$ p = \\frac{1}{1 + e^{-z}} $$\n", + "$$ z = \\beta X $$\n", + "\n", + "* Now we need to set $P(\\theta)$ e.g. priors on $\\beta$." + ] + }, + { + "cell_type": "code", + "execution_count": 237, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/sklearn/utils/validation.py:595: DataConversionWarning: Data with input dtype int64 was converted to float64 by MinMaxScaler.\n", + " warnings.warn(msg, DataConversionWarning)\n" + ] + } + ], + "source": [ + "n = 2000\n", + "x = data[['age', 'educ', 'hours', 'age_squared']].values[:n]\n", + "y = data['more_than_50k'].values[:n]\n", + "\n", + "scaler = preprocessing.MinMaxScaler()\n", + "scaled_x = scaler.fit_transform(x)\n", + "\n", + "# add one for intercept\n", + "scaled_x = np.hstack((np.ones(x.shape[0])[:, None], scaled_x))\n", + "shared_x = shared(scaled_x) # This make it possible to interact date with the Theano computation graph" + ] + }, + { + "cell_type": "code", + "execution_count": 238, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0" + ] + }, + "execution_count": 238, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "shared_x.get_value().max()" + ] + }, + { + "cell_type": "code", + "execution_count": 239, + "metadata": {}, + "outputs": [], + "source": [ + "with pm.Model() as model:\n", + " # 3 features and an intercept is 4 dimensions\n", + " beta = pm.Normal('beta', mu=0, sd=15, shape=5)\n", + " observed = pm.Bernoulli('observed', p=pm.math.invlogit(pm.math.dot(beta, shared_x.T)), observed=y)\n", + " " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.3 Have we got an uninformative prior?\n", + "Below we sample predictions from our posterior. We are uninformative if $P(>50K) \\sim 0.5$" + ] + }, + { + "cell_type": "code", + "execution_count": 240, + "metadata": {}, + "outputs": [], + "source": [ + "with model:\n", + " prior_pc = pm.sample_prior_predictive()" + ] + }, + { + "cell_type": "code", + "execution_count": 241, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/scipy/stats/stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n", + " return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 241, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sns.distplot(prior_pc['observed'].mean(0))" + ] + }, + { + "cell_type": "code", + "execution_count": 242, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [beta]\n", + "Sampling 4 chains: 100%|██████████| 4000/4000 [00:22<00:00, 179.48draws/s]\n" + ] + } + ], + "source": [ + "with model:\n", + " trace = pm.sample()" + ] + }, + { + "cell_type": "code", + "execution_count": 243, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[,\n", + " ]],\n", + " dtype=object)" + ] + }, + "execution_count": 243, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace)" + ] + }, + { + "cell_type": "code", + "execution_count": 244, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([,\n", + " ,\n", + " ,\n", + " ,\n", + " ],\n", + " dtype=object)" + ] + }, + "execution_count": 244, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAA1gAAAIUCAYAAAAHco0LAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAIABJREFUeJzs3Xd4VFX++PH3SQIIKALSEQQV6RCKFQuKiF0RVJBdKerqWlbEAvtj7avi6tpQF7voIigqguiqILoUOxIpYkFFaSsiINIJ3N8fGfIlpJDAJJkk79fz8DBz77k358zMnc987jn33BBFEZIkSZKkPZdU3BWQJEmSpNLCBEuSJEmS4sQES5IkSZLixARLkiRJkuLEBEuSJEmS4sQES5IkSZLixARLkiRJkuLEBEtlWgihUQhhbgHK9wsh1NvNv1U9hDAphPBt7P9qu7MfSZKKOH6dG0KYF0LYFkLouDv7kMoSEyypYPoBuxWggCHAu1EUNQHejT2XJKko9GP349dc4BxgatxqI5ViJlgSpIQQRoYQZocQXg4hVAohdAgh/DeEMDOE8HYIoW4IoSfQERgVQkgLIVQMIdwUQvg0hDA3hPB4CCHk8XfOAkbGHo8Ezi7shkmSSrUiiV9RFM2PoujromuWVLKZYEnQFHg8iqI2wBrgCmA40DOKog7A08AdURS9DHwG9ImiKDWKog3Aw1EUHRpFUSugInB6Hn+ndhRFywBi/9cqvCZJksqAoopfkgogpbgrICWARVEUzYg9/jfw/4BWwKTYCb1kYFku2x4fQrgBqARUB+YBrxdudSVJAoxfUkIywZIg2un578C8KIqOzGujEMJewKNAxyiKFoUQbgH2ymOTn0MIdaMoWhZCqAss35NKS5LKvKKKX5IKwCGCEjQMIWwPRr2Bj4Ca25eFEMqFEFrG1v8O7BN7vD0YrQgh7A303MXfmQD0jT3uC4yPR+UlSWVWUcUvSQVggiXBfKBvCGE2GcMkhpMRbO4OIXwBpAFHxco+C4wIIaQBm4AngDnAa8Cnu/g7w4CuIYRvga6x55Ik7a4iiV8hhO4hhMXAkcAbIYS3C6EtUqkRomjn3mVJkiRJ0u6wB0uSJEmS4sRJLqQ4CyE8AnTaafGDURQ9Uxz1kSQpP4xfUnw4RFCSJEmS4qQgPVhmYpKk/AjFXYEcGMMkSbsSl/jlNViSJEmSFCcmWJIkSZIUJyZYkiRJkhQnJliSJEmSFCcmWJIkSZIUJyZYkiRJkhQnJlhSEUrfVrCZogtaXpKk/DAeSYWnIDca9siS4mDYrBX5LjukXY1CrIlUaLwPllQCGI+kbLwPliRJkiQlEhMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkqRSIH2b99OWEkFKcVdAUu7St0WkJOX/puIFLS9JSlwF/U5PSQoMm7UiX2WHtKuxu9WStAsmWNIeKOyEpiDBEuC6tvsVaP8mZJKUuAoaA0yapMRggiXtgXgHvwUfT+U/D95CtG0b5StVpufYUUDVHMuuXraY+3t2osulN3DshVcAsHbNbxzT84/8/N1XQKDHzQ9yQNtDWfr1HF6743rSN28kKTmFs/76Dxq0am8wlqRSbtabLzP12eEAlK9UmbP/3z+oe0irzPXbtm7l4T+cSJWaden30AvZtp9479/4/rPpjKmYwvr161m+fDmrV6/mvffe45prrsks99VXXzFmzBjOPvts+vXrx3//+1/23XdfAJ599llSU1MLuaVS4jDBkhLIa3ddz4X3PU+tAw/hw5ee5u9//zvNrr43x7IT//k3DunUJcuyq6++mkOOOoE+9zxD+pbNbNm4AYD/PHgbXS69jqadTuSr6ZP4z4O38qcnxhd6eyRJxat6/Yb86cnxVKxSla9nTObVv1/LFc+9nbl+xujHqdX4EDau/T3H7U+/7u9AxgnC4cOHM2vWLACOP/540tLSAFi5ciUHH3wwJ510UuZ299xzDz179iysZkkJzUkuVKYsXLiQZs2acfHFF9OqVSv69OnD5MmT6dSpE02aNOGTTz5h3bp1DBgwgEMPPZR27doxfvz4zG2POeYY2rdvT/v27fnggw8A+P6zGTx+yVmMur4/951zJGOGXkYU7d6FxiEENq7LCHKb1q6hXr16OZab996bVK/fiNoHNstctnHt70ydOpWOZ/8BgJRy5am4T8bZwwBsigXPjWt/p0rNOrtVP0lS3hItzhzQ9jAqVskYCdGwdUfW/Lw0c91vPy/l62mTODQWN3Zl9OjR9O7dO9vyl19+mVNOOYVKlSrlaz9SaWcPlsqcBQsWMHbsWB5//HEOPfRQXnjhBaZPn86ECRO48847adGiBSeccAJPP/00q1ev5rDDDuPEE0+kVq1aTJo0ib322otvv/2W3r1789lnnwGw9Os5XDN2OvvUrMOI/qfxY9rHNGp3RObQiu3GVExh+YZ02nTrTuf+V2er2zk33s+zf+lNuQp7sVflfXgp7VMe/W5zljKbN6zjv88O56J/jWXac49mLl+5ZCE1a9bk5VuuYtk386jfvC1nXH8H5StW5vTr7uDpK8/jzQcyhh9e9sybhfTqSpLiGWd6PvEWkL84sz3GADnGmU9fG5Vl5MPEe4dyytU3s2n92l226ccff+SHH37ghBNOyLZuzJgxDBo0KMuyoUOHctttt9GlSxeGDRtGhQoVCvYiSiWYCZbKnMaNG9O6dWsAWrZsSZcuXQgh0Lp1axYuXMjixYuZMGEC996bMTRv48aN/PTTT9SrV48rr7yStLQ0kpOT+eabbzL32aBle/atndHbVK9pK1YtXUSjdkdkDq3Ybki7GnleszVj1GP0e2g0DVt3YOrIhxk0aBAHXzEsS5nJI/7B0X0upUKlvbMs37Z1K59//jl/evp2GrbuwOv3/D/ef+YhTrr8r3z08jOcfu3ttOpyBrPfeY1XbhvIxSNecZZCSSoExRVn8oox3306nc9eG8WlT08EYOLEiVSuXpP6Ldry/WczdtmmMWPG0LNnT5KTk7MsX7ZsGXPmzKFbt26Zy+666y7q1KnD5s2b+dOf/sTdd9/NTTfdlJ+XTioVTLBU5ux4Fi0pKSnzeVJSEunp6SQnJ/PKK6/QtGnTLNvdcsst1K5dmy+++IJt27ax1157Za5LLlc+83FISmLb1owziLvqwXr68nNZu/IX6rdIpdtVf2PZt/No2LoDAG1OOpsJ113AwVdkrf+iOTOZM/l1/vPgbWz8/TdCUhIp5SvQ+sQz2H///TO3b9XlDP777EMAfD7xRc64/k4AWnc9i1dvz7gw2RmqJCn+iivO5NaDteybebx6+zX0Gz6GylWrAzBjxgzm//ctvp4+mfTNG9m0bi0vDv0z59/xrxzbNGbMGB555JFsy1966SW6d+9OuXLlMpfVrVs383Xo379/ZiIplRUmWNJOunXrxvDhwxk+fDghBGbNmkW7du347bff2H///UlKSmLkyJFs3bp1l/vaVQ/WgEfHZj7emp7OxrVr+OXH76h5wEF8+/H7NG/ePNs+t599hIzerPKVKnNUr4sBaNCgAb8sXEDNRgfz3SfTqNU4I3hXqVGHH2Z+wIEdO/HdJ9PYr8GBBXtRJElxU1hxJqcerNXLFvPv6/px3u2PUPOAgzKX33XXXex73rVAxjVeU597JNfk6peFC1i1ahVHHnlktnWjR4/mrrvuyrJs2bJl1K1blyiKeO2112jVqlW27aTSzARL2smNN97IwIEDadOmDVEU0ahRIyZOnMjll19Ojx49GDt2LMcffzyVK1eO699NTknhnL/dx6jr+xNCEhWr7Mvkl57npd/gy/++xZIv0+j65yF57mP48OGcfkE/tm7ZQvX9D6DnLRk9WOfceB+v3zOUbVu3klKhAuf87b641l2SlH9FGWfefeJe1v+2ivF33QBAUnIKV46anOc2k/41jPotUmlx3MkAfPHWq/Tq1YsQsg4RX7hwIYsWLeK4447LsrxPnz788ssvRFFEamoqI0aM2ON2SCVJKMBsZ7s3LZpUjAp6zdCWbRHlCniNUUGH2JX08lI+JOKFesYwlUiF9Z1e0O//69ru5zW7Kgvi8qG1B0ul2u5cY2TCIUlSVl6zK+Wf98GSJEmSpDgxwZIkSZKkODHBkiRJkqQ4McGSJEmSpDgxwZIkSZKkODHBkiRJKgLp27xbgFQWOE27JElSEXCqc6lssAdLkiRJkuLEBEuSJEmS4sQES5IkSZLixARLkiRJkuLEBEuSJEmS4sQES5IkSZLixARLkiRJcVXQe355jzCVJt4HS5IkSXHlPb9UltmDJUmSJElxYoIlSZIkSXFigiUp3xxTL0n/x+84STnxGixJ+eaYekn6P34nSsqJPViSJEmSFCcmWJIkSZIUJyZYkiRJkhQnJliSJEmSFCcmWJIkSZIUJyZYkiRJkhQnJliSJEmSFCcmWJIkSSpW3shepYk3GpYkSVKx8qbNKk3swZIkSZKkODHBkiRJkqQ4McGSJEmSpDgxwVKJ4kWtkiRJSmROcqESxYtgJUmSlMjswZIkSVKJ4rTuSmT2YEmSJKlEcUSLEpk9WJIkSZIUJyZYkiRJkhQnJliSJEl4nY6k+PAaLEmSJLyuR1J82IMlSZIkSXFigiVJkiRJcWKCpWLleHdJkiSVJl6DpWLleHdJkiSVJvZgSZIkSVKcmGBJkiRJUpyYYEkqNAW9xs5r8iRJUknnNViSCo3X2EmSpLLGHixJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSVCp583JJxcEbDUuSpFLJm51LKg72YElKGAU92+zZaUmSlGjswVJcpW+LSEkKxV0NlVCebZYkSSWdCZbiyh/IkiRJKsscIihJkiRJcWKCJUmSJElxYoIlqcRyUgxJkpRovAZLUonlNX+SJCnR2IMlSZIkSXFigiVJkiRJcWKCJUmSSgSvo5RUEngNliRJKhG87lJSSWAPliRJkko1Z51VUbIHS5IkSaWavZ8qSvZgSZIkSVKcmGApT3aRS5IkSfnnEEHlqSx2qc944TE+Hfdvoiji0O5/4Og+lwEwecQ/+HTc81Suth8AJ105FNr1ZmHax4y/8waSy5en152PUaPhgWz4/TdGD76Y/o+8RAgh2994/JKzOPWaW9m/RSoAq5b+xMir+zBw7DS+/2wGzw36I9XrH8DIkE79487kxEuvz7J8y8YN7F29Jsf2vYrmx55UdC+OJKlIzHjhMVr9cTS/bEjfZSxqdnRXFqZ9TJu+f2Xl1uS4x6L0TZvY1K8PFc68wlgk5YMJlrSDuXPn8um4f3P5c2+TXK48z1x5Ps2O6UqNhgcB0KnPZRx74RVZtpn+/L/oc+/TrFq6iI9ffpbTBt3GlCf+SeeLBuYY0PKjUeoR9HvoBa46pCIHNG9N82NOyrIcYOnXc3h+UF/KVdiLgw8/dg9aLUlKJP9bMJ9Px/2b72fP5P55a/Idi8a98grDJn8R91i0ecM6nu97IicffHSW5VB6Y1H6toiUpPy/bgUtr9LNBEvawfz582nQugPlK1YCoHGHo5g35U2O63dVrtskpaSwZeNGtmzcQHJKCr8u+oE1y5dxYIdOe1yfypUrU795W35d/AN7V6+ZZV29pq3pcsm1fPjSU6UqqElSWffLD9/QoHUHKlWqRHLK+nzHog0bNhRKLCpfsTIdOnQoU7GoLI7gUfyYYEk7aNWqFT98PoR1q1dSrsJefD19Mvu3aJu5/sMXn2LWxJeo36Itpw26DahB5wFXM+7v11Jur7047/ZHefP+m+l6+ZBd/q0Xh15GuQp7AbB1yxZCUvZLIn/99Vd+mjOTEy65lnWrfs22vl7zNkx97pHdb7AkKeHUPqg5bz9yJ7/++iubN6zfZSyqWKUqnQdczZ/+9Cd+2ZoS91i0bvVKPvroI7r3vNJYJOWDCZa0g+bNm3Ncv6t4+vKelK9YmbqHtCQpOeMwOfzcfpxwybUQApMevYs37ruJW497gXpNW3P5c28B8MPMD9inZh2iCF4YfDHJKeU4ddCt7LNfrWx/6/w7RmQb977dwrSPeKj38YytXJ7O/f9C7YOa8f1nM7JXOHISEkkqbWodeAjH9buKrl27sooKu4xFPW95iHpNW/PRRx8xbNaKuMeiEJK4ccgQVhuLpHxxFkFpJ4ee/QeuemEKlz71OpWqVGW/hgcCsM9+tUhKTiYpKYnDzvkji+fNyrJdFEVMeep+ulxyLe8+fg8nXjaY1FN78sHoJwpch0apR/CX0e8xc+ZMDu/ZL9dyS7+aQ63GhxR4/5KkxHbo2X/g888/T4hYdNUL73LZZZflWs5YJGVlgiXtZO3KXwBYvWwx8957g9STzwFgzS//yywzb8qb1D6oWZbtPn99DM2OPpGKVaqyZeMGQlISISmJLRs3FEo9l30zjylP3scR5w0olP1LkoqPsUgquRwiKO1k1HX9Wf/bKpJSynHm4LupWKUqAP958DaWfTOXQKBavQacPfTezG02b1jP5xNfZMAjYwE4us9ljLq+P8kp5eh11+Nxq9v24RpbNm5g72o1OOP6O0vVRcWSpAyjruvPq5vWsCo9Kd+xaP16Y5GUCEywpJ1c+vTEHJef//dHc92mfMVKXPL4a5nPG7c/koEvTc21/J+eGJ/lebV6DRk4dhoAB3bsxIEds8/6dGDHTtwy9fs86668Oe2upJLi0qcnMqRdjWwz2eUViypVMhZJicAES1KZ4bS7kiSpsHkNliRJKhbp25x9TlLpYw+WJEkqFvYqSyqN7MGSJEmSpDgxwZIkSZL2QEGHuzo8tnRziGAZ46xokiRJ8eVwV+3IBKuEK2jC5BeAJEmSVHhMsEo4Eyap8HjfLEmSVFAmWJKUC09gSJKkgnKSi0KyatUqunfvTps2bTjssMOYO3dujuUuuugi2rZtS5s2bejZsydr164FYMSIEbRu3ZrU1FSOPvpovvzySwA2b95M//79ad26NW3btuX9998vqiZJZcrUkQ+TmprKQ70688C5x/D/OtZm/W+rspWLooi3H76De88+nObNm/PQQw9lWf/pp5+SnJzMyy+/XFRVl/K0aNEijj/+eJo3b07Lli158MEHAVi5ciVdu3alSZMmdO3alVWrsn/ef/zxRzp06EBqaiotW7ZkxIgRmes6d+5M06ZNSU1NJTU1leXLlwMwdepU2rdvT0pKiseByrTV/1vCE386m/vOOSrLsffFF19w5JFH0rp1a8444wzWrFmTbduvv/4689hKTU2lSpUqPPDAAwDceOONtGnThtTUVE466SSWLl1apO1SdiZYheTOO+8kNTWV2bNn89xzz3H11VfnWO7+++/niy++YPbs2TRs2JCHH34YgAsuuIA5c+aQlpbGDTfcwKBBgwB44oknAJgzZw6TJk3i2muvZdu2bUXTKKkMObbvlaSlpfGXMe/T7cq/0bj9UVTat1q2cjMnjOa3n5cy6NUPmT9/Pr169cpct3XrVgYPHky3bt2KsupSnlJSUvjnP//J/Pnz+eijj3jkkUf48ssvGTZsGF26dOHbb7+lS5cuDBs2LNu2devW5YMPPiAtLY2PP/6YYcOGZfkxN2rUKNLS0khLS6NWrVoANGzYkGeffZYLLrigyNooJaKk5GROveZWBr36QZZj7+KLL2bYsGHMmTOH7t27c88992TbtmnTppnH1syZM6lUqRLdu3cH4Prrr2f27NmkpaVx+umnc9tttxV107QTE6xC8uWXX9KlSxcAmjVrxsKFC/n555+zlatSpQqQcRZ8w4YNhBCyLAdYt25d5vId91urVi2qVq3Kki/TCrUtUln3xduv0vbkc3Jc9/HLz3LCJdeSlJTxdbr9RyXA8OHD6dGjR5ZlUnGrW7cu7du3B2CfffahefPmLFmyhPHjx9O3b18A+vbty2uvvZZt2/Lly1OhQgUANm3alK8TfI0aNaJNmzaZx4hUVlWpWYf6zdsCWY+9r7/+mmOPPRaArl278sorr+S5n3fffZeDDjqIAw44IGO/ufxmVPHx266QtG3blldffRWATz75hB9//JHFixfnWLZ///7UqVOHr776iquuuipz+SOPPMJBBx3EDTfckDnsqG3btowfP5709HR++OEHZs6cyW8/Lyn8Bkll1OYN6/nmgym06nJ6jut/XbyQOe+8xsN9TuSUU07h22+/BWDJkiWMGzeOyy67rCirKxXIwoULmTVrFocffjg///wzdevWBTKSsO1D/Ha2aNEi2rRpQ4MGDRg8eDD16tXLXNe/f39SU1O5/fbbiSLv8yPlZsH3P2Qee61atWLChAkAjB07lkWLFmUrv+N9s8aMGUPv3r2zrB86dCgNGjRg1KhR9mAlABOsQjJkyBBWrVpFamoqw4cPp127dqSk5DynyDPPPMPSpUtp3rw5L774YubyK664gu+++467776bv//97wAMGDCA/fffn44dOzJw4ECOOuookpKdq0QqLF9NfZsD2h6W4/BAgK2bN5FSYS+uHDWZARddzIABAwAYOHAgd999N8nJybnu2xtNqjitXbuWHj168MADD2Q5A74rDRo0YPbs2SxYsICRI0dmjs4YNWoUs76YzbRp05g2bRrPP/98YVVdKtE2rV/L+ef25Ni/3Maj323miOv+yXXDHqB+87a8+c3PbE0ux7BZK7L82z5D7ebNm5kwYQLnnntuln3ecccdLFq0iD59+mRebqLi4y/zOHrkkUcyr5F68803eeaZZ4CM4X+NGzemcePGuW6bnJzM+eefzz333EP//v2zrOvVqxd//vOfgYyx8/fff3/muqOOOoqmDQ+Md1OkMunDF5/i03EZPwr7DR8D1OCLd17LdXggwL6162X2bvXscQ5/7N+fYbNW8O4HnzB5xnkArF/9Ky9PeIPxP62n5fGnZm7rrIMqLlu2bKFHjx706dOHc87J+HzXrl2bZcuWUbduXZYtW7bLoa316tWjZcuWTJs2jZ49e1K/fn0AHlmwiX07ncG/3vgvS1v/3+d9zsqNbPlhDQt2mJnTY0BlzdYtWxh1XX8u69OHzcdnxI5ajZtw0aNjAfjlx+/4evqkXLf/z3/+Q/v27aldu3aO6y+44AJOO+00br311vhXXvlmD1YcXXHFFZkXIFaqVInNmzcD8OSTT3LsscdmO0MYRRELFizIfPz6669zSNOmAJnDjADeeOMNmjRpAsD69etZt24dAJMmTSIlJYXaBzYt9LZJZcGR51/EX8a8z1/GvE+VmnX47bff+GHmB7TofHKu27TofArffTINgP/+97/UaHgQADdMnMngNz5n8Buf0+rEMzjrr3dnSa6k4hJFERdddBHNmzfPnEAJ4Mwzz2TkyJEAjBw5krPOOivbtosXL2bDhg1Axmy5M2bMoGnTpqSnp7NiRUbitHXLFr6a9g51Dm5eBK2RSo4oinjltoHUbHxIlmNv7cpfANi2bRvvPXkfh/fom+s+Ro8enW144I6/GSdMmECzZs3iXHMVlD1YhWT+/PlceOGFJCcn06JFC5566qnMdaeeeipPPvkkderUoW/fvqxZs4Yoimjbti3/+te/GDZrBa/fcw8LPp5KckoKFatU5cwhDzBs1gpWLf2Jp684jxCSqFKrLu++9DyjVxZjQ6VSbNy4cTQ5ojPlK1bOsvyZq3rR46YHqFKzDsf1v5oXh17G9Bceo3GNfelx0/257E1KDDNmzOD555/PvBUIZMx8O2TIEM477zyeeuopGjZsyNixGWfUP/vsM0aMGMGTTz7J/PnzufbaawkhEEUR1113Ha1bt2bdunV069aNLVu28PO6zRx8+LEc2v2PACyaN4t/X9uXDWt+Y/7Ud5g84h9c8/L0Ymu/VFx+TPuYWW+8RJ2DW2TcymBDOiddOZRff/qeD196GoBWJ5xGh7MyZtxc88v/eOW2gfQfPgbIOMk+adIkHnvssSz7HTJkCF9//TVJSUkccMABWW6foOJhglVIjjzyyCxnFHb05ptvZj6eMWNGDiVWcMb1d+a4bbV6Dbl23EeZzw84oAaszP+NUCXlX79+/fhf2+yTW2wPdgAV99mXfg+NBjKGO+V0Y+Jzb3U8vBLH0UcfnesEFO+++262ZR07duTJJ58EMmY4mz17drYylStXZubMmQDZjoEGLdvx17eybyOVNY3aHcFdn2f0Vu0cLzpdcGm28lVq1skSbypVqsSvv/6ardyuZh1U0XOIoCRJZURBJ1ZxIhYpMXjsliz2YEmSVEakJIUce1lz4yQUUmLw2C1Z7MEqZJ5BkFRcPOMpSWWT3//FKxTgRoC+8mR8ALffiyC/CnrGoaDlvWO3FD/bx8fD7h2PiXaGsZjqk4hfSsawmML+TOxq/39tX7PA+5RKk7s+/6VI4kuixaMSIi7xyyGCBWQXraR4KegJm905wSPtCT9zklRwJliSVEwKesLmurb7FWJtlAgSLen2pKKknBT2d1WifRcWVJlPsBLtDZGk3Phjt/gVdtA36ZZUHBLtu6qkx7t8X4N16623vgUUZu3rAUsLcf+JyDaXHWWx3WWxzVA2271zm1fcfPPNJxdXZXJSBDEs3krL58h2JJ7S0hbbkVhKSztWAB/dfPPNt+zRXqIoSoh/t9xyS1TcdbDNttl222bbbZsT4V9peU1tR+L9Ky1tsR2J9a+0tCNebXGadkmSJEmKk0RKsG4t7goUA9tcdpTFdpfFNkPZbHdZbHNhKy2vqe1IPKWlLbYjsZSWdkAc2lKQ+2BJkiRJkvKQSD1YkiRJklSimWBJkiRJUpyYYEmSJElSnBRZghVCODeEMC+EsC2E0HGndX8NISwIIXwdQuiWy/aNQwgfhxC+DSG8GEIoXzQ1j58QQtsQwochhDkhhNdDCFVyKbcwViYthPBZUdczngrQ5pNj7/+CEMKQoq5nvIUQUkMIH21/D0MIh+VSbmusTFoIYUJR1zOeCtDmvrHj+NsQQt+irme8xb6Ptr+HC0MIabmUK03HdX7bXKqO63gIITwdQlgeQpi7w7IS9xkKITR0a8pwAAAgAElEQVQIIbwXQpgfi+1Xx5ZXDyFMih3fk0II1XLZPiG+B/Joxz0hhK9CCLNDCONCCFVz2T4h3pM82nFLCGHJDp+vU3PZPiGO1TzaURKPkb1CCJ+EEL6IteXW2PLGIR+/Z0M+fhsXhTzaMSpWt7mx77VyuWyfEL9z8mjHsyGEH3aoY2ou2xfsO6uo5pQHmgNNgfeBjjssbwF8AVQAGgPfAck5bP8S0Cv2eATw5+KeJ383XoNPgeNijwcAt+dSbiFQo7jrW1RtBpJj7/uBQPnY56FFcdd9D9v9DnBK7PGpwPu5lFtb3HUtyjYD1YHvY/9Xiz2uVtx1j+Nr8E/gplzWlZrjOj9tLo3HdZxer2OB9sDcgryesXUJ8xkC6gLtY4/3Ab6JxfN/AENiy4cAd+ewbcJ8D+TRjpOAlNjyu3NqRyK9J3m04xbgul1smzDHam7t2KlMSTlGArB37HE54GPgCPLxe5Z8/jYu5nacGlsXgNE5tSO2TUL8zsmjHc8CPXexbYG/s4qsByuKovlRFH2dw6qzgDFRFG2KougHYAGQ5cx3CCEAJwAvxxaNBM4uzPoWkqbA1NjjSUCPYqxLUclPmw8DFkRR9H0URZuBMWR8LkqyCNjeW7cvpePu5ruSnzZ3AyZFUbQyiqJVZHwmTi6i+hWq2PfUeWQEmjJhF20ujcf1HouiaCqwMqd1JekzFEXRsiiKPo89/h2YD9Qn4z0eGSuWW6xOmO+B3NoRRdE7URSlx4p9BOxfHPXLrzzej/xImGN1V+0oYcdIFEXR2tjTcrF/Efn7PbvL38ZFJbd2RFH0ZmxdBHxC4h8jub0f+VHg76xEuAarPrBoh+eLyf6lsB+weocvu5zKlARzgTNjj88FGuRSLgLeCSHMDCH8qUhqVnjy0+b8fAZKmoHAPSGERcC9wF9zKbdXyBhO91EIoSSeNNhRftpcGt/r7Y4Bfo6i6Ntc1pem43q7vNpcmt/rwlIiP0MhhEZAOzLOCNeOomgZZPxYBmrlsElCfjZ2aseOBgD/yWWzhHtPcmjHlbGhjk/nMmSzJL0fJeoYCSEkx4YzLifjR/l35O/3bEK9Jzu3I4qij3dYVw74I/BWLpsnzO+cPNpxR+wYuT+EUCGHTQv8fqTEpcYxIYTJQJ0cVg2Nomh8bpvlsGznjDI/ZRJCXq8BGV/SD4UQbgImAJtz2U2nKIqWhhBqAZNCCF/FznompDi0ucS8vzvaRbu7ANdEUfRKCOE84CngxBzKNoy91wcCU0IIc6Io+q7war1n4tDmUvde7/Dd1pu8z6qWmuM6n20uke91MStxn6EQwt7AK8DAKIrWZHQw7HqzHJYV62dj53bssHwokA6MymXThHpPcng//gXcTsbrezsZw+sG7LxZDrtKyPeDEnaMRFG0FUgNGdfwjSPjcplsxXJYllDvyc7tCCG0iqJo+3WkjwJToyialsvmCfM7J6d2kHEy+H9kDI99HBgM3LbTpgV+P+KaYEVRlNMPyF1ZTNZejf3JPrRoBVA1hJASy/pzKpMQ8vEanAQQQjgEOC2XfSyN/b88hDCOjG7hhP0hFoc25+czkHDyancI4Tng6tjTscCTuexj+3v9fQjhfTLO1iVsghWHNi8GOu/wfH8yrstMaLv6jIcQUoBzgA557KNUHdf5aHOJPK6LS0n8DMXOXL8CjIqi6NXY4p9DCHWjKFoWQqhLxpninSXU90Au7SB2IfvpQJfYMKhsEuk9yakdURT9vMP6J4CJOWyaUMdqHu9HiTtGtouiaHUsxh9B/n7PJtR7st0O7TgZmBtCuBmoCVyaxzYJ9ztnx3ZEUXRvbPGmEMIzwHU5bFLg76xEGCI4AegVQqgQQmgMNCFjLGem2Bfbe0DP2KK+QG49YgkrdkaFEEIS8DcyLm7cuUzlEMI+2x+TkZzM3blcSZGfNpMxEUaTkDGzTnmgFxmfi5JsKXBc7PEJQLbhDCGEatu7okMINYBOwJdFVsP422WbgbeBk2Jtr0bG5/vtIqpfYToR+CqKosU5rSxtx3VMnm2mdB7XhalEfYZCRlfVU8D8KIru22HVBDJiNOQeqxPmeyC3doQQTibjTPaZURStz2XbhHlP8mhH3R2KdSfn+iXMsZrH5wpK3jFSM9ZTQgihIhn1n0/+fs/u8rdxUcmlHV+FEC4m49qk3lEUbctl24T5nZNHO+rGlgUyrofL6TNT8O+sqOhm7+hORga4CfgZeHuHdUPJyGa/JjYLWWz5m0C92OMDyfhwLSDj7HiFoqp7HF+Dq8mYEecbYBgQYsvrAW/u0M4vYv/mkTEcp9jrXphtjj0/NVbmu5Le5lh7jgZmxt7Hj4EOseUdgSdjj48C5sTKzAEuKu56F3abY88HxI7jBUD/4q53nNr+LHDZTstK7XGdnzbHnpeq4zpOr9toYBmwJRYTLyqJn6HY8R4Bs4G02L9Tybhm+l0yTrC8C1SPlU/I74E82rGAjGsuti8bkcjvSR7teD4WX2aT8aO97s7tiD1PiGM1t3bE1pW0Y6QNMCvWlrnEZj4kl9+zZFyvftsO2+f42ziB2pEeq9/292n78oT8nZNHO6bE6jYX+Df/N9PgHn1nbf+xK0mSJEnaQ4kwRFCSJEmSSgUTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyyVaSGERiGEuQUo3y+EUG83/9Y9IYSvQgizQwjjQghVd2c/kiRBkcew22PxKy2E8M7u7kcqC0ywpILpB+xuUJkEtIqiqA3wDfDXeFVKkqR86Mfux7B7oihqE0VRKjARuClutZJKGRMsCVJCCCNjZ+ZeDiFUCiF0CCH8N4QwM4TwdgihbgihJ9ARGBU7g1cxhHBTCOHTEMLcEMLjIYSQ2x+JouidKIrSY08/AvYvisZJkkq1oopha3Z4WhmICrthUkkVosjjQ2VXCKER8ANwdBRFM0IITwPzge7AWVEU/RJCOB/oFkXRgBDC+8B1URR9Ftu+ehRFK2OPnwdeiqLo9Xz83deBF6Mo+ndhtEuSVPoVdQwLIdwBXAj8BhwfRdEvhdc6qeSyB0uCRVEUzYg9/jfQDWgFTAohpAF/I/fepuNDCB+HEOYAJwAtd/XHQghDgXRg1B7XXJJU1hVZDIuiaGgURQ3IiF9XxqX2UimUUtwVkBLAzt24vwPzoig6Mq+NQgh7AY8CHaMoWhRCuAXYaxfb9AVOB7pEdh9LkvZckcWwHbwAvAHcXMC6SmWCPVgSNAwhbA9Evcm4Pqrm9mUhhHIhhO1n9X4H9ok93h6IVoQQ9gZ65vVHQggnA4OBM6MoWh/PBkiSyqyiimFNdnh6JvBVPCovlUb2YEkZ49X7hhAeA74FhgNvAw+FEPYl4zh5AJgHPAuMCCFsAI4EngDmAAuBT3fxdx4GKpAxbAPgoyiKLot3YyRJZUpRxbBhIYSmwDbgR8D4JeXCSS4kSZIkKU4cIihJkiRJceIQQSnOQgiPAJ12WvxgFEXPFEd9JEnKL2OYtOccIihJkiRJceIQQUmSJEmKk4IMEbSrS5KUH6G4K5ADY5gkaVfiEr/swZIkSZKkODHBkiRJkqQ4McGSJEmSpDgxwZIkSZKkODHBkiRJkqQ4McGS9kD6toJNTFbQ8pIk5VdBYozxSCo8BbnRsEeiSr30bREpSQWboXPYrBX5LjukXY2CVkkqiZymXSom+Y1JxiMpR3GJXwW5D5ZU6qUkBRMmSZIk7TaHCEqSJElSnJhgSZIkSVKcmGBJkiRJUpyYYEmSJElSnJhgSZIkSVKcmGBJkiRJUpyYYEmSJElSnJhgSZIkSVKcmGBJkiRJUpyYYEmSJClP6duiQi0vlSYmWFIR+/TTT0lOTubll1/OcX3nzp1p2rQpqamptE1NZfny5ZnrXnrpJVq0aEHLli254IILMpePHDmSJk2a0KRJE0aOHFnobZAklR3jx4+nfWpb6jVtxf4tUrns6YkMm7Ui27+rRr1LnSYt2K9BYwYNvJooykiyzj//fFJTU0lNTaVRo0akpqYCMGnSJDp06EDr1q3p0KEDU6ZMKc5mSnGTUtwVkMqSrVu3MnjwYLp165ZnuVGjRtGxY0cAhs1aAUtWsOKn73jhptu55LEJVKxSlbUrf2HYrBWs/20VDw+9mSv/PYlr2tagQ4cOnHnmmVSrVq0omiRJKuW6dOnCmWeeyd1pv7Lsm3mMHnIxg179MFu51+66nu5D/0nDNh2ZOvRC3nrrLU455RRefPHFzDLXXnst++67LwA1atTg9ddfp169esydO5du3bqxZMmSImuXVFjswVKptXDhQpo1a8bFF19Mq1at6NOnD5MnT6ZTp040adKETz75hHXr1jFgwAAOPfRQ2rVrx/jx4wFYtfQnHhtwOsMvOIHhF5zAj198AsD3n83g8UvOYtT1/bnvnCPp06dP5hm6/Bg+fDg9evSgVq1aBW7Pp6/+myPPG0DFKlUB2Lt6TQC++fA9mhx+HJX2rUa1atXo2rUrb731VoH3L0lKDIkWv/bee29CCABs3rAeCNnKrPnlf2xa9zsHtD2UEAIXXnghr732WpYyURTx0ksv0bt3bwDatWtHvXr1AGjZsiUbN25k06ZNu/WaSYnEHiyVagsWLGDs2LE8/vjjHHroobzwwgtMnz6dCRMmcOedd9KiRQtOOOEEnn76aVavXs1hhx3GH56dROVqNRjwr5cpV2EvVvz0HWP+eilXjpoMwNKv53DN2OnsU7MOr195FvukfUyjdkcw8d6/8f1n07PVoU237nTufzW/LV/Gf8aNY8qUKXz66ad51rt///4kJyfTo0cPUk67jBACK376DoAR/U9l29ZtdLn0epp26sKa5cvYt069zG33339/zwBKUgm3O/HrxBNPzHf8mnDlWcyYMYOjjz6aa665hvfeey9bHXr16sWQIUMAGDduHPcNuoG1K1fQ98EXspVd88v/qFIr71g0bdo0ateuTZMmTbJt/8orr9CuXTsqVKiwR6+blAhMsFSqNW7cmNatWwMZZ8e6dOlCCIHWrVuzcOFCFi9ezIQJE7j33nsB2LhxI6uXLaFKzTqMv3sIy76ZS1JSEit++j5znw1atmff2hlBJDU1lZVLF9Go3RGcft3f86zLxHuH8sTdd5OcnJxnuVGjRlG/fn1+//13evToQVWq0/7089mans6KRd9zyePj+W35Uh676AwGjp0GOZyB3H6mUZJUMu1O/Prpp5/Yll4hX/GrXWoqw9+fw/TKzah94VB6XTg0x3oMm7UCgCHdu/N1o2P4YeYHTPrXMC4e8UqWcjn1hu0ci0aPHp3Ze7WjefPmMXjwYN555538vjxSQjPBUqlWoUKFzOAwb/Vmti7dxKJZK1i1dDX/W7uJ5HIRve58kpqNDgZgSLsaDJu1gskj/sE++9Xk3DHvE23bxk1H7p+5z+Ry5f/vcXIy27amA+yyB2vJl1/Qq1cvAFasWMGbb75JSkoKZ599dpby9evXB2Cfffbhggsu4LH/TKP96eezb+16NGzdgeRy5ahe/wBqHnAwK376niq16/HDZzMyt1+8eDGdO3eOw6snSSouO/bkJCUlZT5PSkoiPT2d5ORkXnnlFZo2bZplu+kP3BD3+LWjxh2OYuXNV7Fu1a9UrrZf5vJ9a9VlzfKlmc8XL16cOfwPID09nVdffZWZM2dm2d/ixYvp3r07zz33HAcddNCuXxipBDDBUpl2yJHH88GYJzhz8DBCCMyaNQtowMa1a9i3dj2SkpL47PUxbNu6dZf72lUP1g0TZzKkXQ0A+vXrx+mnn54tuUpPT2f16tXUqFGDLVu2MHHiROo0PQKAFp1P4Yu3X6XDmb1Zt+pXVvz0HdXrH8B++zfinYfvYMOa1axalcw777zDXXfdtXsviCSpROjWrRvDhw9n+PDhmfGrXbt2hRK/Vvz0PVFqRjK1ZP4XbN2ymUpVq2cpU6VmHcpX2pufZn9Gg9YdeO6557jqqqsy10+ePJlmzZqx//7/l/CtXr2a0047jbvuuotOnToVpPlSQnOSC5VpJ1xyLdvS03nw/ON44NxjuPHGGwE44rz+fP76izx64cms+Ok7ylesVKj12D5l7aZNm+jWrRtt2rQhNTWV+vXrc2j3PwJwyFEnUGnf6tzfoxNPXNqdUwbeQuWq1am0bzVOuHgQD/+hK4ceeig33XQT1atXz+vPSZJKuBtvvJEtW7bQpk0bWrVqVajxa96UibRq1YqHenVm/LAh9B72RObwv4d6dc4sd/b/u4dXb7+Ge886jMYHHsgpp5ySuW7MmDHZhgc+/PDDLFiwgNtvv522sWncd7w1iVRShQLMgOYd41QibR8imB/bhwgWZvmCKuz9S4UgES8CNIapTMhvzCiKeGf8UgkUl/hlD5ZUhLyzvSRJUunmNVhSEUpJCoV6Ri99W0RKUv5PvhS0vCRJkvJmgiWVIoWdwEmSJClvDhGUJEmSpDgxwZIkSZKkODHBkiRJkqQ4McGSJElSsSroLLvOyqtE5iQXkiRJKlZO0qTSxB4sSZIkSYoTEyxJkiRJihMTLEmSJEmKExMslShe1CpJkqRE5iQXKlG8CFaSJEmJzB4sSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkiRJihMTLEmSJEmKExMsSZIkSYoTEyxJkqQElL4tKu4qSNoN3mhYkiQpAaUkBYbNWpHv8kPa1SjE2kjKL3uwJEmSJClOTLAkSZKKgEP+pLLBIYKSJElFwCF/UtlgD5YkSZIkxYkJliRJkiTFiQmWVIYV9HoArx+QJJVExjsVJa/BksowrweQJJUFxjsVJXuwJEmSJClOTLAkSZIkKU5MsCRJkiQpTkywJEmSJClOTLAkSZJUojjLnxKZswhKkiSpRHFWQCUye7AkSZIkKU5MsCRJkiQpTkywJEmSJClOTLAk5VtBLyr2ImRJklTWOMmFpHzzomJJkqS82YMlSZIkSXFigqVi5RAySZIklSYOEVSxcsiZJEmSShN7sCRJkiQpTkywJEmSJClOTLAkSZIkKU5MsCRJkiQpTkywJEmSJClOTLAkFZqCTsPvtP2SJKmkc5p2SYXGafglSVJZYw+WJEnSbrDXXVJO7MGSJEnaDfbSS8qJPViSJEmSFCcmWJIkSZIUJyZYkiRJkhQnJliSJEnSDrzNiPaEk1xIkiSR8SM5JSkUdzWUAJzARHvCBEtxZXCSJJVU/qiWFA8mWIorg5MkSZLKMq/BUp4cUyxJkiTlnz1YypM9UpIkSVL+2YMlSZIkSXFigiVJkiRJcWKCJSlheN8RSZJU0nkNlqSE4TV/kiSppLMHS5IkSZLixARLkiRJkuLEBEuSJEmS4sQES5IkSdoDTtKkHTnJhSRJkrQHnKRJO7IHq4zxjIkkSZJUeOzBKmM8wyJJkiQVHnuwVGbNeOExHjj3GO7veTTTR43IXD55xD+4q1trHurVmYd6dear6ZMAWJj2MQ+edxwP/6ErK376HoDVq1fz9OXnEkU59ww+fslZLP4yLfP5woULeeDcYwD4/rMZ3HLsgTzU+3juO+coJj92T7blTZs25bGLzmD+1HcK5TWQJCWuBx98sEBxasaMGdni1IbffytQnFq19Kcc41Tz5s1zjFP/7H6EcUraiT1YKpP+t2A+n477N5c/9zbJ5crzzJXn0+yYrhDrsevU5zKOvfCKLNtMf/5f9Ln3aVYtXcTHLz/LaYNu4/bbb6fzRQMJIexWPRqlHkG/h15g84Z1PNTreJofc1KW5UPa1eAvY97j+UF9KVdhLw4+/Ng9a3gpk74tIiUp/699QctLUnH534L5TH7iiWxxqkbDg4Cc49Q///nPbHFqyhP/jEucuuqQihzQvHW2OAWw9Os5xilpByZYKpN++eEbGrTuQPmKlQBo3OEo5k15E846PNdtklJS2LJxI1s2biA5JYVfF/3AkiVLSP1Dpz2uT/mKlanfvC2/Lv6BvavXzLKuXtPWdLnkWj586SkD104c8iopLyX5pMovP3zDEUcckS1OHdfvqly3KVeuXLY4tWb5Mg7ssOdxqnJl45SUXyZYKpNqH9Sctx+5k3WrV1Kuwl58PX0y+7dom7n+wxefYtbEl6jfoi2nDbqNilWq0nnA1Yz7+7WU22svzrv9Ud68/2ZefvgfvLI277/14tDLKFdhLwCeS96WY5l1q1fy05yZnHDJtaxb9Wu29fWat2Hqc4/sfoMlqRQoaMJUkk/C1D6oOROfvJu6ffIfp/76179y5h8vzhKnul4+ZJd/a8c4tXXLFkJS9itIfv31V+OUlE8mWCqTah14CMf1u4qnL+9J+YqVqXtIS5KSMw6Hw8/txwmXXAshMOnRu3jjvpvoectD1GvamsufewuAH2Z+wD416xBFES8MvpjklHKcOuhW9tmvVra/df4dI9i/RSoAvaqt5YgTT8lctzDtIx7qfTwhJNG5/1+ofVAzvv9sRvYK5zJ2XpLKkpKcMBVUrQMPYfDgwdxUgDiVmpqaQ5yiQHFq1dKfGHl1n8x12+PU2MrljVNSPjnJhcqsQ8/+A1e9MIVLn3qdSlWqsl/DAwHYZ79aJCUnk5SUxGHn/JHF82Zl2S6KIqY8dT9dLrmWW2+9lRMvG0zqqT35YPQTBa5Do9Qj+Mvo97jqhXc5vGe/XMst/WoOtRofUuD9KytvBCmpJLnooov2OE69+/g9cYlTM2fONE5J+WQPlsqstSt/Ye/qNVm9bDHz3nuDPz/7HwDW/PI/qtSsA8C8KW9S+6BmWbb7/PUxNDv6RCpWqcr69esJSUmEpCS2bNxQKPVc9s08pjx5H+fceH+h7L8sKUtnvyWVfMuXLweS9ihObdm4wTglFTETLJVZo67rz/rfVpGUUo4zB99NxSpVAfjPg7ex7Ju5BALV6jXg7KH3Zm6zecN6Pp/4IgMeGQvAoEGDOHdAf5JTytHrrsfjVrftQzKeiTazuVI1zrj+Ti8clqQypkePHnyzZPkexamj+1zGqOsLL05t2biBvavVME5JOzDBUpl16dMTc1x+/t8fzXWb8hUrccnjr2U+P+aYYxj40tRcy//pifFZnjdq1IiBY6cBcGDHThzYMfvMTgd27MQtUzPuXzKkXY0C9bhIkkqPadOm5RgDChKnGrc/skBxqlq9hgWKU5Ky8xosSZIkqQh5TXDpZg+WJEmSVIS8Jrh0swerhPOMhiRJkpQ47MEq4TwDIkmSJCUOe7AkSZIkKU5MsCRJkiQpTkywJElSsfA6YkmlkddgSZKkYuF1xJJKI3uwJEmSJClOTLD2wMaNGznssMNo27YtLVu25Oabb85W5pprriE1NZXU1FQOOeQQqlatmrlu8ODBtGrVilatWvHiiy9mLr/oooto27Ytbdq0oWfPnqxdu7ZI2iOVRXef1p4HzjuWh3p15uE+J2ZbP378eNq0aUNqaiodO3Zk+vTpmetOPvlkqlatyumnn55lm4cffpiDDz6YEAIrVuT/7LxUlAYMGECtWrVo1apVjutXrVpF9+7dadOmDYcddhhz587NXLd69Wp69uxJs2bNaN68OR9++CEAt9xyC/Xr18+Me2+++WaRtEUqDbZt3cpDvY/n2b9ckG3dpk2bOP/88zn44IM5/PDDWbhwIQCTJk2iQ4cOtG7dmg4dOjBlyhQAfv/998zjMDU1lRo1ajBw4MCibE6Z5hDBPVChQgWmTJnC3nvvzZYtWzj66KM55ZRTOOKIIzLL3H///ZmPhw8fzqxZswB44403+Pzzz0lLS2PTpk0cd9xxnHLKKVSpUoX777+fKlWqADBo0CAefvhhhgwZUrSNk8qQSx4bR+Vq+2Vbnr4tokuXLpx55pmEEJg9ezbnnXceX331FQDXX38969ev57HHHsssn5IU6NSpE6effjqdO3cuymZIBdKvXz+uvPJKLrzwwhzX33nnnaSmpjJu3Di++uorrrjiCt59910Arr76ak4++WRefvllNm/ezPr16zO3u+aaa7juuuuKpA1SaTJj9OPUanwIG9f+nm3dU089RbVq1ViwYAFjxoxh8ODBvPjii9SoUYPXX3+devXqMXfuXLp168aSJUvYZ599SEtLy9y+Q4cOnHPOOUXZnDLNHqw9EEJg7733BmDLli1s2bKFEEKu5UePHk3v3r0B+PLLLznuuONISUmhcuXKtG3blrfeegsgM7mKoogNGzbkuU9JhSclKfDwtxu5O+1Xhs1awb8+X8LKTdsYNmsFw2at4NPqbXn9f9tY8Ntmhs1aQUpSxrHarl07GjVqVLyVl3bh2GOPpXr16rmu//LLL+nSpQsAzZo1Y+HChfz888+sWbOGqVOnctFFFwFQvnz5LKMzJBXcbz8v5etpkzj07D/kuH78+PH07dsXgJ49e/Luu+8SRRHt2rWjXr16ALRs2ZKNGzeyadOmLNt+++23LF++nGOOOaZwG6FMJlh7aOvWraSmplKrVi26dv3/7d17nM3V/sfx92dmy31yQqJRw/lVchkzrokkcjnym45SknPk0kVH1CminEi/TqlT5xS6usYplEtJ6kRyRGlyGXIrEhHFiMoQxqzfH7PbzZgZZsx3Zl/m9Xw8POz9/a7v3p/v2mvPXp+91nft9mrevHmu5Xbs2KGvv/5abdu2lSQ1bNhQ7777rg4fPqzU1FR9+OGH2rlzZ6B8nz59dN5552nz5s0aOHBgsZwLUBKZmSYNuEFjb26n5NlTcy2zYfE7+ud1LfTK3Tfr+pHPFnOEQHA0bNhQc+bMkSQlJydrx44d2rVrl7Zt26aqVauqT58+SkxM1K233qq0tLTAcePGjVN8fLz69u2rAwcOBCt8IKzMf2q4/nD3SFlU7l3zb7/9VjVr1pQk+VXauUUAACAASURBVHw+nX322dq/f3+2MrNnz1ZiYqJKly6dbYXO6dOnq3v37nxhX4xIsAopOjpaKSkp2rVrl5KTk7PNUc9qxowZ6tatm6KjoyVJHTp0UOfOnXX55ZerR48eatGihXy+32ZsTp48Wbt379all16a7fosAN7qP/kdDXxtsfqMm6FPXp+kr1d9nKNMvbbX6N45n+jPT7+ihS+MDkKUQPEbNmyYDhw4oISEBI0dO1aJiYny+XxKT0/X6tWrdeedd2rNmjUqX768Ro/OfF/ceeed+uqrr5SSkqLq1avrvvvuC/JZAKFv09L3Vf6cqjq/bsM8yzjn9Nz6HwIzKA4ey9Czn/92/6+zlumOvw5R4qDHs82okDL7oL/OoELxIMHySKVKldSmTZvANL+T5da4hw8frpSUFC1cuFDOOV100UXZvnGIjo5W9+7dNXv27CKNHSjJYqqeJ0mqcE5V1buqs3ZuWJNn2VqNL9cPu7Yr7cD+PMsAkSImJkaTJ09WSkqKpk6dqn379qlWrVqKjY1VbGxsYMZGt27dtHr1aklStWrVFB0draioKN12221KTk4O5ikAYWHH2k+16b/v6YlrGmn6A7dp28plmjn8zmxlYmNjdfC7byVJJ9LT9cuhn1Tu7N9JypxeOO2+W3TDI+NUuWatbMetXbtW6enpaty4cfGcDCSxyEWh7Nu3T6VKlVKlSpV05MgRLVq0SEOHDs1WJj3D6astX+rAgQNq0aJFYPuJEyd08OBBVa5cWevWrdO6devUoUMHRZs0+K1kVbmgtpxzenfi69I5F+b5OyH8Jghw5o4dSZPLcCpdvoKOHUnTlhVL1Pa27N+4p36zTZVr1pKZ6dtNa3Xi+DGVq5T3dStApDh48KDKlSuns846SxMmTFDr1q0VExOjmJgY1axZU1988YUuueQSffDBB6pbt64kac+ePapevbokae7cuXmuUAjgN50GPqROAx+SJG1buVxLpz6n7n9/IVuZpKQkTZ0/Uxc2bKr1H7yt3zdtJTPTkZ9/1JRBN6vTwL8pLiHnZSpZr/9H8SHBKoQ9e/bolltu0YkTJ5SRkaEbb7xRXbp00YgRI9SkSRMlJSXJF2Ua8M+JirsqSU+k/Pat9/Gjv2jczZkXD5cuX1F//NtYPfX5Qd3f8BzNGnmXfkk7JDmn8y6upz8+8I9gnSIQ0Q7t36dp9/WWJGWcSFdCp+t0Sct2+nTWlMwCiYO1YfF8rZ7/uqJ9PvlKl1WP0eMD89hf6ttF+7Zv1dEjaXq8U7wSp05Wx44dNWbMGD355JP67rvvFB8fr86dO2vChAnBOUkgDz169NCSJUuUmpqq2NhYjRo1SsePH5ck9e/fX5s2bVKvXr0UHR2tunXrauLEiYFjx44dq549e+rYsWOqXbu2Jk+eLEkaPOR+rVubIjNTXFxcYIVNAAW38IXROr9ugupe2Un9+vXTi2/+R/9IaqpyZ/9OPR5/WZL0ycwJ2r/zay0e/7QWj39aktT3+TckZX4B//rrr/NzCUFAglUI8fHxgWXXs3rkkUey3b+6//05ypQqXUZ/nb08x/aoqCj1n8wbASgO58TG6e6ZS3Jsb96td+D2lb0H6creg3I9/o5J87Pd7+gfUR40aJAGDcr9GCBUTJ8+/ZT7W7RooS1btuS6LyEhQStXrsyx/dV/T8s24+KV7yR9l/dvwTELA8iudpOWqt2kpSSp/Z2//URPmTJl1PPJSTnKt731PrW9Ne9rHbdt2+Z9kPrtZ0mKqny4I8ECAAAAIkhRJ0C+KMvz8pXclLQvU0iwAMAjfKMHAAgFJEDBRYIFAB4p6Afa4IaVC/T4JGQAAIQ+c86dvlSmfBdEdgX9BuHk8g80qup1SAD8Hl+9L899ub0fT6U4yoeJUMwC+Qw7A2eS1PMZBpyZYH8eFRSfX3ljBAsAwkRBO7vHM5xKMWUxohV1m2CaEVAy8PffW8WeYIV7B4EGCCBYzqSzS+c4stEmAHiBL1O8VewJVrh/GNAAAQAAgPwraYtARdwUwUh8AYM9J5fylC+p5YGTReJnTFHjMyw0y4dSLJSPfCVtEah8L3IxatSo9/Trz0JHphqSdgc7iBBEveSOeskd9ZK7klYvqSNHjuwU7CCyyuUzLNxfE+IPvnA/B+IPrnCPXwr/c8gtfm8+v5xz/HNODz/8sAt2DKH4j3qhXqgX6iUS/4X7a0L8wf8X7udA/MRf0s+hKOOPKnSGBgAAAACQJBKsLEYFO4AQRb3kjnrJHfWSO+ol9IT7a0L8wRfu50D8wRXu8Uvhfw5FFn9BfmgYAAAAAHAKjGABAAAAgEdIsAAAAADAIyUqwTKzMmaWbGZrzWyDmeWYe2lmvc1sn5ml+P/dGoxYg8HMos1sjZnNz2VfaTObaWZbzexTM4sr/giL32nqpCS3le1m9rn/vFfmst/MbIy/vawzs0bBiLM45aNO2pjZj1nay4hgxFmSmNkkM9trZuvz2B/S7TQf8Yd0mzKzmmb2oZlt8n/m3p1LmZB9DfIZf6i/Bvnp94Ts53uk9NvCvX8V7n2hYPRZIu6Hhk/jqKS2zrlDZlZK0jIze9c5t+KkcjOdc3cFIb5gu1vSJkkxuezrJ+mAc+5/zOwmSU9I6l6cwQXJqepEKrltRZKucs7l9auBf5B0kf9fc0kv+P+PdKeqE0n6yDnXpdiiwRRJ4yRNzWN/qLfTKTp1/FJot6l0Sfc551abWUVJq8xsoXNuY5Yyofwa5Cd+KbRfg/z0e0L58z1S+m3h3r+KhL5QsfZZStQIlst0yH+3lP8fq3xIMrNYSddImpBHkWslveK/PUtSOzMLnZ/MLgL5qBPk7VpJU/3vuRWSKplZ9WAHhZLFObdU0g+nKBLS7TQf8Yc059we59xq/+2fldlBO/+kYiH7GuQz/pCWz35PyH6+R0K/Ldz7VyWkL+T536ESlWBJgWHOFEl7JS10zn2aS7Hr/UOEs8ysZjGHGCzPSLpfUkYe+8+XtFOSnHPpkn6UVLl4Qgua09WJVDLbipT5Afe+ma0ys9tz2R9oL367FGYdkzNwujqRpBb+qS7vmlm94gwOuYqEdhoWbco/7SlR0smfuWHxGpwifinEX4N89HtC+vM9Avpt4d6/ioS+ULH3WUpcguWcO+GcS5AUK6mZmdU/qcjbkuKcc/GSFum3bxUilpl1kbTXObfqVMVy2RZW3yIVRD7rpMS1lSxaOucaKXNYfYCZtT5pf4lqL36nq5PVki50zjWUNFbSm8UdIHII93YaFm3KzCpImi3pHufcTyfvzuWQkHoNThN/yL8G+ej3hPRrEM79tnDvX0VQX6jY+ywlLsH6lXPuoKQlkjqdtH2/c+6o/+54SY2LObRgaCkpycy2S5ohqa2Z/fukMrsk1ZQkM/NJOlthPHUlH05bJyW0rUiSnHO7/f/vlTRXUrOTigTai1+spN3FE11wnK5OnHM//TrVxTm3QFIpM6tS7IEiq7Bup+HQpvzXzcyW9Kpzbk4uRUL6NThd/OHwGvwqr36PwuTzPUz7beHev4qIvlAw+iwlKsEys6pmVsl/u6ykqyVtPqlM1jmXScqccx3RnHMPOOdinXNxkm6StNg596eTis2TdIv/djd/mZD4hqUo5KdOSmJbkSQzK++/4FtmVl5SB0knr3I2T1Iv/8o8l0n60Tm3p5hDLTb5qRMzO+/XefVm1kyZf3/3F3esyCas22motyl/bBMlbXLO/TOPYiH7GuQn/jB4DU7b71EIf76He78t3PtXkdAXClafpaStIlhd0itmFq3MP4KvO+fmm9kjklY65+ZJGmRmScpcPegHSb2DFm2QnVQvEyVNM7OtyqyXm4IaXJDQViRJ1STN9fcpfJJec869Z2b9Jck596KkBZI6S9oq6bCkPkGKtbjkp066SbrTzNIlHZF0U6h8iEYqM5suqY2kKma2S9JIZV4kHxbtNB/xh3qbainpz5I+919DI0kPSrpACovXID/xh/prkJ9+Tyh/vkdkvy2M6j9XYVb/QemzWGj9HQAAAACA8FWipggCAAAAQFEiwQIAAAAAj5BgAQAAAIBHSLAAAAAAwCMkWAAAAADgERIsAAAAAPAICRYAAAAAeIQECwAAAAA8QoIFAAAAAB4hwQIAAAAAj5BgAQAAAIBHSLAAAAAAwCMkWAAAAADgERIslGhmFmdm6wtQvreZ1Sjkcw42M2dmVQrzOAAAAAg9JFhAwfSWdMYJlpnVlNRe0jdeBQQAAIDQQYIFSD4ze8XM1pnZLDMrZ2aNzey/ZrbKzP5jZtXNrJukJpJeNbMUMytrZiPM7DMzW29mL5uZnea5/iXpfkmuyM8KAAAAxY4EC5AukfSycy5e0k+SBkgaK6mbc66xpEmS/u6cmyVppaSezrkE59wRSeOcc02dc/UllZXUJa8nMbMkSd8659YW8fkAAAAgSHzBDgAIATudc8v9t/8t6UFJ9SUt9A9IRUvak8exV5nZ/ZLKSTpH0gZJb59cyMzKSRouqYO3oQMAACCUkGABOafr/Sxpg3OuxakOMrMykp6X1MQ5t9PMHpZUJo/iv5dUS9Jaf9IWK2m1mTVzzn1XmOABAAAQOpgiCEgXmNmvyVQPSSskVf11m5mVMrN6/v0/S6rov/1rMpVqZhUkdcvrCZxznzvnznXOxTnn4iTtktSI5AoAACCykGAB0iZJt5jZOmVO8xurzGTpCTNbKylF0uX+slMkvWhmKZKOShov6XNJb0r6rJjjBgAAQIgx51jMDAAAAAC8wAgWAAAAAHiERS4Aj5nZc5JanrT5Wefc5GDEAwAAgOLDFEEAAAAA8EhBRrDIxAAA+WHBDgAAgGDhGiwAAAAA8AgJFgAAAAB4hAQLAAAAADxCggUAAAAAHiHBAgAAAACPkGABhZCeUbDFNQtaHgAAAOGlIL+DRc8QyMXoNan5LjsssUoRRgKEDJZpBwCUWIxgAQAAAIBHSLAAAAAAwCMkWAAAAADgERIsIAsWoQAAAEBh+IIdABBKfFHGohUAAAA4Y4xgAQAAAIBHSLAAAAAAwCMkWAAAAADgERIsAAAAAPAICRYQwgq6qiGrIAIAAAQXqwgCIYxVDQEAAMILI1gAAAAA4BFGsIBCmjG8v77dmKJoXynF1ktU1+FPK7pUKW1buVxT7/2zzqlxgSSpXtsuGvbC6DwfZ+DAgZo8ebIOHTokSdqxY4f69u2rjd98p7JnV1L3R1/Q2dVqSJImDbhROz9fpQsTmqv3mNeK/iQBAACQLyRYQCEl/OF6dX/0BUnSjAfv0Gdv/luX3dBHkhSXcFm+EqCVK1fq4MGD2bYNHjxYvXr10p74a/RV8kd6b+yj6v7o85Kk1r3u0vFfjujT2a94fDYAAAAoDKYIIuRt375dderU0a233qr69eurZ8+eWrRokVq2bKmLLrpIycnJSktLU9++fdW0aVMlJibqrbfeChx7xRVXqFGjRmrUqJE+/vhjSdKSJUvUpk0bdevWTXXq1FHPnj3l3JktEFGnVXuZmcxMNes10o/f7y7Q8SdOnNCQIUP05JNPZtu+ceNGtWvXTpJUu2krbfrvu4F9/9O8tUqXr3BG8QIAAKDoMIKFsLB161a98cYbevnll9W0aVO99tprWrZsmebNm6fHHntMdevWVdu2bTVp0iQdPHhQzZo109VXX61zzz1XCxcuVJkyZbRlyxb16NFDK1eulCStWbNGGzZsUI0aNdSyZUstX75crVq10vyn/qZtK5fliCG+Y1e16XN3njGeOH5caxa8ri6D/x7Y9s3nK/Vs9zaKqVpNnf86SukNW8oXZdmOGzdunJKSklS9evVs2xs2bKjZs2dLrXtqw+J3dDTtkNIO/qDylc4pTFUCAACgCJFgISzUqlVLDRo0kCTVq1dP7dq1k5mpQYMG2r59u3bt2qV58+bpqaeekiT98ssv+uabb1SjRg3dddddSklJUXR0tL788svAYzZr1kyxsbGSpISEBG3fvl2tWrVSl8GPnlGMb42+X3GJLVSrUQtJUo068Rr6zmqVLldBm5ct1LR7e+lf3bZlWxXwp33f6bUpr+m2l9/S6DWpOp7hAvvjej+o/744QitemKBajVoo5tzqio7mLQsAABDK6K0hLJQuXTpwOyoqKnA/KipK6enpio6O1uzZs3XJJZdkO+7hhx9WtWrVtHbtWmVkZKhMmTK5PmZ0dLTS09Ml6bQjWJP+coMO/bBP59dN0LC5/5YkLXrpH0o7sF89n3o6UL5MhYqB23Vatddbjw9Vamr2Jdd3b16n/Tu/1lPXNpMkHf/liP6R1FRD5n2mmKrnac6cORq9JlVHDx/S+g/mq0zFmIJVHAAAAIoVCRYiQseOHTV27FiNHTtWZqY1a9YoMTFRP/74o2JjYxUVFaVXXnlFJ06cOO1jnW4Eq+/zb2S7/9ncadryyYe69cXZior67bLGn1O/V4XK58rMtHP9ajmXocqVK0s79wfK1Lmig4Yv3Bi4P7LlhRoy7zNJUtqB/crIyJwOuGTSs2py7c2nrwgAAAAEFQkWIsJDDz2ke+65R/Hx8XLOKS4uTvPnz9df/vIXXX/99XrjjTd01VVXqXz58p4/95uPDVGl6jX1Qu8/SMpcjr3d7YP1+aK39emsKYqK9qlU6TLq8fjLMsu8/mrywJt0/YhnFFP1vDwfd9uq5brkji46cCxDtRq10LXDngjse6lvF+3bvlVHj6Tp8U7xun7EM7r48raenxsAAAAKxgqwctqZLbEGhJms10idzrDEKiFXHggBdvoiAABEJpZpBwAAAACPkGABAAAAgEdIsBDR0jOY2QoAAIDiwyIXiGi+KOMaJgAAABQbRrAAAAAAwCMkWAAAAADgERIsAAAAAPAICRYAAAAAeIQECwAAAAA8QoIFRJCCLkvPMvYAAADeYpl2IIKwLD0AAEBwMYIFAAAAAB4hwQIAAAAAj5BgAQAAAIBHSLAAAAAAwCMkWAAAAADgERIsAAAAAPAICRYAAAAAeIQECwAAAAA8QoIFAAAAAB4hwUJYSc9wwQ4BAAAAyJMv2AEABeGLMo1ek5rv8sMSqxRhNAAAAEB2jGABAAAAgEdIsAAAAADAIyRYAAAAAOAREiwAAAAA8AgJFgAAAAB4hAQLQcWy6wAAAIgkLNOOoGLZdQAAAEQSRrAAAAAAwCMkWAAAAADgERIsAAAAAPAICRYAAAAAeIQECwAAAAA8QoIFAAAAAB4hwQIAAAAAj5BgAQAAAIBHSLDgqfQMF+wQAAAAgKDxBTsARBZflGn0mtR8lx+WWKUIowEAAACKFyNYQAlW0BFHRigBAABOjREsoARjxBEAAMBbjGABAAAAgEdIsAAAAADAIyRYAAAAAOAREiwAAAAA8AgJFgAAAAB4hAQLAAAAADxCggUAAAAAHiHBAgAAAACPkGABAAAAgEdIsAAAAADAIyRYAAAAAOAREiwAAAAA8AgJFgAAAAB4hAQLAAAAADxCggUAAAAAHiHBAgAAAACPkGAByLf0DFek5QEAAMKdL9gBAAgfvijT6DWp+S4/LLFKEUYDAAAQehjBAgAAAACPkGABAAAAgEdIsAAUGa7ZAgAAJQ3XYAEoMlyzBQAAShpGsAAAAADAIyRYAAAAAOAREiwAAAAA8AgJFgAAAAB4hAQLAAAAADxCggUAAAAAHiHBAgAAAACPkGABAAAAgEdIsAAAAADAIyRYiFjLX3tJ9evX17+6tdKyV18MbF/04pN6vGMDjbmpjcbc1Eably2UJG1P+VTx8fEa96f2Sv1mmyTpyM8/atJfbpBzLtfnaNOmjXZtTAncP7D7Gz1zwxWSpG0rl+vh1rU1psdV+ud1l2vRS//Isf3prpfppX7/q01L3y+SOgAAAEDx8gU7AKAofLd1kz6b+29tW7dK/9rwkybf1V11rmivKhf8XpLUsmd/te41INsxy6a9oLmzZ2v0orX6dNYUXXPvI1o8/mm16XePzOyM4ohLuEy9x7ymY0fSNOamq7Rq1Y3ZtkvS7i8+17R7b1Gp0mX0P81bF+KsAQAAEGyMYCEi7fv6S9Vs0FjlypVTtM+nWo0v14bFC055TJTPpyNHjuj4L0cU7fNp/86v9dPeParduGWh4zmrbHmdf2lDffXVVzn21bikgdrddp8+eX1ioZ8HAAAAwcUIFiJStd9fqv8895j279+vY0cO64tlixRbt2Fg/yczJ2rN/Nd1ft2GuubeR1Q2ppLa9L1bt99+u/ad8OnG/3teC/41Uu3/Muy0zzVzeH+VKl1GknTi+HFZVM7vLdIO/qBvPl+levUe1aKPt+bYX+PSeC2d+lwhzhgAAAChgAQLp5Se4eSLOrPpccF0bu2LdWXvgWrfvr0OqLSqX1xPUdGZzb35Db3V9rb7JDMtfP5xvfPPEer28BjVuKSBVqxYodFrUvX1qo9Vsep5ck56beitivaVUud7R6li5XNzPFf3v7+o2LoJkjKvwXrl7p6BfdtTVmhMj6tkFqU2fQapXr16Ui4JlvK4xgsAAADhhQQLp+SLMo1ek5rv8sMSqxRhNAXT9I9/0uxR92j0mlT9Z+yjiqlWQ5KyJUnNrvtztoRIkpxzWjzxX7p59Hi99cQwXd1/qA7s/kYfTx+vjncNL1AMWa+1OpXdmz/XubUuLtBjAwAAIPRwDVYJk55RckZKDv2wT5J0cM8ubfjwHSV0uk6S9NO+7wJlNixeoGq/r5PtuNVvz1CdVlerbEwlHf/liCwqShYVpeO/HCmSOPd8uUGLJ/xTl93Yt0geHwAAAMWHEawSJpxHpArq1cF9NOfoTzqQHqWkoU+obEwlSdK7zz6iPV+ul8n0uxo19cfhTwWOOXz4sFbPn6m+z70hSWrVs79eHdJH0b5Suunxlz2L7depg8d/OaIKv6ui/x3yGCsIAgAARAASLESsOybN17DEKjkSyu6PPp/nMeXKldNtL78ZuF+rUQvd8/rSPMsvWbIk2+P/rsYFuueNjyRJtZu0VO0mOVcgrN2kpR5eui3f5wEAAIDwwRRBAAAAAPAICRYAAAAAeIQEC0DIKOgiLCVp0RYAABAeuAYLQMgoSYuwAACAyMQIFgAAAAB4hAQLAAAAADxCggUAAAAAHiHBAgAAAACPkGAVwltvvaX4+HglJCSoSZMmWrZsWWBfp06dVKlSJXXp0iXP45cuXapGjRrJ5/Np1qxZOfb/9NNPOv/883XXXXdJkn7++WclJCQE/lWpUkX33HOP9ycGhKi9X2/R87f8QX9rfr6WTn0u275nn31W9evXV7169fTMM8/kevyBAwfUtWtXxcfHq1mzZlq/fn1gX1xcnBo0aBB4PwMAAJwJVhEshHbt2ikpKUlmpnXr1unGG2/U5s2bJUlDhgzR4cOH9dJLL+V5/AUXXKApU6boqaeeynX/Qw89pCuvvDJwv2LFikpJSQncb9y4sa677jqPzgYIfeXOrqT/vf8xbfxwQbbt69ev1/jx45WcnKyzzjpLnTp10jXXXKOLLrooW7nHHntMCQkJmjt3rjZv3qwBAwbogw8+COz/8MMPVaUKKxMCAIAzxwhWIVSoUEFmJklKS0sL3JYyk6+KFSue8vi4uDjFx8crKirny7Bq1Sp9//336tChQ67HbtmyRXv37lWLlq0KcQZAeKlwTlXVrJeoaF+pbNs3bdqkyy67TOXKlZPP59OVV16puXPn5jh+48aNateunSSpTp062r59u77//vtiiR0AAJQMjGAV0ty5c/XAAw9o7969eueddzx5zIyMDN13332aNm1atm/Xs5o+fbq6d++uUtFR/G4QSrz69etr+PDh2r9/v8qWLasFCxbkOs2vYcOGmjNnjlq1aqXk5GTt2LFDu3btUrVq1WRm6tChg8xMd9xxh26//fYgnAkAAAh3JFiF1LVrV3Xt2lVLly7VQw89pEWLFhXq8dIznF58/nl17txZNWvWzLPcjBkzNG3atEI9FxApLr30Ug0dOlTt27dXhQoV1LBhQ/l8Of+8DRs2THfffbcSEhLUoEEDJSYmBsotX75cNWrU0N69e9W+fXvVqVNHrVu3Lu5TAQAAYY4Eq4Cee+45jR8/XpK0YMEC1ahRQ5LUunVrffXVV0pNTS3UNRy+KNOEBUu0fc0KPf7MOB07kqYTx49pfVqUOg0aIUna8+V67U07qoVRF6px4U8JCGmfzJyoz+ZmfpnQe+wMxVQ9L7AvPcPJF5U5Nbdfv37q16+fJOnBBx9UbGxsjscqV6GiJk+eLElyzqlWrVqqVauWJAXey+eee666du2q5ORkEiwAAFBgJFgFNGDAAA0YMECStHXrVjnnZGZavXq1jh07psqVKxf6OW76+4uB26vmTdeujSmB5EqS1r43Rw07srgFSoYW3fupRfd+ue7zRVlgiuyhH/apwjlVdXDPLk2a/obunPJujumz/Wv5VK5cOZ111lmaMGGCWrdurZiYGKWlpSkjI0MVK1ZUWlqa3n//fY0YMSK3pwQAADglEqxCmD17tqZOnapSpUqpbNmymjlzZmChiyuuuEKbN2/WoUOHFBsbq4kTJ6pjx44aMWKEmjRpoqSkJH322Wfq2rWrDhw4oLffflsjR47Uhg0bTvu86xbOU+8x04v69ICQ83Pq9xr3p/Y6mvazzKIU+8Z43Tr9I5WpUFGvDu6jwz8eUJSvlJKGPqGyMZUkSZ/OmiJJat6ttzZt2qRevXopOjpadevW1cSJEyVJ33//vbp27SpJSk9P180336xOnToF5RwBAEB4I8EqhKFDh2ro0KG57vvoo49y3f7II48Ebjdt2lS7du065XM0Tuqhxkk9sm27/+2VBYwUiAwVq1TTA++tC9wfllglMEp1x6T5uR7TvFvvwO0WLVpoy5YtOcrUrl1ba9eu9TZYAABQIrFMO4ASIz3DFWl5AAAARrAAlBhZr9nKD37WAAAAFBQjWEWMb8AB+aYcPAAABJVJREFUAACAksOcy3cCQKZwhgr6jXlByj/QqOqZhASElcdX78t1e0HfL2dSHmfEgh0AAADBwggWAAAAAHiEBKuAmPIHlBwFfb8fZxENAABKPBa5KCAukgdKjjN5v/P3AQCAkq3YE6z0DCdfVP6n5x/PcCoVQuVDjXOuyDuAlKd8qJYPd6H297Cg8QAAgJzyvcjFqFGj3pMUDl+31pC0O9hBhDnqsPCow8KjDgsvWHWYOnLkyE5BeF4AAIKuIKsIhoVRo0a5kSNH8hVsIVCHhUcdFh51WHjUIQAAxY9FLgAAAADAI5GYYI0KdgARgDosPOqw8KjDwqMOAQAoZhE3RRAAAAAAgiUSR7AAAAAAIChIsAAAAADAIxGTYJnZ/5nZOjNLMbP3zayGf3sbM/vRvz3FzEYEO9ZQdYo6NDMbY2Zb/fsbBTvWUGVm/zCzzf56mmtmlfzb48zsSJZ2+GKwYw1VedWhf98D/nb4hZl1DGacoczMbjCzDWaWYWZNsmynHQIAUMQi5hosM4txzv3kvz1IUl3nXH8zayNpsHOuS1ADDAOnqMPOkgZK6iypuaRnnXPNgxhqyDKzDpIWO+fSzewJSXLODTWzOEnznXP1gxlfODhFHdaVNF1SM2X+vtMiSRc7504EL9rQZGaXSsqQ9JIy//6t9G+PE+0QAIAiFTEjWL8mBn7lJUVG5liMTlGH10qa6jKtkFTJzKoXe4BhwDn3vnMu3X93haTYYMYTjk5Rh9dKmuGcO+qc+1rSVmUmWziJc26Tc+6LYMcBAEBJFDEJliSZ2d/NbKeknpKyTgVsYWZrzexdM6sXpPDCQh51eL6knVmK7fJvw6n1lfRulvu1zGyNmf3XzK4IVlBhJmsd0g69QTsEAKAI+YIdQEGY2SJJ5+Wya7hz7i3n3HBJw83sAUl3SRopabWkC51zh/xT3d6UdFGxBR1izrAOLZfyJXaE8HR16C8zXFK6pFf9+/ZIusA5t9/MGkt608zqnTRqWGKcYR3SDrPITx3mgnYIAEARC6sEyzl3dT6LvibpHUkjs3YcnHMLzOx5M6vinEstkiBD3JnUoTJHCmpm2RcrabfHoYWN09Whmd0iqYukds5/kaNz7qiko/7bq8zsK0kXS1pZxOGGpDOpQ9EOsynAeznrMbRDAACKWMRMETSzrKNSSZI2+7efZ2bmv91Mmee8v/gjDH151aGkeZJ6+VcTvEzSj865PcUeYBgws06ShkpKcs4dzrK9qplF+2/XVuYo6rbgRBna8qpDZbbDm8ystJnVUmYdJgcjxnBFOwQAoOiF1QjWaYw2s0uUuXLWDkn9/du7SbrTzNIlHZF0U5ZvxJFdXnW4QJkrCG6VdFhSn+CEFxbGSSotaaE/r1/hnOsvqbWkR/zt8ISk/s65H4IXZkjLtQ6dcxvM7HVJG5U5dXAAKwjmzsy6Shorqaqkd8wsxTnXUbRDAACKXMQs0w4AAAAAwRYxUwQBAAAAINhIsAAAAADAIyRYAAAAAOAREiwAAAAA8AgJFgAAAAB4hAQLAAAAADxCggUAAAAAHiHBAgAAAACP/D8MWZ3W2TsBmgAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pm.plot_posterior(trace)" + ] + }, + { + "cell_type": "code", + "execution_count": 247, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 247, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "trace_age = trace['beta'][:, 1]\n", + "trace_education = trace['beta'][:, 2]\n", + "trace_hours = trace['beta'][:, 3]\n", + "trace_age_squared = trace['beta'][:, 4]\n", + "sns.distplot(trace_age_squared, label='age^2')\n", + "sns.distplot(trace_age, label='age')\n", + "plt.legend()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.4 Examine the the joint distribution of Betas" + ] + }, + { + "cell_type": "code", + "execution_count": 246, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(336.9714285714286, 0.5, 'beta_hours')" + ] + }, + "execution_count": 246, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "sns.jointplot(trace_age, trace_hours, kind='kde')\n", + "plt.xlabel(\"beta_age\")\n", + "plt.ylabel(\"beta_hours\")\n", + "\n", + "# and so forth" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 2.3 Posterior Predictive Check\n", + "With the posterior predictive check we sample predicitons for our inferred model with the posterior distribution for $\\theta$.\n", + "Below we make a plot of our probability of making more than 50K. $P(>50K| m)$. Note that this is the probability given our inferred model." + ] + }, + { + "cell_type": "code", + "execution_count": 248, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "100%|██████████| 1000/1000 [00:00<00:00, 1209.03it/s]\n" + ] + }, + { + "data": { + "text/plain": [ + "(1000, 2000)" + ] + }, + "execution_count": 248, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "with model:\n", + " ppc = pm.sample_ppc(trace, samples=1000)['observed']\n", + "ppc.shape" + ] + }, + { + "cell_type": "code", + "execution_count": 249, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.251, 3, 'Average P(>50K)')" + ] + }, + "execution_count": 249, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.title('Overall P(>50K)')\n", + "sns.distplot(ppc.mean(1))\n", + "plt.vlines(y.sum() / y.shape[0], 0, 35)\n", + "plt.annotate('Average P(>50K)', (y.sum() / y.shape[0] + 0.002, 3))" + ] + }, + { + "cell_type": "code", + "execution_count": 250, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "array([[1. , 0.04109589, 0.26666667, 0.39795918, 0.01421073],\n", + " [1. , 0.04109589, 0.26666667, 0.12244898, 0.01421073],\n", + " [1. , 0.04109589, 0.26666667, 0.39795918, 0.01421073],\n", + " ...,\n", + " [1. , 0.04109589, 0.26666667, 0.29591837, 0.01421073],\n", + " [1. , 0.04109589, 0.26666667, 0.39795918, 0.01421073],\n", + " [1. , 0.04109589, 0.26666667, 0.47959184, 0.01421073]])" + ] + }, + "execution_count": 250, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "def prepare_shared_x(col_idx, new_value):\n", + " \"\"\"\n", + " :param col_idx: (int) 0 = age, 1 = education, 2 = hours\n", + " :param new_value: (flt) Replace the column values with this new value.\n", + " \"\"\"\n", + " shared_x.set_value(scaled_x)\n", + " feat = np.array(x)\n", + " feat[:, col_idx] = new_value\n", + " if col_idx == 0: # age is also squared\n", + " feat[:, -1] = new_value**2\n", + " feat[:, 1] = 5\n", + " feat = scaler.transform(feat)\n", + " feat = np.hstack((np.ones(feat.shape[0])[:, None], feat))\n", + " shared_x.set_value(feat)\n", + " \n", + "prepare_shared_x(0, 20)\n", + "shared_x.get_value()" + ] + }, + { + "cell_type": "code", + "execution_count": 257, + "metadata": {}, + "outputs": [], + "source": [ + "quants = []\n", + "age = np.arange(15, 80, step=5)\n", + "with model:\n", + " for a in age:\n", + " prepare_shared_x(0, a)\n", + " ppc = pm.sample_ppc(trace, samples=100, progressbar=False)['observed']\n", + " quants.append(np.quantile(ppc.mean(1), [0.05, 0.5, 0.95]))\n", + "quants = np.stack(quants)" + ] + }, + { + "cell_type": "code", + "execution_count": 258, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 258, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(age, quants[:, 1])\n", + "plt.ylabel('P(>50k)')\n", + "plt.xlabel('age')\n", + "plt.fill_between(age, quants[:, 0], quants[:, 2], alpha=0.5)" + ] + }, + { + "cell_type": "code", + "execution_count": 260, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'Bachelors': 13,\n", + " 'HS-grad': 9,\n", + " '11th': 7,\n", + " 'Masters': 14,\n", + " 'Some-college': 10,\n", + " 'Assoc-acdm': 12,\n", + " 'Doctorate': 16,\n", + " '9th': 5,\n", + " 'Assoc-voc': 11,\n", + " '10th': 6,\n", + " '7th-8th': 4,\n", + " 'Prof-school': 15,\n", + " '1st-4th': 2,\n", + " 'Preschool': 1,\n", + " '5th-6th': 3,\n", + " '12th': 8}" + ] + }, + "execution_count": 260, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "education_map" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercise\n", + "\n", + "* Make a probability plot hours worked and P(>50K).\n", + "* Plot P(>50K) for HS-grad, Bachelors and Masters.\n", + "\n", + "Note, columns are: 0 = age, 1 = education, 2 = hours" + ] + }, + { + "cell_type": "code", + "execution_count": 253, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 253, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "quants = []\n", + "age = np.arange(1, 80, step=5)\n", + "with model:\n", + " for a in age:\n", + " prepare_shared_x(2, a)\n", + " ppc = pm.sample_ppc(trace, samples=100, progressbar=False)['observed']\n", + " quants.append(np.quantile(ppc.mean(1), [0.05, 0.5, 0.95]))\n", + "quants = np.stack(quants)\n", + "plt.plot(age, quants[:, 1])\n", + "plt.ylabel('P(>50k)')\n", + "plt.xlabel('hours')\n", + "plt.fill_between(age, quants[:, 0], quants[:, 2], alpha=0.5)" + ] + }, + { + "cell_type": "code", + "execution_count": 262, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 262, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "age = np.arange(1, 80, step=5)\n", + "with model:\n", + " for education in ['HS-grad', 'Bachelors', 'Masters']:\n", + " quants = []\n", + " for a in age:\n", + " # prepare shared\n", + " shared_x.set_value(scaled_x)\n", + " feat = np.array(x)\n", + " feat[:, 0] = a\n", + " feat[:, -1] = a**2\n", + " feat[:, 1] = education_map[education]\n", + " feat = scaler.transform(feat)\n", + " feat = np.hstack((np.ones(feat.shape[0])[:, None], feat))\n", + " shared_x.set_value(feat)\n", + " ppc = pm.sample_ppc(trace, samples=100, progressbar=False)['observed']\n", + " quants.append(np.quantile(ppc.mean(1), [0.05, 0.5, 0.95]))\n", + " \n", + " quants = np.stack(quants)\n", + " plt.plot(age, quants[:, 1], label=education)\n", + " plt.fill_between(age, quants[:, 0], quants[:, 2], alpha=0.5)\n", + " \n", + "\n", + "plt.ylabel('P(>50k)')\n", + "plt.xlabel('age')\n", + "plt.legend()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3 Markov Chain Monte Carlo [MCMC]\n", + "\n", + "* Markov Chain: A stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event.\n", + "* Monte Carlo: Probablistic simulation of events with stochastic variables.\n", + "\n", + "\n", + "Or as I like to put it:\n", + "\n", + "*\"\n", + "Markov chain Monte Carlo (MCMC) is a technique for estimating by simulation the expectation of a statistic in a complex model. Successive random selections form a Markov chain, the stationary distribution of which is the target distribution. It is particularly useful for the evaluation of posterior distributions in complex Bayesian models. In the Metropolis–Hastings algorithm, items are selected from an arbitrary “proposal” distribution and are retained or not according to an acceptance rule. The Gibbs sampler is a special case in which the proposal distributions are conditional distributions of single components of a vector parameter. Various special cases and applications are considered.\n", + "\"* (Encyclopedia of Biostatistics)\n", + "\n", + "![](images/donotunderstand.jpg)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 3.1 King Markov\n", + "[statistical rethinking](http://xcelab.net/rm/statistical-rethinking/)\n", + "Let's take a look at an analogy to understand what is really going on.\n", + "\n", + "![](images/islands.png)\n", + "\n", + "* King Markov has many islands and amnesia. He doesn't know how many islands he has nor the number of residents living on those islands.\n", + "* King Markov wants to visit islands proportional to number of people living on it. For example, with two islands, with distribution `[1, 2]`, spend twice as much time on the second island as one the first.\n", + "* He doesn't recognize islands from earlier visits.\n", + "* He can only count the current island and one other island.\n", + "\n", + "**GOAL:** \n", + "Find the distribution of number of residents on each island.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Simple algorithm\n", + "* Count the number of inhabitants, stay that amount of day, then move to the next one.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 92, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 92, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD4CAYAAAAAczaOAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAGMxJREFUeJzt3X+QVeWd5/H3h98ihBDsWBtapJPgDwRFaMGSiDgabMcacLa0BFfDmMxSihS6ZqvCbFJImGTLZCxn1ipcpUbi7KyIUcdNb0IkJkoyDEFpFIVWkYZhoYdJZBqB+AOk4bt/3ANzbW5zT3ffvn3hfF5VXZzznOc559s/+Nynzz3ntCICMzPLhl49XYCZmZWPQ9/MLEMc+mZmGeLQNzPLEIe+mVmGOPTNzDLEoW9mliEOfTOzDHHom5llSJ+eLqCts846K0aOHNnTZZiZnVI2bNjwbxFRVaxfxYX+yJEjaWho6OkyzMxOKZL+X5p+Pr1jZpYhDn0zswxx6JuZZUjFndM3Mzvm8OHDNDc3c/DgwZ4upWIMGDCA6upq+vbt26nxDn0zq1jNzc0MHjyYkSNHIqmny+lxEUFLSwvNzc3U1NR0ah8+vWNmFevgwYMMGzbMgZ+QxLBhw7r0m49D38wqmgP/07r69XDom5lliM/pd9LIBT8r2mfHAzeUoRKz7Ejz/64jsvh/1DN9M7Myam1t7dHjpwp9SXWStkhqkrSgwPY7JW2StFHSGkmjk/aRkj5O2jdKerTUn4CZWXe68cYbmTBhAhdddBFLly4FYNCgQXzzm99k/PjxXHPNNezZsweAqVOncu+993LFFVcwZswYXn31VQAWLVrEnDlzmDZtGl/72tc4ePAgd9xxB2PHjuXSSy/l5ZdfBuChhx7i61//OgCbNm1izJgxfPTRRyX9fIqGvqTewBLgemA0MOtYqOdZHhFjI2Ic8EPgobxt2yJiXPJxZ6kKNzMrh2XLlrFhwwYaGhp4+OGHaWlp4cMPP2T8+PG89tprXHXVVXz3u9893v/DDz9k7dq1PPLII8cDHGDDhg385Cc/Yfny5SxZsgTIBftTTz3F7NmzOXjwIPfeey9NTU08//zz3HHHHTz22GMMHDiwpJ9Pmpn+RKApIrZHxCfACmBGfoeIOJC3eiYQpSvRzKznPPzww1xyySVcfvnl7Nq1i61bt9KrVy9uueUWAG677TbWrFlzvP+sWbMAmDJlCgcOHGDfvn0ATJ8+nTPOOAOANWvWcPvttwNwwQUXcO655/Luu+/Sq1cvnnjiCW6//XauuuoqJk+eXPLPJ80bucOBXXnrzcCktp0k3Q3cB/QD/ihvU42k14EDwHci4h87X66ZWfmsXr2aX/7yl/z2t79l4MCBTJ06teA18vmXUba9pPLY+plnnnm8LaL9efHWrVsZNGgQu3fv7mr5BaWZ6Re6KPSEiiNiSUR8CfgW8J2k+V+BERFxKbkXhOWSPnPCAaQ5khokNRw7N2Zm1tP279/P0KFDGThwIO+88w7r1q0D4OjRozz77LMALF++nK985SvHxzz99NNAbjY/ZMgQhgwZcsJ+p0yZwpNPPgnAu+++y86dOzn//PPZv38/99xzD7/5zW9oaWk5foxSSjPTbwbOyVuvBk72ErQC+J8AEXEIOJQsb5C0DTgP+NQD8yNiKbAUoLa21qeGzKygcl9iWVdXx6OPPsrFF1/M+eefz+WXXw7kZu2NjY1MmDCBIUOGHA96gKFDh3LFFVdw4MABli1bVnC/c+fO5c4772Ts2LH06dOHJ554gv79+3PXXXcxd+5czjvvPB5//HGuvvpqpkyZwuc///mSfU462a8ZAJL6AO8C1wD/AqwHbo2Ixrw+oyJia7L8J8D9EVErqQrYGxFHJH0R+EdgbETsbe94tbW1cSr8ERVfp2/W/d5++20uvPDCni7jBIMGDeKDDz44oX3q1Kk8+OCD1NbWduvxC31dJG2IiKIHLjrTj4hWSfOAVUBvYFlENEpaDDRERD0wT9K1wGHgfWB2MnwKsFhSK3AEuPNkgW9mZt0r1R25EbESWNmmbWHe8j3tjHsOeK4rBZqZVZpCs3zIvfFb6XxHrplZhjj0zcwyxKFvZpYhDn0zswzxo5XN7NSx6MQbnbq2v/0n3bxv3z6WL1/O3LlzS3vcHuSZvplZO/bt28cjjzxyQvuRI0d6oJrScOibmbVjwYIFbNu2jXHjxnHZZZdx9dVXc+uttzJ27Fh27NjBmDFjjvd98MEHWbRoEQDbtm2jrq6OCRMmcOWVV/LOO+/00GdwIp/eMTNrxwMPPMDmzZvZuHEjq1ev5oYbbmDz5s3U1NSwY8eOdsfNmTOHRx99lFGjRvHKK68wd+5cXnrppfIVfhIOfTOzlCZOnEhNTc1J+3zwwQesXbuWm2+++XjboUOHuru01Bz6ZmYp5T8euU+fPhw9evT4+rFHLh89epTPfvazbNy4sez1peFz+mZm7Rg8eDB/+MMfCm47++yzee+992hpaeHQoUP89Kc/BeAzn/kMNTU1PPPMM0Du2flvvPFG2WouxjN9Mzt1FLnEstSGDRvG5MmTGTNmDGeccQZnn3328W19+/Zl4cKFTJo0iZqaGi644ILj25588knuuusuvve973H48GFmzpzJJZdcUtba2+PQNzM7ieXLl7e7bf78+cyfP/+E9pqaGl544YXuLKvTfHrHzCxDHPpmZhni0Dezilbsr/tlTVe/Hg59M6tYAwYMoKWlxcGfiAhaWloYMGBAp/fhN3LNrGJVV1fT3NzMnj17erqUijFgwACqq6s7Pd6hb2YVq2/fvkXvgLWO8ekdM7MMSRX6kuokbZHUJGlBge13StokaaOkNZJG5237i2TcFknXlbJ4MzPrmKKhL6k3sAS4HhgNzMoP9cTyiBgbEeOAHwIPJWNHAzOBi4A64JFkf2Zm1gPSzPQnAk0RsT0iPgFWADPyO0TEgbzVM4Fjb7XPAFZExKGI+GegKdmfmZn1gDRv5A4HduWtNwOT2naSdDdwH9AP+KO8sevajB1eYOwcYA7AiBEj0tRtZmadkGamrwJtJ1w0GxFLIuJLwLeA73Rw7NKIqI2I2qqqqhQlmZlZZ6QJ/WbgnLz1amD3SfqvAG7s5FgzM+tGaUJ/PTBKUo2kfuTemK3P7yBpVN7qDcDWZLkemCmpv6QaYBTwatfLNjOzzih6Tj8iWiXNA1YBvYFlEdEoaTHQEBH1wDxJ1wKHgfeB2cnYRkk/Bt4CWoG7I+LU/TPyZmanuFR35EbESmBlm7aFecv3nGTs94Hvd7ZAMzMrHd+Ra2aWIQ59M7MMceibmWWIQ9/MLEMc+mZmGeLQNzPLEIe+mVmGOPTNzDLEoW9mliEOfTOzDHHom5lliEPfzCxDUj1wzTpp0ZAi2/eXpw7L8ffDzDN9M7MsceibmWWIQ9/MLEMc+mZmGeLQNzPLEIe+mVmGOPTNzDIkVehLqpO0RVKTpAUFtt8n6S1Jb0r6laRz87YdkbQx+agvZfFmZtYxRW/OktQbWAJ8FWgG1kuqj4i38rq9DtRGxEeS7gJ+CNySbPs4IsaVuG4zM+uENDP9iUBTRGyPiE+AFcCM/A4R8XJEfJSsrgOqS1ummZmVQprQHw7syltvTtra8w3g53nrAyQ1SFon6cZCAyTNSfo07NmzJ0VJZmbWGWmevaMCbVGwo3QbUAtcldc8IiJ2S/oi8JKkTRGx7VM7i1gKLAWora0tuG8zM+u6NDP9ZuCcvPVqYHfbTpKuBb4NTI+IQ8faI2J38u92YDVwaRfqNTOzLkgT+uuBUZJqJPUDZgKfugpH0qXAY+QC/7289qGS+ifLZwGTgfw3gM3MrIyKnt6JiFZJ84BVQG9gWUQ0SloMNEREPfBXwCDgGUkAOyNiOnAh8Jiko+ReYB5oc9WPmZmVUarn6UfESmBlm7aFecvXtjNuLTC2KwWamVnp+I5cM7MMceibmWWIQ9/MLEMc+mZmGeLQNzPLEIe+mVmGOPTNzDLEoW9mliEOfTOzDHHom5lliEPfzCxDHPpmZhni0DczyxCHvplZhjj0zcwyxKFvZpYhDn0zswxx6JuZZYhD38wsQxz6ZmYZkir0JdVJ2iKpSdKCAtvvk/SWpDcl/UrSuXnbZkvamnzMLmXxZmbWMUVDX1JvYAlwPTAamCVpdJturwO1EXEx8Czww2Ts54D7gUnAROB+SUNLV76ZmXVEmpn+RKApIrZHxCfACmBGfoeIeDkiPkpW1wHVyfJ1wIsRsTci3gdeBOpKU7qZmXVUnxR9hgO78tabyc3c2/MN4OcnGTu87QBJc4A5ACNGjCha0MgFPzvp9h0P3FB0H3b6KfpzMaBMhZhVsDQzfRVoi4IdpduAWuCvOjI2IpZGRG1E1FZVVaUoyczMOiNN6DcD5+StVwO723aSdC3wbWB6RBzqyFgzMyuPNKG/HhglqUZSP2AmUJ/fQdKlwGPkAv+9vE2rgGmShiZv4E5L2szMrAcUPacfEa2S5pEL697AsoholLQYaIiIenKncwYBz0gC2BkR0yNir6S/JPfCAbA4IvZ2y2diZmZFpXkjl4hYCaxs07Ywb/nak4xdBizrbIFmZlY6viPXzCxDHPpmZhni0DczyxCHvplZhjj0zcwyxKFvZpYhDn0zswxx6JuZZYhD38wsQxz6ZmYZ4tA3M8sQh76ZWYY49M3MMsShb2aWIQ59M7MMceibmWWIQ9/MLEMc+mZmGeLQNzPLEIe+mVmGpAp9SXWStkhqkrSgwPYpkl6T1CrppjbbjkjamHzUl6pwMzPruD7FOkjqDSwBvgo0A+sl1UfEW3nddgJ/BvzXArv4OCLGlaBWMzProqKhD0wEmiJiO4CkFcAM4HjoR8SOZNvRbqjRzMxKJM3pneHArrz15qQtrQGSGiStk3RjoQ6S5iR9Gvbs2dOBXZuZWUekCX0VaIsOHGNERNQCtwJ/I+lLJ+wsYmlE1EZEbVVVVQd2bWZmHZEm9JuBc/LWq4HdaQ8QEbuTf7cDq4FLO1CfmZmVUJrQXw+MklQjqR8wE0h1FY6koZL6J8tnAZPJey/AzMzKq2joR0QrMA9YBbwN/DgiGiUtljQdQNJlkpqBm4HHJDUmwy8EGiS9AbwMPNDmqh8zMyujNFfvEBErgZVt2hbmLa8nd9qn7bi1wNgu1mhmZiXiO3LNzDLEoW9mliEOfTOzDEl1Tv+Us2hIij77u78OM7MK45m+mVmGOPTNzDLEoW9mliEOfTOzDHHom5lliEPfzCxDHPpmZhni0DczyxCHvplZhjj0zcwyxKFvZpYhDn0zswxx6JuZZYhD38wsQ07PRyub2amh2GPQ/Qj0kks105dUJ2mLpCZJCwpsnyLpNUmtkm5qs222pK3Jx+xSFW5mZh1XNPQl9QaWANcDo4FZkka36bYT+DNgeZuxnwPuByYBE4H7JQ3tetlmZtYZaWb6E4GmiNgeEZ8AK4AZ+R0iYkdEvAkcbTP2OuDFiNgbEe8DLwJ1JajbzMw6IU3oDwd25a03J21pdGWsmZmVWJrQV4G2SLn/VGMlzZHUIKlhz549KXdtZmYdlSb0m4Fz8targd0p959qbEQsjYjaiKitqqpKuWszM+uoNKG/HhglqUZSP2AmUJ9y/6uAaZKGJm/gTkvazMysBxQN/YhoBeaRC+u3gR9HRKOkxZKmA0i6TFIzcDPwmKTGZOxe4C/JvXCsBxYnbWZm1gNS3ZwVESuBlW3aFuYtryd36qbQ2GXAsi7UaGZmJeLHMJiZZYhD38wsQxz6ZmYZ4tA3M8sQh76ZWYY49M3MMsTP0zfLojI8x37kgp8V7bNjQJcPYx3kmb6ZWYY49M3MMsShb2aWIQ59M7MMceibmWWIQ9/MLEMc+mZmGeLr9M3KrQzXyJu1xzN9M7MMceibmWWIQ9/MLEN8Tt/sNFTsuTd+5k12eaZvZpYhqUJfUp2kLZKaJC0osL2/pKeT7a9IGpm0j5T0saSNycejpS3fzMw6oujpHUm9gSXAV4FmYL2k+oh4K6/bN4D3I+LLkmYCPwBuSbZti4hxJa7bzMw6Ic1MfyLQFBHbI+ITYAUwo02fGcDfJcvPAtdIUunKNDOzUkgT+sOBXXnrzUlbwT4R0QrsB4Yl22okvS7p15Ku7GK9ZmbWBWmu3ik0Y4+Uff4VGBERLZImAP9H0kURceBTg6U5wByAESNGpCjJrDL5r0VZpUsz028GzslbrwZ2t9dHUh9gCLA3Ig5FRAtARGwAtgHntT1ARCyNiNqIqK2qqur4Z2FmZqmkCf31wChJNZL6ATOB+jZ96oHZyfJNwEsREZKqkjeCkfRFYBSwvTSlm5lZRxU9vRMRrZLmAauA3sCyiGiUtBhoiIh64HHg7yU1AXvJvTAATAEWS2oFjgB3RsTe7vhEzMysuFR35EbESmBlm7aFecsHgZsLjHsOeK6LNZqZWYn4MQynu2KP8QU/ytcsQ/wYBjOzDHHom5lliEPfzCxDHPpmZhni0DczyxBfvXOK8x/LMLOO8EzfzCxDHPpmZhni0DczyxCHvplZhjj0zcwyxKFvZpYhDn0zswxx6JuZZYhD38wsQ3xHrpVHsef6+5n+1lMy9rPpmb6ZWYZ4pm9dVuz5P+BnAFnP8fOpPs0zfTOzDEkV+pLqJG2R1CRpQYHt/SU9nWx/RdLIvG1/kbRvkXRd6Uo3M7OOKhr6knoDS4DrgdHALEmj23T7BvB+RHwZ+GvgB8nY0cBM4CKgDngk2Z+ZmfWANDP9iUBTRGyPiE+AFcCMNn1mAH+XLD8LXCNJSfuKiDgUEf8MNCX7MzOzHqCIOHkH6SagLiL+PFm/HZgUEfPy+mxO+jQn69uAScAiYF1E/O+k/XHg5xHxbJtjzAHmJKvnA1u6+HmdBfxbF/dRCpVQRyXUAJVRRyXUAJVRRyXUAJVRRyXUAF2v49yIqCrWKc3VOyrQ1vaVor0+acYSEUuBpSlqSUVSQ0TUlmp/p3IdlVBDpdRRCTVUSh2VUEOl1FEJNZSzjjSnd5qBc/LWq4Hd7fWR1AcYAuxNOdbMzMokTeivB0ZJqpHUj9wbs/Vt+tQDs5Plm4CXInfeqB6YmVzdUwOMAl4tTelmZtZRRU/vRESrpHnAKqA3sCwiGiUtBhoioh54HPh7SU3kZvgzk7GNkn4MvAW0AndHxJFu+lzylexUURdVQh2VUANURh2VUANURh2VUANURh2VUAOUqY6ib+Samdnpw3fkmplliEPfzCxDHPpmZhlyWjxlU9IF5O7+HU7uPoDdQH1EvN2jhWWUpIlARMT65FEcdcA7EbGyh+v6XxHxtZ6swXpW3hWIuyPil5JuBa4A3gaWRsThHi2wDE75N3IlfQuYRe7xEM1JczW5b+yKiHigp2rrCckL4HDglYj4IK+9LiJeKMPx7yf3nKY+wIvk7sxeDVwLrIqI73d3DUkdbS8rFnA18BJAREwvRx1tavoKuceQbI6IX5TxuJOAtyPigKQzgAXAeHJX1f33iOj2vxIiaT7wfETs6u5jFanjSXI/mwOBfcAg4B+Aa8jl4eyTDC9lHV8C/pTcfUytwFbgqbJ8L06D0H8XuKjtK3Tyit4YEaN6prJP1XJHRPyoDMeZD9xNbtYyDrgnIn6SbHstIsaXoYZNybH7A78DqvPC5pWIuLi7a0jqeI1cqP0t/353+FP8++XEvy5DDa9GxMRk+T+T+948D0wD/m+5JiSSGoFLksuvlwIfkTwjK2n/j2WoYT/wIbCN3PfhmYjY093HLVDHmxFxcXIT6b8AX4iII8mzwt4ox89n8v/0T4BfA38MbATeJ/ciMDciVndrARFxSn8A75B75kTb9nOBLT1dX1LLzjIdZxMwKFkeCTSQC36A18tUw+uFlpP1jWX8mvcC/gu53zbGJW3by/x9z/9arAeqkuUzgU1lrOPtvOXXeuJ7AryefE+mkbuvZw/wArmbOgeX8WuxGegHDAX+AHwuaR+Q/3Xq5ho2Ab2T5YHA6mR5RDn+n54O5/TvBX4laStw7FfHEcCXgXntjioxSW+2twk4u0xl9I7klE5E7JA0FXhW0rkUfg5Sd/hE0sCI+AiYcKxR0hDgaJlqICKOAn8t6Znk399T/vewekkaSi7sFMnMNiI+lNRaxjo25/22+Yak2ohokHQeUK5z2JF8T34B/EJSX3KnAWcBDwJFHxRWIo+Tmyj2Br4NPCNpO3A5uVPE5dIHOELuN+LBABGxM/m6dKtT/vQOgKRe5M6VDicXbs3A+ijP3b/Havg9cB25X9M+tQlYGxFfKEMNLwH3RcTGvLY+wDLgP0VEt/8tA0n9I+JQgfazgP8QEZu6u4ZCJN0ATI6I/1bGY+4g90IncqeYroiI30kaBKyJiHFlqmMI8D+AK8k9xXE8uQnSLmB+RLxRhhpej4hL29l2RkR83N015B3vCwARsVvSZ8m937QzIsryiBhJ95D7GyTrgCnADyLiR5KqgOciYkq3Hv90CP1KkDw2+kcRsabAtuURcWsZaqgGWiPidwW2TY6If+ruGqw4SQOBsyP3NybKedzBwBfJzTKbI+L3ZTz2eRHxbrmOV+kkXQRcSO5N/XfKemyHvplZdvjmLDOzDHHom5lliEPfzCxDHPpmZhny/wFU1pN6zgUzyQAAAABJRU5ErkJggg==\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "distribution = np.array([100, 200, 30, 10, 200, 50, 60, 80, 10, 1])\n", + "\n", + "def generate_path(distribution, start=0):\n", + " current_position = start\n", + " while True:\n", + " for _ in range(distribution[current_position]): # stay the number of days\n", + " yield current_position # return the current island to the distribution stack\n", + " current_position = (current_position + 1) % len(distribution)\n", + "\n", + "gen = generate_path(distribution, 0)\n", + "\n", + "path = np.array([next(gen) for _ in range(1000)])\n", + "plt.plot(path)\n", + "plt.show()\n", + "(pd.Series(path).value_counts(normalize=1)\n", + " .reindex(np.arange(len(distribution)))\n", + " .rename('approx').to_frame()\n", + " .assign(true=distribution / distribution.sum())\n", + ").plot.bar()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After 1000 iterations we have visited al the islands, but the approximation is not very good." + ] + }, + { + "cell_type": "code", + "execution_count": 150, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.5, 1.0, 'distribution ratio per island')" + ] + }, + "execution_count": 150, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "distribution = np.array([50, 100, 10])\n", + "gen = generate_path(distribution, 0)\n", + "\n", + "n = 1000\n", + "path = np.array([next(gen) for _ in range(n)])\n", + "\n", + "for i in range(len(distribution)):\n", + " # cumulative mean\n", + " plt.plot(np.arange(n), np.cumsum(path == i) / np.arange(1, n + 1), label=f'proportion_{i}')\n", + " plt.plot(np.arange(n), distribution[i] / distribution.sum() * np.ones(n), ls='--', label=f'true_proportion_{i}')\n", + "\n", + "plt.xlabel('days')\n", + "plt.title('distribution ratio per island')" + ] + }, + { + "cell_type": "code", + "execution_count": 120, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "0.34" + ] + }, + "execution_count": 120, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(path == 0).sum() / path.shape[0]" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/training_bayesian/images/donotunderstand.jpg b/training_bayesian/images/donotunderstand.jpg new file mode 100644 index 0000000..f94d07c Binary files /dev/null and b/training_bayesian/images/donotunderstand.jpg differ diff --git a/training_bayesian/images/islands.png b/training_bayesian/images/islands.png new file mode 100644 index 0000000..6342dcc Binary files /dev/null and b/training_bayesian/images/islands.png differ diff --git a/training_bayesian/images/weights.png b/training_bayesian/images/weights.png new file mode 100644 index 0000000..03987de Binary files /dev/null and b/training_bayesian/images/weights.png differ