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@mlaves
Last active September 17, 2020 14:18
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Linear Regression Metropolis-Hastings.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "Linear Regression Metropolis-Hastings.ipynb",
"provenance": [],
"collapsed_sections": [],
"authorship_tag": "ABX9TyMqsLf+ja9rvSOkcaS5ArB4",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/mlaves/752ae71a852753b69cb7e8e2f66f0997/linear-regression-metropolis-hastings.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "in_lubYXoB3S",
"colab_type": "text"
},
"source": [
"# Bayesian Linear Regression with Metropolis-Hastings MCMC\n",
"\n",
"In this simple example, I will use the Metropolis-Hastings Markov chain Monte Carlo (MCMC) algorithm with symmetric proposal distribution to sample from the exact posterior of a Bayesian linear regression model."
]
},
{
"cell_type": "code",
"metadata": {
"id": "2ljE70zHqevN",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 71
},
"outputId": "5c3ae16a-4308-4b9a-c573-4f0412577fe9"
},
"source": [
"import numpy as np\n",
"import scipy.stats as stats\n",
"from matplotlib import pyplot as plt\n",
"from tqdm import tqdm\n",
"import seaborn as sns"
],
"execution_count": 1,
"outputs": [
{
"output_type": "stream",
"text": [
"/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
" import pandas.util.testing as tm\n"
],
"name": "stderr"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "OlkAVyWHqhIS",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 295
},
"outputId": "224d09a1-1ced-4963-ba32-5d5d35249094"
},
"source": [
"# create some training data\n",
"x = np.linspace(-20, 20)\n",
"params_true = [0, 5, 10]\n",
"y = params_true[0] + params_true[1]*x + stats.norm.rvs(loc=0, scale=params_true[2], size=x.shape)\n",
"\n",
"plt.plot(x, y, '.')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.title('data');"
],
"execution_count": 88,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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xnaVYXRtDWkyWp2aoz9r+NEtElpskrbGlMUNrF9sjR491frGd5vKpLsUqaY19GjNmbV/SvLFPo0fW9iUtEvs0JEmtmTTmiFNzSOqb5ak54dQckobAlsaccGoOSUNg0pgT3ishaQgsT80J75WQNAQmjTni8F1JfbM8JUlqzaQxQA6tlTRUlqcGxqG1kobMlkaPNmpROLRW0pDZ0ujJpBZFnzPjStLxmDSmZKuz2U5a2MihtZKGzKQxBdvph9isReHQWklDZdKYgu0uh2qLQtK8MWlMwXb7IWxRSJo3Jo0psNUgaVmYNKbEVoOkZeB9GpKk1kwakqTWTBpb5LxQkpZZL0kjyQ8nuS/JsSQr6469M8mBJA8kec3Y/quafQeSXN991H92P8Z7P/4Ab/rAPhOHpKXTV0vjXuANwKfGdya5DLgGeAlwFfCfkuxIsgO4CXgtcBnwI81zO+W8UJKWXS+jp6rqfoAk6w9dDdxaVU8DX0pyALiiOXagqh5qXndr89zPdxPxiPNCSVp2QxtyewGwb+zxo80+gEfW7X/5Rm+QZA+wB2Dnzp1TDc77MSQtu5kljSR3AS/a4NANVfWRWf3cqtoL7AVYWVmpab+/92NIWmYzSxpV9eptvOwQcNHY4wubfWyyX5LUkaENub0duCbJqUkuAXYDnwbuAXYnuSTJKYw6y2/vMU5JWkq99GkkeT3wH4Fzgf+a5LNV9Zqqui/JbYw6uI8Cb6+qZ5rXXAfcAewAPlhV9/URuyQts1RNvew/GCsrK7W6utp3GJI0V5Lsr6qVjY4NrTwlSRowk4YkqTWTxgTOMSVJzze0m/sGYTtrfkvSMrClsQHnmJKkjZk0NrA2x9SO4BxTkjTG8tQGnGNKkjZm0pjAOaYk6fksT0mSWjNpSJJaM2lIklozaUiSWjNpSJJaM2lIklpb6KnRkzwJHDyBtzgH+MqUwpkm49oa49oa49qaRYzr4qo6d6MDC500TlSS1UlzyvfJuLbGuLbGuLZm2eKyPCVJas2kIUlqzaSxub19BzCBcW2NcW2NcW3NUsVln4YkqTVbGpKk1kwakqTWTBrrJPm3Sb6Q5HNJPpzkjLFj70xyIMkDSV7TcVw/nOS+JMeSrIzt35XkT5J8tvn6xSHE1Rzr7Xytl+TdSQ6NnafX9RjLVc05OZDk+r7i2EiSh5P8YXOOVnuM44NJnkhy79i+s5LcmeTB5nvnaxdMiKvXz1aSi5J8Isnnm7/FH2/2z+Z8VZVfY1/A9wMnN9s/A/xMs30Z8AfAqcAlwBeBHR3G9ReA7wE+CayM7d8F3Nvj+ZoUV6/na4M43w385AA+Xzuac3EpcEpzji7rO66x+B4GzhlAHN8HvGz8sw38LHB9s3392t/mAOLq9bMFnA+8rNk+Hfij5u9vJufLlsY6VfXxqjraPNwHXNhsXw3cWlVPV9WXgAPAFR3GdX9VPdDVz2trk7h6PV8DdgVwoKoeqqpvAbcyOlcaU1WfAv543e6rgZub7ZuBH+w0KCbG1auqeqyqPtNsfwO4H7iAGZ0vk8bmfhT4b832BcAjY8cebfYNwSVJ/m+S/5HklX0H0xji+bquKTt+sI/SRmOI52VcAR9Psj/Jnr6DWee8qnqs2f4ycF6fwawzhM8WSXYB3wv8H2Z0vpZyudckdwEv2uDQDVX1keY5NwBHgVuGFNcGHgN2VtVTSS4Hfi/JS6rq6z3H1bnN4gTeD7yH0UXxPcB7Gf1ToOd6RVUdSvKdwJ1JvtD8dz0oVVVJhnK/wCA+W0leCPwO8E+r6utJnj02zfO1lEmjql692fEkbwF+AHhVNQVB4BBw0djTLmz2dRbXhNc8DTzdbO9P8kXgxcDUOjG3ExcdnK/12saZ5JeBj84ylk10fl62oqoONd+fSPJhRuW0oSSNx5OcX1WPJTkfeKLvgACq6vG17b4+W0lewChh3FJVv9vsnsn5sjy1TpKrgHcAf6eqvjl26HbgmiSnJrkE2A18uo8YxyU5N8mOZvtSRnE91G9UwMDOV/NHs+b1wL2Tnjtj9wC7k1yS5BTgGkbnqndJvj3J6WvbjAaF9HWeNnI7cG2zfS0wiFZu35+tjJoUvwLcX1X/fuzQbM5XXz3+Q/1i1GH7CPDZ5usXx47dwGjkywPAazuO6/WM6t9PA48DdzT7fwi4r4n1M8DfHkJcfZ+vDeL8NeAPgc81f0zn9xjL6xiNcPkioxJfb+dlXVyXMhrN9QfNZ6q32IDfYFR6PdJ8vt4KnA3cDTwI3AWcNZC4ev1sAa9gVBr73Nh163WzOl9OIyJJas3ylCSpNZOGJKk1k4YkqTWThiSpNZOGJKk1k4YkqTWThiSpNZOG1KEkf7mZ2O605g7s+5L8xb7jktry5j6pY0l+CjgN+Dbg0ar66Z5DklozaUgda+acugf4U+CvVtUzPYcktWZ5Sure2cALGa2ydlrPsUhbYktD6liS2xmt2HcJo8ntrus5JKm1pVxPQ+pLkjcDR6rqQ82U9v8ryd+sqv/ed2xSG7Y0JEmt2achSWrNpCFJas2kIUlqzaQhSWrNpCFJas2kIUlqzaQhSWrt/wMNl7/UbWNOawAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "AnN8CopBa8LZ",
"colab_type": "code",
"colab": {}
},
"source": [
"# our linear model a + b*x\n",
"\n",
"def model(x, params):\n",
" return params[0] + params[1]*x"
],
"execution_count": 90,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "-JCDmlbBq2uM",
"colab_type": "code",
"colab": {}
},
"source": [
"def log_likelihood(x, y, params, model):\n",
" pred = model(x, params)\n",
" ll = stats.norm.logpdf(y, loc=pred, scale=params[2])\n",
" return np.sum(ll)"
],
"execution_count": 31,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "BcNguqnR-jxO",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 296
},
"outputId": "3a9072d7-b9ff-4a72-c046-fa62d76d6fe5"
},
"source": [
"# Exmaple: Plot the likelihood profile for the slope a\n",
"ll = []\n",
"a_test = np.linspace(3, 7)\n",
"for a in a_test:\n",
" ll.append(log_likelihood(x, y, [params_true[0], a, params_true[2]], model))\n",
"\n",
"ll = np.array(ll)\n",
"plt.plot(a_test, ll)\n",
"plt.grid()\n",
"plt.xlabel('param[1]')\n",
"plt.ylabel('log-likelihood');\n",
"print('ML result:', np.round(a_test[np.argmax(ll)], decimals=2))"
],
"execution_count": 32,
"outputs": [
{
"output_type": "stream",
"text": [
"ML result: 4.8\n"
],
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "zICoY3Wm3xMQ",
"colab_type": "code",
"colab": {}
},
"source": [
"def log_prior(params):\n",
" prior_0 = stats.norm.logpdf(params[0], loc=0, scale=5)\n",
" prior_1 = stats.uniform.logpdf(params[1], loc=0, scale=10)\n",
" prior_2 = stats.uniform.logpdf(params[2], loc=0, scale=30)\n",
" return prior_0+prior_1+prior_2\n",
"\n",
"def log_posterior(x, y, params, model):\n",
" return log_prior(params) + log_likelihood(x, y, params, model)"
],
"execution_count": 33,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "yCoYnuxF7WBq",
"colab_type": "code",
"colab": {}
},
"source": [
"def proposal_function(params):\n",
" return stats.norm.rvs(loc=params, scale=[0.1, 0.5, 1.0], size=(params.shape))\n",
"\n",
"\n",
"def metropolis_hastings(x, y, start_params, model, iter=1000):\n",
" params = np.array(start_params)\n",
" chain = np.zeros((iter, len(params)))\n",
" chain[0] = params\n",
"\n",
" log_post = lambda p: log_posterior(x, y, p, model)\n",
"\n",
" for i in tqdm(range(iter-1)):\n",
" proposal = proposal_function(chain[i])\n",
" post_prob = np.exp(log_post(proposal) - log_post(chain[i])) # symmetric proposal\n",
" if np.random.rand() < post_prob:\n",
" chain[i+1] = proposal\n",
" else:\n",
" chain[i+1] = chain[i]\n",
"\n",
" return chain"
],
"execution_count": 34,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "uBdEWIImI6r_",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 34
},
"outputId": "6a64eec7-7758-46f6-cd9e-a7ba7291380a"
},
"source": [
"# We start using the true parameters.\n",
"# Alternatively, we could also perform maximum likelihood or maximum posterior\n",
"# estimation to find good start parameters for MCMC sampling.\n",
"\n",
"start_params = params_true\n",
"chain = metropolis_hastings(x, y, start_params, model, iter=10000)"
],
"execution_count": 35,
"outputs": [
{
"output_type": "stream",
"text": [
"100%|██████████| 9999/9999 [00:10<00:00, 944.50it/s]\n"
],
"name": "stderr"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "cPqO2ssPXNnG",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 51
},
"outputId": "a5da4a1c-ecaa-4cbe-a420-5a497959fbbf"
},
"source": [
"print('mean:', np.round(np.mean(chain, axis=0), decimals=2))\n",
"print('std: ', np.round(np.std(chain, axis=0), decimals=2))"
],
"execution_count": 36,
"outputs": [
{
"output_type": "stream",
"text": [
"mean: [0.01 4.84 9.78]\n",
"std: [0.1 0.11 0.7 ]\n"
],
"name": "stdout"
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "6VXc_CfyKFqp",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 297
},
"outputId": "3c8aa3f0-b6b8-4b04-b32b-a0180067ec46"
},
"source": [
"# let's see the posterior\n",
"\n",
"burn_in = 1000\n",
"fig, ax = plt.subplots(1, 3)\n",
"for i in range(len(ax)):\n",
" sns.distplot(chain[burn_in:,i], ax=ax[i])\n",
" ax[i].set_xlabel(f\"param[{i}]\")\n",
"ax[0].set_ylabel('posterior density')\n",
"fig.tight_layout()"
],
"execution_count": 37,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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x2Dv39PG1R57nXw8O0BYL86u7rOkjq9utfrgTI9NNs9FtjINqEIOTedZ1Jlb0GYloiJAEs0iihlEstX6OL5Xuc6Wl7UE52oxBXKwYXoiq8uNDQxzsT/Oh114wU1a+2v7v8WETQRlWgKMisdIISkRIRsNkisFzUA7zjWKhanCdiESALiAwJUzZQpnEElN8YBxU0DkyOMmXHj7BAwcHuHxzF7/5i+fPvJeKhelIRDgxbCIowwpwVCRWGkEBJGMRMgGLoERkjYh028+dUSzPzjptN/Ae+/k7gR9qQCoEVJV8qbzkKj4wDirIHDyT5q2feYiTYxnedtkGbty1hVDo3LariLCpO0n/RNZFK5uLUZJoAE4P1OHBKS7f3L2iz2qLhckWAndTqmUUyxeAr4rIEaxRLDe5Z259yRTKVLQ2FQmHlD0a3qhJBJNcscy/PHGaneva+aXLNs6r4bmhK0F/C6nLGAfVAOrRA+XQFgsHToOrxlEsOeDGZtrVLGaUzJfQghAOCW2xsImgAsqTp8aZzpf44xtexjP9k/Oet74ryf5TE020zF1Miq8BDKRXriLhYEVQwUrxtTrprD2sMLa0HjkjdxRcnu2fpCcV44otC2dcNnQlGJkukC+1xj3BOKgGMDhZvwgqGQ0Hbg+q1ZmcmQW1tD8/IxgbTHLFMseGp7hoXQeLtfqt77L2tQftLE3QMQ6qAdRDRcKhLR6hUK60zIqpFVhOig9MBBVUDg9MUSwr23tTi577TH8aoGX2oRrmoFpZb60eKhIOzkb6hJmmGhhmUnxLKJIA46CCiuN0NnQtXvXbZW8btEolXyMjqJbVW6tHD5RDm71PMR6wQolWxomgkkvcg0rFI+SKlZbSYmsFDvaniYVD9KRii57bZc+Xa5U5cQ1zUK2stzYwmatLDxRAm11ePDZtxn0HhUlbrigRWdqfn6PNODId7P0HEbleRJ6zMysfn+P994rIkIg8YT9+3Q0768Uz/WnWdcZrGr0Sj4bpiEdMiq8etKLemqoymM6bCMowL+lskWhYiISXXiQBMDIV3MWK3Rt3G/Bm4GLgZhG5eI5T71bVK+zHHU01ss48P5JhTUftC9r1XQkTQTmIyIscRq20ot5aPVUk4FwaaDwT3JtSq5HOFZdcIAHWyA2AoalAR1BXA0dU9ZiqFoC7sDItgSRXLHM2naMntbSWlKfPtEYvVC1LuEdE5Jsi8pblpt9aSW+tWkWiHsxEUKZIIjCks6UlF0gAtNsb5EGOoKjKqticso/N5h0isl9E7hGRLc0xrf44ozNq2X9y6ExGSbdIRqUWB3UhcDvwn4DDIvL/iciFi/1Qq+qt1VNFAiAWDhEWYcw4qMCQzhWX3AMFkLIjqJFgR1C18B1gu6peBjzAuX3sF+H17YG+UcdB1b4l0JWMMpkrUSwHv1hm0b8Su9jhAVW9GfgNLIfyqIj8REReucCPbgB+JCL7gb1Ye1D3isinROTt9jlfAFbbemu/C7xoQ9Rv1FNFAiyBSEvuKNCr5pYinS0uuYIPIB4JEw0Lw8F2UDNZFZvN9rEZVHVEVZ1fwh3AVfN9mNe3B/pGlh5BdSQiKAT9OgBq0OKz96DejRVBDQD/FSvyuQL4JrBjrp9rVb21eqpIOCRjYcamTQQVFCZzpZn5TkulPR4JeopvL7BTRHZgOaabgHdVnyAiG1S13375duCZ5ppYP06PZ0lEQ6SWsGBxFr+D6TwbupKNMs0T1PJX8jPgq8Avq+qpquP7ROTzjTHLvwykc8QjobqoSDi0xcKMmwgqMKRzxZkhdEulIxHlbDq4FVyqWhKRDwP3A2Hgi6p6YJbS/UfsLEwJS+n+va4ZvEIG0nnWdyYWlTiqxln8OovhIFOLg/qEqn6j+oCI3Kiq31TVQDTW1pOhyfy8UvnLJRmLmCKJgKCqyy6SAOhui3J6PNgqAqp6H3DfrGPVmZdbgVubbVcjOJvOsXaJFb/O/WUgwAsVh1p2aufaFwrExVFP7tzTx517+hhI5+qa3gNoi4aNgwoI+VKFQrlCchlFEgDdyRhnxrNUKr6uJTLYDKaX3tTfHo8gtHgEJSJvBt4CbBKRz1S91YkVWhvm4OjQFFt72ur6mckAzoRqVZzy4KWO2nBYlYpSLCuDk/kZZWuDP1FVBtJ53rhE3c5wSGiLRxiabO0I6gywD8gBj1U9dgNvarxp/kNVmcyVGpDiC5Mtlo2ieQBI55YnFOvQnbSqvU6PZ+pmk8EdcsUK2WJ5WU39nYlIS4zcmDeCUtUngSdF5Gu2DJFhEXLFCqWK0lnnFN+Monm2yNqO+hVfGJrPckdtOKxqsxY/J0ezXLWtbmYZXMC5FtZ2JpiyFy537umr6Wc7EhEGWiCCWijF9w1V/VXgcRGpTngLVnvUZQ23zmc4F1xHss4RlO2g0tkia5eg2WXwHk6Kb7E9qPluVKtSMUICx4en626bobk4o1PWtMdnHFStdCSinBwNfhS90FL/o/Z/39YMQ4KAo1Jd7yIJp6kzKPtQtjTNV4B1WAr3t6vqX8865zrg28Bx+9A/q+qnmmlnI1hpii8aDrFtdYpDA5P1NMvgAs6k7FWpKMeHl/azHYkIw1N5yhUlHPL9AIh5WSjF5zTCDQNZVa3YEkcvAb7XDOP8hhNBdcYbE0EFxUFhFdn8nqr+XEQ6gMdE5AFVPTjrvJ+qaqAWSCstkgC4cF07z9kOyom03nXN1pUbZ2gqWdtBOfuKS6EjEaWiluzVUsvU/UQtta4PAgkR2QT8K5aixJcaaZRfmbZD9uWqBMxH0CIoVe1X1Z/bzyexlADmEgQNHE6UnVxmBAVw0boOTgxPkyuaohk/ky1Y10J329IXtJ0t0qxbi4MSVc0A/wH4nKreCFzSWLP8yXS+RDgkxJc4iG4xgjz2XUS2Y0lizZ4VBvBKEXlSRL4nIoG45tI5exbUCtIyF67voKLw2R8eqaNlhmaTKZRJREPLSvc6lcKDAS+UqMlB2aKw/xH4rn3MlJLNwVS+TCoWXpJsSS04F3DQhhaKSDvwT8Bvq2p61ts/B7ap6uXA3wDfmuczPK1WPZt0tkhnIrqia+SidR1AaygJBJlMsbys9B5UyR0FvNS8Fgf1USzliH+xNbHOw5rtZJjFdL40M/W0noRDQns8EpgUH4CIRLGc09dU9Z9nv6+qaVWdsp/fB0RFpHeO8zytVj2bdK5E5wqrPLf3pgiLzIx2MfiTTKG8rPQeQId9nwn6NbDo3VRVH8Tah3JeHwM+0kij/Mp0oTEOCqwZMEFxUPbgyy8Az6jqX8xzznpgQFVVRK7GWkz5epglOBHUyq6RaDjEmo544NM7QSdbKC1bDSQSDpGMhhmZbnEHZVfu/T6wvfp8VX1d48zyJ9P50rJVqhcjYFM0X41VbPOUiDxhH/t/gK0Aqvp5rAGWvykiJSAL3OT3YZZg7UHVQ2lkbWe8JfpggkymsPwUH0Aq+KNXalIz/ybweazBYKZsaAGmC+UlzXVZCl3J4KT4VPUhrIbvhc75LPDZ5ljUPMYzRTZ1r3yGz6q2GAdOp6moEqrznqehOWQLZVallr9YaY+HAz+0sBYHVVLVv224JT6nWK5QKFUaluLrTsY4NjzVkM82NI+xTIFVbctfNTt0t0UpqzJVhz0tQ/NRVTLFMl0riKDa45HAO6haiiS+IyK/JSIbRKTHeTTcMp/h9EClYmYPyjA35YoykS3O6OmthC7bKQWtsrNVyBbLlCu67CIJsFN808FO8dXioN4DfAx4mHOK5vsW+yER2SIiPxKRgyJyQEQ+Osc514nIhIg8YT8+Oddn+YHpvJX9TMUblOJri5qZUD4nnS2iCt31iKDslfd4Jtg3qKAyZv8tr2Sx0h63BpkWy5V6meU5aqni27HMz24pOZtpuyu8kVV8+VKFXLG8bB03g7uM2c5kVSpKtrCym4qz8jZRtT9xFhYrSfE595qx6UJg5Y4WjaBEpE1EPiEit9uvd4rIog6l1eRsZlJ8DXJQzj5DgCr5Wg5n1VyPCCoRDROPhExU7VMmZq6FlUVQAMMBruSrJcX3D0ABeJX9+jTwP5fyJSuVs/GDWkAz9qDArJj9jLNqrkeRBFg3KGdkg8FfOIuVh4+O1DwDajbnHFRwCyVquZuer6q/JiI3A6hqRpag01KjnM2UiLwFS85m5+zPUNXbgdsBdu3a5clemKl8mbAIiUXm/CyXbuOgfM/otOOg6lN1l4pHyBSMg/Ij41nrWmhbJF2/kPNyHFSQm3VruZsWRCSJNbcHETkfqOk3Ui85Gz8wXSjRFq+/Dp+DiaD8z3gdU3wAqVh4ZqaQwV8410JyBX2TztSEBw4M1MUmL1KLg/oj4P8CW0Tka8APgD9Y7IdqlbNxojG/y9lM50szK5pGMFNWbPYcfMtopkAkJCuWOnJoi0dmUssGfzGeKRANC9Hw8jMu8UiIcEiYygd3kVJLFd8DIvJz4Fqs7v+Pqmot8x9bSs5mOl9q2P4TmAgqCDx6fJTV7bG6RdlOBOXTP5l5EZHrgb/Gmppwh6r+r3nOewdwD/AKVV209cVLjGeKtK3wfiEigd+HnPc3JCJXzjrkTNjdKiJbnQq9+Wg1OZtMocyqVH1SN3PRaRyU75nOlwiJLHtTfDZtsQililIIUB+MiISB24A3AqeAvSKye3Z7it268lHmLrzyPOPZ4oqGVjqk4uFAR9ELufD/Y/83AewCnsRyOJdhNeq+srGm+YtMoUxbg3T4wBq50RGwkRutxlSd08BOU3gmWCmeq4Ej9tQEROQu4AZgdv/kHwN/hiUi4DvGM4W63C+CHkHNmwBV1deq6muxIqcr7Zk7V2GVi59uloF+oFJRcsUyyWjjUnxgqUmYPij/Um8H5aSIpoNVybcJOFn1+hSz+ift7M4WVf0ui+DVFpXxTHFFBRIO7QHfh6xlh+4iVX3KeaGqTwMvbZxJ/mMyV0KhoREUGD0+P6O2sGs9G7kd5fzpYEVQCyIiIeAvgN+r5XyvDrQczxbrcr9I2RFU0PYhHWpxUPtF5A5bN+86Efl7YH+jDfMTTk9DPVZEC9GVjHJ40Cia+5HpQplSRRsSQWWLgXJQp4EtVa8388KMTQfwMuDHInICq3hrt4jsapqFK0RV7RTfyq+F9ri1Dzkd0HaDWhzU+4ADWBuSH8XKBb+vkUb5jZmehgZr5HUlo0G7GbUMw5NW62A9HJRTZJGwF0S5YF0Te4GdIrJDRGLATcBu501VnVDVXlXdrqrbgUeAt/upii9TKFMsa52KJOxm3YCqSdRSZp4D/tJ+GObASbs1I8WXC+hKKeg4cjT1TPElItb6MkiLFlUticiHgfuxysy/qKoHRORTwD5V3b3wJ3gfRzS4Lim+2Dk9vm2rUyv+PK/R2F39FsGZyWMiKMN8DNoRVGeyfn9ykXCIaFgCt2ixVWXum3VszlE8qnpdM2yqJ07GpV5VfHBORitoNEY4rsWYyDRpD6otSqmiZAN2Q2oFBtI5ADoS9Z1+m4iGzaLFZzgZl2Qd9qCcVoOgpvgWdFAiEhaR/90sY/xKPXS1asFRwR4zQ+p8x+BknrBI3dPAiWg4aHtQgWesjgvamT2oVoygVLUMvKZJtviW8WyRWCREJNTYgLTHVqrwezhf47RlEZHPiMgREdk/h7KJrxhI5+hIRAjVWUw4GQ2TKwZHSaIVqGeKLxoOEY+EAjtyo5YY83ER2Q18E5h2Ds6lTt6qjGeKi8rm14PVtoMKwMVYy7TlN2ONXtkJXAP8rf1fXzKYztNRJ5HYahLRUEv1QQWBiTrvWafiEd8vWuejlr+YBJbC+OuqjilgHJTNRLbQ8PQewOr2OOD/CEpV+7G1HVV1UkScacvVDuoG4Cu2ePAjItItIhvsn/UdA+ncjJ5iPUlEw4wEeKJqEBmbLpCMhlekZF5Nezwy5zXgtCO865qtdfkeN6ilzNz0PC1CvWRLFiMoKb5qFpi2PJ/kzQsclIjcAtwCsHWrd/8QB9I5Lt7YWffPTZoiCd8xni3WbWglWBFUALIqc7KoCxeRzSLyLyIyaD/+SUQ2N8M4vzCebXyK7849fdz75BnCIoHZEF1k2nJNeFXKppp0rkg6V6I7WX+1+6RdJBFUqZsgMp4p0lWnoYFv1n0AACAASURBVJVgSV4F5Z4wm1pizH/A6uTeaD++Yx8z2FgRVONbykSEtniY0QCkdBabtszikje+4dRoFqAh41gS0TAVDVazbtAZzxTormO6tz0eYWy6QKUSvEVKLQ5qjar+g6qW7MeXAG8uVV1AVUnXabZLLaRiEd+vlmqZtoy1KPrPdjXftcCEX/efTo1lAOqa1nFwrrt0NriK1kFjPFtkVaq+Kb5SRUnngickXcuyf0RE3g183X59Mz4dy94IssUyhXKl4TJHDu3xCCPTvs831zJt+T7gLcARIIOP9R9PjlkRVE8d0zoOjh7fRLbI+q5E3T/fUH/GM0W66pjuddQkhqcKdDfgGnOTWhzU+4G/wdLiU+BharhZiMgW4CvAOvvnblfVv551jmCNdn4L1k3ovYtN6vUazWrSdWiLh31fJFHjtGUFPtQcixrLqbEMqVi4IddIImolQYK4eg4ijpJ5d52LJMBSk7hgbXvdPtcL1FLF9zzw9mV8dkv0ujRLydwhFY9wfGh68RMNnuHUWJbNq9qQOjfpQnWKzzgoP+CMXalvFZ91Dfh94ToX8zooEfkDVf20iPwNVgT0AlT1Iwt9cKv0ujizoJqV4kvFIkzmS+RLZeKR5nynYWWcHM2wpSfZkM9OOA7KRFC+YMx2Il3JKOU6CYA4Kb6hAJaaLxRBPWP/d8VzVoLc69LsFJ+zWhqbLrK+yzgor6OqnB7Lcu15qxvy+QlTJOErHB2+nlScocn6OJRUPEIkJJydyNXl87zEvA5KVb8jImHgUlX9/eV+Qb16XYDbAXbt2uWpWspzs12aM7nEmf8yMp03m+I+IJ0tMZkvsXlVoyIoew/KpPh8gaP40JOK1c1BhURY15kIpIOqRSz21cv98Fbodamn8GMtOOH8PY+dasr3GVbGSbvEfPOqtoZ8fiRkzYQyKT5/4LSI9LbXt9puQ1eC/gA6qFqW/U8sRyx2Cb0uHxaRu7CKI3zX61JvXa3FcCp2pvMmpeMHTs04qGTDNrGT0bBJ8fmEUbtFpKfOTdvruxIcOLOsBJWnaaRYbEv0uoxlinUtGV0MZw/KKFj7g5O2isSWnjb2n5poyHckomETQfmEkekCsXBoJhNSLzZ0JXjg4ACq2pBqUbdomFhsq/S6TGSb2xyXiIYJCUyZCMrz3Lmnjx88O0hHIkJXA5TMHZLGQfmGkakCq9tjdXci67uS5EsVxjLFukdnblKLWOyFIvIDEXnafn2ZiHyi8ab5g7FMfZWJFyMkQmciajbFfcJ4ptCw/SeHRDQ8M2PI4G1GpwsNcSBOb+SJEeu/xXKFcgC0+WrZOPl74FagCKCq+4GbGmmUnxjLFGZGsTeLzmSUCbNi9gWj0wW2NKiCzyEZM3tQfmGkQQ7Kqeh97uwk5Ypy8+2P8PmfHKVUr2Yrl6jFQbWp6qOzjpm/BpvxJu9BAXQmIuaG5AMsWZtiEyKokEnx+YSRqTy99uDRetLdFiUWDvFsf5q7955k3/NjnB7P8uiJ0bp/VzOpxUENi8j52GoSIvJOZjXStiqViqWr5UYEZW5I3me6YAkJN6oHyiERDZPOFgMzE0pErheR50TkiIh8fI73PygiT4nIEyLykIhc7IadS6VSUQbTedZ11r9/0eqFivPs2Um++sjzvGxTJ91tUfpGM3X/rmZSi4P6EPB3wEtE5DTw28AHG2qVT5jMlagoTY+gupJRCqUKk8ZJeZpxu4l7S09jI6ikPRNquuD/yk5bHOA2LJ3Oi4Gb53BAd6rqpap6BfBpYL42Fk8xmilQKFdY31n/CApge2+KPcdHeaY/zU2v2MqGTv/3RtXioFRV34A1A+olqvqaGn8u8DgqEs+enWzq93YmLIc4kPb3xRd0xuwm7v2nxrlzT1/DvicRLMHYq4EjqnpMVQvAXVianTPMUqRJMYdWqBdxlB7WdzUmov53O60xfeevSXHjrs2s70oyPJkn5+NhlrU4mn8CUNVpVXXuxPc0ziT/cE7mqLmaeJ12ybLfV0dBxxEGbXQKOGCCsfPpc74AEfmQiBzFiqAWFK72CuccVGMkytrjEfb8P6/nux/5d8QjYdZ3JVDgyOBUQ76vGSykZv4S4BKgS0T+Q9VbnVjNuy3PjMxRk0ZtOHQmrH+2IGpvBYmxjKUykmjw9dGKU3VV9TbgNhF5F/AJ4D1znecloemzdsZjQwM1NKv3t5z2lzPjWV62qath39lIFoqgLgLeBnQDv1T1uBL4jcab5n2aLRTr4ERQJsXnbcYyhbqO9p6PgM2EWqo+513AL8/3pqrerqq7VHXXmjVr6mTi8jg7kSMckoZU8c2F0xx+737/1rQtpGb+beDbIvJKVf1ZE23yDc0WinWIhkO0xcIzKzKDNxnLFFnb0fibUcCm6u4FdorIDizHdBPwruoTRGSnqh62X74VOIwPOJvOsbYjTjjUHCmiVDxCSPB1E3cte1C/IiKdIhK1FSWGROTdDbfMB4xnCgiQaLKDAqtQwqT4vM1EtthQiSMHJ4Ly843IQVVLwIeB+7Fm0n1DVQ+IyKdExJns/WEROWBrfP4u86T3vMYTfeNEmuScwCo97/C56kwtual/r6p/ICK/ApwA/gPwIPCPjTTMD4xlirY2XvPFGTuTERNBeZjJXJFCqdIUBxUPkIMCUNX7sISkq499sur5R5tu1Aq5c08fE7nmRNTVdCYivladqSWCcv7C3gp8U1UbI8nsQ8Yyhaan9xysCCrPnXv6GlrC3AhE5IsiMujoO87x/nUiMmE3Yj4hIp+c6zwv40S3nU1wUOGQ0JmIzFQNGrxJOltsyvVQTVcy6uvimVoiqO+IyLNAFvhNEVkDmKU71h6UWw6quy3G8PNjFEoVYhHftaV9Cfgs8JUFzvmpqr6tOebUH6cFwOlZazQ9qdjMMDyD98gVy+RLFbqacD1UL1g7klEO+bjMfNE7m6p+HHgVsEtVi1hDC29Y+Kdag+GpfN3nutTKansi52jGfzclVX0Q8LdI2CI46ddmpPjAclCNGohoWDnOPlCzI6iOeIRCqeLbZt1axm1EgXcDd4vIPcAHsAYYtjzDU3nam7RCnk1vysplj0zlXfn+JvBKEXlSRL4nIpfMd5KI3CIi+0Rk39DQUDPtW5CZFF+iOQuYnlTcOCgPk85ZabZmLVgcUnYLjF+j61pyQ38LXAV8zn5caR9raUrlCiPTBTqadAOajSPZPzLlzwtvEX4ObFPVy4G/Ab4134le6nOppn8iRyoWJhJuTvp1tYmgPI1TwNKsBYtDys7wjPr0PlHLb+sV9o3C4Yci8mSjDPILo9MFVHEtxZeMhQO771Cttaaq94nI50SkV1WH3bRrKQykc01dLfe0xxjLFAI38jsoOD1qzU7xtcetPfLhaX9mWmpZ3pXtcRsAiMh5wKIJzaBXag3ZqTW3HBTAttVtgUzxich6se+yInI11nXqq7Ry/0SuqTej1akYxbLOpJIM3mIiaxVURZsUUTs4EZRfMy213F0/BvxIRI4BAmwD3lfDz32JAFdqDU1ajsGtFB/AjtUpfjA06Nr3LxcR+TpwHdArIqeAP8JuZ1DVzwPvxKoYLWFVj96kPht2dHYiy851HU37PiflOzpdaPo+h2Fx0tli0yo6q5lJ8fk0glr07qqqPxCRnVjafADPqeqi/7eq+qCIbF+Zed7lnINy72awbXWKiWyRos/GOqvqzYu8/1msxY0vyRXLjGWaoyLhsLr9XNHMjt5U077XUBvpKlWRRvYtzv7seCREJCTBjaBEJAH8FvAarLkrPxWRz6tqPXqhXmnvZ50Bfl9VD8xjg2cUiR28kOLb3msNwjOb497CEfFt5op5nT0EbyDtz5Vy0JnIldjU4MnKcyEipOIRhn3qoGpJiH4Fa+zG32Ctai8BvlqH7/Z1pdbwZIFULOxqk+y21dZK2a+ro6DiNOk2M4Ja12GNWbjvKf8qVweVQqnCdL7kSooPIBUPBzfFB7xMVatHLv9IRA6u9Iv9Xqk1NJVnTZN1tWazw3ZQwwEslPAzMxFUsnnRdXdblEhImPSx7lpQcf4+3XJQ7fGIb6t9a1n+/1xErnVeiMg1wL6VfrHfK7WGJnOuO6iutigd8QiDk8ZBeYmZCKqJNyQRoSMRMVV8HsRxUO0uFVSlYhHfZllq+Y1dBTwsIs7u21bgORF5ClBVvWyuHwp6pdbwVIGda9vdNoM1nXEGJ400opc4O5GjIx6ZURlvFp0+H60QVJyCKrf2q1PxCCNn077skavlN3b9cj446JVaQ5N5XnX+arfNYF1Hgsf6xnx58QWVsxM51jdwrPd8dCSjnJ3INv17DQvjdktKezxCrlghUyjPlJ37hVrKzJ9vhiF+4isPn2AiW2RNk0Y3L8TazjiFUoUzEzk2dTe/SsjwYvrTzXdQd+7poysR4dCASfF5DSfF55ZzSNlqEiNTBd85KN/NafACU3nrJtDr8h4UwFq7euvwwKTLlhgcBiZyrO90IYJKRCmUKjPXp8EbDE3mSURDTVeRcJhRk/BhJZ9xUMtg0t6I9kQEZTvJIz6e+RIkSuUKg5PupPicqkFHSd3gDYam8nTE3Wvob/ex3JFxUMvAUSbe0N38m9BsUvEIqViYwwPGQXmBv//pcSqKOw7KrhocTBsH5SWGJvOuVfBB9cgNE0G1BDMOqssbez5rOxMcHjQpPi+Qnrk23HNQA6aq01MMTxVcVZw5l+IzEVRLkM4WiYSEVW3eEOVc2xHn8OAUPqrSDyzO4mWdG3tQMyk+/62Ug8zQZN5VUelYJERbLGxSfK3CuC386JWy7rWdCSZzJaPD5gEcB/Xwkeb3nMcjYeKR0IyShcF9soUyU/mSqxEUWGr3ftTsNA5qGaSzxaYPHlsIp1DCpPncJ52zouu2WHObdB06E1HjoDyEU2LuZgQFltq9HyXRjINaBhPZIt1edFCmUMJ1JuzFi1vRdVcyyhmfV/GJyPUi8pyIHBGRj8/x/u+KyEER2S8iPxCRbW7YWQuDMyoS7t4velMxk+JrBcoVJZ2zbkKNnOuyFNrjEbrbohw2peau49ZgOoeutij94/5VkxCRMHAb8GbgYuBmEbl41mmPA7tsmbV7gE8318ramZE5cjmCMim+FmFkKk9FmztKYT4cByki7FzbzhGT4nOddK7UVBXz2XQlowxN5SmU/DXEsoqrgSOqekxVC8BdwA3VJ6jqj1Q1Y798BNjcZBtrZibF5/Ie1Or2OCPTed8VUhkHtUTOuDDrpxYuWNvBoQFTyecmqspEtrmTdGfTnYyiip/3oTYBJ6ten7KPzccHgO/N96aI3CIi+0Rk39DQUJ1MrB0ngnJbYqhvZJpiWX2ndm8c1BJxxDi95qAuXNfORLY4M+nX0HxGpwuUK+rqteF89xkfp/lqRUTeDewC/ny+c9wedjo0lacnFSMccrfi13GQfkvzGQe1RM6MezOC2rm2A4AjPimUEJEvisigiDw9z/siIp+xN8r3i8iVzbZxqZx1YdT7bJzrst+/hRKngS1Vrzfbx16AiLwB+EPg7arq2VXZ8GTeE5JoM826PlvAGge1RM6mc66WEc/H+Wut6bpHh6ddtqRmvsTCo1zeDOy0H7cAf9sEm1bEWQ+kf7vs5vEz/h27sRfYKSI7RCQG3ATsrj5BRF4O/B2Wcxp0wcaaGZrK09sRc9uMmT6sYZ9V8hkHtUTOjGc91aTrsK4jQTIa5viQPxyUqj4IjC5wyg3AV9TiEaBbRDY0x7rl4UQtbvbIxSNhupJR+sf9GUGpagn4MHA/8AzwDVU9ICKfEpG326f9OdAOfFNEnhCR3fN8nOsMeSyC8luKz1/DQTzA2Ymcp5p0HUIhYUdvimPD/kjx1cB8m+X97pizOGcncoTEvcmpDslomH7/RlCo6n3AfbOOfbLq+RuabtQyUFWGp/Ks8cBYnlTMmQllUnxAMPcYwFole6lJt5oda1LsPzXhthlNxe0qrWpOj2fpTERd3xDvSkZn9koN7jGVL5ErVjg56v5iIRIOkYiGfCcY28gU35cI2B5DuaIMpL0ZQQGc15tibLrg5x6YamraLHe7Squa0+NZuj0gINzVFvXzHlRgcHvU+2xSsYhxUA5B3GMYmcpTcrmMeCHOW5NCgb5Rf+xDLcJu4D/bkfa1wISqeja9B3B6LEt3m/sb4t3JKOOZItlC2W1TWhqvqEg4pOIRk+JbAkttyHMdrzbpOuzobQfgmA8KJUTk68DPgItE5JSIfEBEPigiH7RPuQ84BhwB/h74LZdMrYlyRTmb9kb6d6YXykRRrjJgOyg32w6qaY9HTJFEIxCRW7DSgGzdutU1O7zapOuwo9cqNT/ug1JzVb15kfcV+FCTzFkxg5M5q0nXIyk+gP7xHOevaXfZmtZl0AN9cdWk4mGOD2cWP9FDuBlB1bTHAN7ZZzg1ZjkoL+wzzEVXMkoqHvFFBBU0TjvXRtILKT7Lhn95/JTLlrQ2A+kc0bCQiHqjmycVjzCWKVCp+EcOzc0IajfwYRG5C7gGH+wx9I1m6ExEaIt5L/B0hGN722O+iKCCxulx7yxeOu09j3F7eKLBHc6m83QkvNMz2R6PUK5YepGrUu4vpGqhYXdae4/hOqBXRE4BfwREAVT181h7DG/B2mPIAO9rlC31om80w9bVbW6bsSC97XGOGQfVdLzkoCLhEO3xCBMZ46DcZCCdm1kseIGUvbAemc4bBxW0PQaAvpGM5ySOZrOmPc5jz49ZM6s8kvtuBc7YJebxiDeuj65kdGb8vMEdBtM5Ojz0N5iqkju6YK3LxtSIN5KjPqBcUU6NZenx+Mqjt92yzy+SR0Hh9FiWjV1Jt82YoSsZNSk+F1FVBtJ5T0VQ7T6UOzIOqkYG0jkK5YrnQ+PVtu6X2YdqHnfu6ePMeI5Nq7zjoLrbrAjKzAdzh8l8iWyx7Kmm/lTcf3JHxkHVSN+oVZ7p9QhqdSpGSDD7UE1EVTk9nmVTt3ccVFcySqFU8d2AuqDglJh7KcXnFHf5SdHcOKgacRzU6pT7wo8LEQmH2LyqjWNDgRGN9TzThTJT+RLbPFRAc24ulGnWdYOBtN2km/ROii8cEnpSMV8NNTUOqkb6RjKEQ+LZJt1qdvSmTIqviTgpk+2rUy5bcg5H0cKvYzf8jjMbzGuFShu7E76atmwcVI30jWbY2J1wXam6Fs5bYzkos//QHBwBTi+1IHTZmoCnfXQzChIDk06KzzsRFMCm7uRMU7kfMA6qRvpGM2xZ5Z0b0EKc15siUygzOOmfUN7PjE4XCAls9lCRREciQkhMis8tBtN5OuIRz7QdOEzlSpwez/pm8WocVA2oKkeHpjhvjXdSOAvhiMYeNftQTWFkKs/G7qSnbkYhsdLRp3y0Wg4SZydyrO303n51V1uMTKHMuE+auI2DqoGBdJ7JXIkL13W4bUpNOI7U7EM1h5Hpgqf2nxxWpWIzxT2G5nJyLMOWHu9lXJy9Sb+kfo2DqoHDg5MAXLDWH8rQ6zsTJKIh06zbJEamChTKlRk9RK+wOhWjb8Q4qGajqvSNZNjqQQfl9HGe9MnCxTioGjg0YKXK/BJB3bX3JN3JmOmFagLjmQLZYpnVHuyP60nFGZkuMJU3vVDNZCJbZDJfYtiDe8C99nXql3uDcVA18Gx/mp5UzJM3ofno7YibFF8TeH7E6Y/z3rXhNJWbKKq5nBy10mdeVJ2JR8Os6/TPvcE4qBrYf2qCyzZ3eUY2vxbWdsR5fmTajP1uMCdGrD/0Hg82cDtO07HR0By8rjqzozflm0Z+46AWIVMocXhwkss2dbltypLY0JWgovDs2bTbpgSao4NTCLC63Xs3o972OCJwZNAfNyMHEbleRJ4TkSMi8vE53v8FEfm5iJRE5J1u2LgQx4et37dXHdR5a9pNii8oHDiTpqJw2eZut01ZEo6y9oEzxkE1kkMDU6xujxENe+9PKRYJsak76SsHJSJh4DbgzcDFwM0icvGs0/qA9wJ3Nte62jg6NM3GroSn2g6qSWeLjGeKM3qBXsZbbc4e5MmT44DVUzS4x3ubnvPR3RYlGQ1zsN84qEZyaGCStR0Jt82Yl51r2znsIwcFXA0cUdVjAPbE7RuAg84JqnrCfq/ihoGLcWRwivM9XPHrLF6fPjPB6zq9e+2CiaAWZf+pCTZ0JTylSlwLIsKGroRnI6ga0jjvFZEhEXnCfvy6G3YuRK5Y5sTINOs82JDpcMHado4NTVGu+EM5ANgEnKx6fco+tixE5BYR2Sci+4aGhlZs3GI4Tf3nr/Gug9rQlUCAp055895QjYmgFuHfjgyzzuOrjPnY2J1k74lRSuUKEQ+loKrSOG/EugHtFZHdqnpw1ql3q+qHm25gjRwbmqaisNbD18dLN3SSL1U4OjTlmzaJeqKqtwO3A+zatauhXvrOPX2MZwpkCmVPR1DxaJjV7XGeOj3utimL0tC7lt9Xybc/eIyR6YKnNNaWwoauBPlSxYsbojNpHFUtAE4ax1c4DdzrPJziu2yzVdyz/9SEy5bUzGlgS9XrzfYxX9Bvq5hfvMHbi4FtPW3sPTHm+ci6YQ6qxs1OsFbJV9iPOxplz3I4Yd/Yz+v1noxNLWywB+g9fdpzN6da0zjvEJH9InKPiGyZ4/2mp3CqOTQwSSQk9HZ4s1oLLF3GVCzMU6e8v1q22QvsFJEdIhIDbgJ2u2xTzfRPZBGBi9Z3um3Kgpy/NsVEtsgzHt+jbmQE5ftV8rHhaaJhYZNPVMxns7YjTioW5vE+39ycqvkOsF1VLwMeAL4810mqeruq7lLVXWvWrGmqgYcGptjemyIS8k76dDbhkPCyTV081jfmtik1oaol4MPA/cAzwDdU9YCIfEpE3g4gIq8QkVPAjcDficgB9yx+If0TObavTtEe9/buyXn2HtlPDjV3UbdUGvmX5ftV8rGhKbavTvliBtRchES4Yms3jz3vuZvTomkcVR1RVads8g7gqibZVjPPnZ3kIh/s67z6gl4OnEkzOu2PUd+qep+qXqiq56vqn9jHPqmqu+3ne1V1s6qmVHW1ql7irsXn6J/IkYpHPKfLOJvORJTLt3Rz31P9bpuyIG4v/Ty7Sh6eyjM4mWeHT9N7DldtXcWzZ9NMe0uPbdE0johsqHr5dqzVtGe448Fj9I1muHSz9xu4X7OzF1Wr4MfQOHLFMqPTBTZ2eXdPsppfumwDB86k+cz3D7ttyrw00kH5epX86PFRwL/7Tw5XbltFRc/1c3mBWtI4wEdE5ICIPAl8BKsx0zOcsscVXO6DBu7LNnWRiIb46WFvp3P8jlMgsaHLH0VVb7tsIyKw38PVfI1MlM6skrEc003Au6pPEJENqurEmJ5aJT9ybIRYOOTb/SeHl29dBcBjz4/xqgt6XbbmHKp6H3DfrGOfrHp+K3Brs+2qlZNjGUTg0s1dnhfejIRDnL+mnYcOD6OqvtKU9BPO9OIN3f6IoH747CDbeto8XeHZsAjK76vkR46NsG11m2/3nxy6klF2rm3n3v39ns+L+4m+kQwXru3w/Ga4w861HZyZyPlK9shvnBnP0h6P0Omjpv5LN3czOJnn0MCk26bMSUP3oGrY7LxVVS9R1ctV9bWq+mwj7amV4ak8hwamfJ/ec7hq2yr6RjNU1Ns9D36hVK7w/GiGV+xY5bYpi3Lnnj7u3NPHReutYo5P3/+cyxYFl5OjWd/1TL5sYycC3PvkGbdNmRO3iyQ8iZOr93I3eK3cuaePYrlCtlj25AA1P/Ls2UkKpQqv2N7jtik105WMsrWnzYs9cYEgnSsyNJX35Jj3hehIRNnRm+Lep/pRDy5gjYOagy8+dIL2eISN3f5aDc2H80fT55Mxz15n3wmrgGaXjxwUWKvl/okcz5v5UHXnKXsfx28RFFj7qMeGpvmLBw65bcqLMA5qFsVyhcODk1y0voNQQDaTe9vjtMXCZnBdndj7/BjdySibfLaAucSeaXbfU2ddtiR4PGFXyW7u9lcEBXDJxi4EePq091QljIOaxWPPj5ErVnzRgFkrIRHOW9POkcEpT4bxfkJV2XdilG2r/XcjWtUWY8uqJN9+4rS5DurMEyfH6W2Pk4x5cwbUQrTHI2xbnfKk7JFxULP4/sEBwiLsDMD+UzU717STzpU46pNRz17lxEiGgXSe7b2pmQIEP3HltlU8e3bSk6tlv6KqPHlynC0+TO85XLKxk7Np76V/W95BVd9kCqUK33riNBeuayce9d9KaCEusB3uTw8bNYGV8PBR6/d3fq8/FzCXbeomHgnxjX0nFz/ZUBMnRjIMTvqvQKKaizdY4rb3H/BW+rflHVQ133nyDMNTBa7e4a/N71pYlYrRk4rx0OFhX678vcLPjo6wrjPO6nbvKpgvRDIW5k2XrOfbT5wmVyy7bU4geMiu+vVz1mVVKsaGrgTfe9o4KE9yYniaP/3es1y+uYudAdp/quaCte08cmyEYtmTk7I9j6ryyLERXnV+r6/VGNZ0xEnnSnzHo70vfsFZ5P3k0BCbVyXpSflz0eJw+eZuHu8b56+/f9gzC9iWdlB37uljdLrA1/Y8zxv+4ieUKhX+1zsuC0z13mwu3tDJdKHMc2e92TXudQ4PTjE8VeCV569225QVcV5virUdcb78sxOmWGKFjEzl+cmhIa6/ZL2vFy0AV2ztJhwS9tptFF6gpR3U2HSBz/34CEcGp3jfq7dz7399DS/d4O1BYyvh/DXt9LbHeNI/w+s8haMG/srz/O2gRIRrz1vN06fT/Nyfs8I8w9cf7aNYVm7cNeekIF/RmYjy1ks38OiJUTIFb0w/aFkHpap887GTVFT5zevO5w/fejGbfS4MuxjhkPC2yzby3NlJsgWz/7BUvv/MABesbff1ZrjDy7daxRJf+dkJt03xLWfGs9z2o6O84aXrZqSk/M6HXnsBxVKF7z8z4LYpQAs6KCe3et9TZzkxkuH6SzawXJiTpgAAEMhJREFUtiPxoveDyi+/fBOlihrJmyUyninwyLFR/v3F69w2pS7EI2Gu2raK+57qZ3Ay57Y5vuOx50f5+58eoycV41M3eGZe4oq5aH0H1563mj3HRj0xoqflHBRYg8X+9HvPsL4zwa7t3hf8rCeXb+5ifWeCfzs6TKVi9h9q5V8eP025orzl0g2Ln+wTrt2xmmJZ+foeU3K+FJ4fmeb9X9pHezzCNz74ysBIojm88eJ1tCci/ME9+13PtLSkg/rMDw5zaizLWy/bMFMQ0Sql1yLCL1zYy+BknnvnGffcKr+LWimVK9z2oyNsXpXkZZu8P0G3Vno74vzihWv42p7nTcn5EvgvX32MXLHM+169Y0buKkh/L4lomHdeuZlDg5P80e6nAffuCS3noPonsvzdg8e48arNnL/Gv30LK+Gyzd1s6ErwJ989yJBROF+Uf/i3EwxPFfjFC9cEznn/l188j8HJPF9++ITbpviCnx4e4tmzk7z2orX0pGKBux4cdq7r4EPXXcA39p3i0//3WddG9fhj2lqdSOeKfP3Rk6xqi/KHb31py4pmhkR4x5WbueOhY7zz8w/zq7u20JWM0hYL8/TpNDt6U74f1FgPJnNFvvDQcf76B4d56fqOmW77IHFiOMNL1nfwFw8c4lXn93Lp5uBEiPWmXFH+5LvP0JOK8SqftxrUwu+88UKGp/J87sdH2dbTxg1XbALORYvvumZrw21oGQdVKlf46NcfZ3Q6z52/cS3dbf5uqlsuzsW1sTvJV95/DZ/41lP8+awhdql4hNe/ZC03X73F970dy6FUrvD1R/v40+89S6ZQ5pcu38hVW1cF9nfxKy/fxJcfPsE7P/8wb3jpOv7y164gFmm55Mqi/NNjp3j27CQ3X72VSDiYv5/qaPDuvSe5dFMX15zXw63//BR/88PDnJnIsqY93rR9t5ZwUOWK8nvffJIfPTfEDVds5Fqf97HUi6t39PCvv/OLTOaKfG1PH8VShYF0joePjbD7yTNM5Uv81U1X+GqE9Ur5yaEh/ue9Bzk8OMWO3hTXX7Ke//bmlwQyjePQkYjy7mu38c8/P813n+rn8b4xPvDvzuOmV2wh5ZOR9o0mUyjxfx54jiu3dvOyjcGLpOdDRPiVl29mZKrAT54bYveTZyiUKkTDwvee7udXXr6JG67Y1LAFTUOXASJyvYg8JyJHROTjc7wfF5G77ff3iMj2ettwYniaD/7jY3z7iTN87E0Xcc0O45yquXNPH995sp/ORJTV7XEu3tjFB169g1+6bAMPHhriHZ97mJMNGHTohWsDLIHgh48M88f3HuR1//vHvOeLjzIyXeDd12zl11+zIxA9T7XQ3Rbjfa/ezvtetZ3NPW388b0H2fU/v89fPHCI0elCU23xyrXhUCpXuPWfn2JwMs8fvvWlgY2kF6ItFuHNl27gZx9/HTdfvZVd23oYSOf42D37ecWffJ+vPvI8+VL9C20atjwSkTBwG/BG4BSwV0R2q+rBqtM+AIyp6gUichPwZ8CvLfW7VJViWRlI5zg+PM0z/Wke7xvn4aPDpHMlYuEQn3zbxbz/NTsCvRKuFyLCK8/v5eZrtvLBrz7G2z/7EB99/U6uu2gtW3raVrw/1cxrA6wIOlcsMzyV58x4jv6JLGfGsxw4k+aHzw6SL1WIhUNce/5qLt3cxVVbV70ghdMq14yIsHNdBzvXdXDl1lU8eGiIz/zgMLc/eJS3XrqRX7iwlzUdcVKxCIlomHgkRFs8TGciSjwSqsuNu9nXBlj3j0K5wkS2yMhUwXpM5xmZKjA4aUkZPdOf5mNvuoirtvXw3NnWGllTff3ff2CASzd1cemmLm6+egsPHh7mv3/raf77t57mth8esTJU56/mvN4UnYkoHYnIitKh0igtLhF5JfA/VPVN9utbAVT1T6vOud8+52ciEgHOAmt0AaN27dql+/btm3l91R8/wFimwOyWnq09baxqi7Klp42LN3S+YM/J2dxrlRvPcnnXNVs5OjTFx/9pP3tPjAEgAq9/yTrueM+uF5wrIo+p6q65Pmc2zbo2br79EfY9P0qxPPePbOhKsHlVkpes7+T8Ne1m32UOrt6xir9/8Di7nzxDdoFS9EhIiISFTd1JfvB7173gPS9cG/DC6+O/f+tpvvnYSUplpbRAP2BIYENXkv/25pcwlfOG/I/XUFW29LTxD/92nJ8cGnrRvTgWDhEKWcVZ+z7xBtpi5+Kixa6NRiaYNwHVHYCngGvmO0dVSyIyAawGXjC0SERuAW6xX06JyAt39efg+QXe+48vfNk7+/uahFvfW/N3/8d5jn8B+MJ7X3R42xK+39Vrw2GBa8TNf5uV4qrtzwHy+y867Mq1Acu+Pl7wOzwO3HBrreY3Da9fo3Pal/rjF5234LXhix1QVb0duL0Rny0i+2pd3QXhe93+7nrTiGvDz78fP9veCJZzffjhd+h1G+tlXyNzGqeBaonfzfaxOc+xQ/UuYKSBNhm8gbk2DPNhrg3DDI10UHuBnSKyQ0RiwE3A7lnn7AbeYz9/J/DDxfLIhkBgrg3DfJhrwzBDw1J8dm74w8D9QBj4oqoeEJFPAftUdTfWdsZXReQIMIp1MTabhqQOPfy9bn+3H64NV38/K8TPtnvl2vDD79DrNtbFvoZV8RkMBoPBsBJMXa3BYDAYPIlxUAaDwWDwJIF3UCLSIyIPiMhh+78vmlAoIleIyM9E5ICI7BeRX6t670siclxEnrAfV9TwncuWahGRW+3jz4nIm5bx/7vYd/+uiBy0/z9/ICLbqt4rV/1/zt6YDiQiEhaRx0Xk3jnee6+IDFX9Tn7dDRvnQkROiMhTtl375nhfROQz9nWwX0SudMNOryIiF1X9uz4hImkR+e1Z51wnIhNV53yyCXZ9UUQGReTpqmOL3sPs895jn3NYRN4z1zkNsu/PReRZ+zr7FxHpnudnF7xm50RVA/0APg183H7+ceDP5jjnQmCn/Xwj0A9026+/BLxzCd8XBo4C5wEx4Eng4lnn/Bbwefv5TcDd9vOL7fPjwA77c8J1/u7XAm328990vtt+PeX2v5cL18fvAncC987x3nuBz7pt4zx2nwB6F3j/LcD3AAGuBfa4bbNXH/bfzVlg26zj1811XTTYll8ArgSerjpWyz2sBzhm/3eV/XxVk+z790DEfv5nc9lnv7fgNTvXI/ARFHAD8GX7+ZeBX559gqoeUtXD9vMzwCCwZpnfdzVwRFWPqWoBuMu2YT6b7gFeLyJiH79LVfOqehw4Yn9e3b5bVX+kqo766yNYfSYtiYhsBt4K3OG2LQ3gBuAravEI0C0iwZlXX19eDxxV1YUEaJqCqj6IVZlYzaL3MOBNwAOqOqqqY8ADwPXNsE9V/1VVHR2out5TWsFBrVNVZ7b5WWDdQieLyNVY0cfRqsN/Yoevfyki8UW+by6plk3znWP/wzpSLbX87Eq/u5oPYK2yHRIisk9EHhGRuf4IgsZfAX8AVBY45x32v/09IrJlgfOajQL/KiKPiSXnM5uVXkutxE3A1+d575Ui8qSIfE9ELmmmUVXUcg/zyr/3+3nhPaWaxa7ZF+ELqaPFEJHvA+vneOsPq1+oqorIvHX19grzq8B7VNW5ad2KdVHEsGr7/xvwqXrY7SYi8m5gF/CLVYe3qeppETkP+KGIPKWqR+f+BH8jIm8DBlX1MRG5bp7TvgN8XVX///bOLsSqKorjv3+gVFpiRUSIqBUZKCRNYOqDiUSKzlNgmmVloJAIihgxQdJL9BA+JFZoRKCIGJhSluQXlRWCpqmYNqX0QYwplhghE60e1r7M6c5c7x1n5t494/rB4Z577j73rH32/5x99sdZ67KkRfjT67R62ViFKamsbgc+lfRderoNuoH8ZeBm/Dov5xB+TVySNBP4ALinnvaVU+0e1kgktQD/ABsrJOm2ZgdEC8rMppvZuC6WbUBbqWsjfZ7t6j8k3Qx8BLSkLpHSf/+WukkuA+9SvcutJ65aatm3p8dG0nS88m5O+QLAzH5Nnz8C+4AJ3Th2f2My0CzpDN4VOk3ShmICMztfOD/rgQfqa2JlCmV1FthKZ132VEvXCjOAQ2bWVv6DmV00s0tpfQcwSNJt9TaQ2u5hDS1vSU8Ds4AnLA04lVODZjsxICqoKhTdoiwAtpUnSE9RW/E++/fLfisJQ3jf77Hy/cvoiauW7cDj8ll+o/GntQM15bLGY0uaALyNV05nC9uHl7ov00U4GSjG4BlQmNmLZjbCzEbh52mPmc0vpikbs2kGTtTRxIpIGiLpptI6PkhdrsvtwFNpNt9E4M9CN1HQwVwqdO9JuiNd96Wu/+tojM+/qvcw3PPGI+k6Ho5rYmc9jJP0KN5V3lwY3y5PU4tmO9PbszxyW/Cxnd3A98Au4Ja0vQlYn9bnA+3A4cJyf/ptD3A0ncwNwNAajjkTOIWPY7Wkba+kAgS4HtiCT4I4AIwp7NuS9jsJzLiK/FY79i6grZDP7Wn7pJTPI+lzYaPLro4amUqarVV2rl4FjqdzshcY22hbk11jkk1Hkn2lcl4MLE7rwgP//ZDKs6nRdue2AEPwCmdYYVvxHC4plP/XwKQ62LQJn0Xcjo8jLazlHpa+P5vuKa3AM3W0rxUf/yrdU0ozlO8EdlxJs9WWcHUUBEEQZMm10MUXBEEQ9EOiggqCIAiyJCqoIAiCIEuiggqCIAiyJCqoIAiCIEuiguoHFLwAN6Xvo+Ve0FvlXtEHp+3LJP0kaU1jLQ7qRRfaWJJ0YcWXSiXNSds7eW0PBiZdaGOjPNLBseSVfFDanq02ooLqY5KniN7gYTMruah/DVhtZncDF/B3ETCz1UCfhwQIeoc+0sZ+YDrwP8enZrYZyCZcSHBl+kgbG4GxwHjgBpIectbGgPDF19fI4zV9AhzEXc0fB54CVgCz8cL+ElhkZiZpH/7C2hRgk6RTwEu4P7/zuDuQNkmr8LAaY4CRwDI8NMIM3E3JbDNrL7NFuD+4eWnTe8Aq4M1ez3hQlZy0AWBm3yS7+iS/Qe1kqI0dBdsO0A8iGUQLqnbuBdaa2X3ARTym0xoze9DMxuFim1VIP9jMmszsdeALYKKZTcD9vq0spLsLr3CacU8Ve81sPPA3HgqinFuBP6zDvX14qW48uWgjyI/stJG69p7EK8+siRZU7fxsZvvT+gZgKXBa0krgRjxQ2HHcAzbA5sK+I4DNybfbYOB04bePzaxd0lE8cFpJNEeBUX2RkaDXCW0ElchRG2uBz8zs86vLUv2IFlTtlPuEMrygH0tPLutwH3sl/iqsv4E/NY0HFpWluwxgHt6j3Tp8T/1L1w8Q5/Hgc6Xfwkt148lFG0F+ZKUNSS/jwViXdz8r9ScqqNoZKemhtD4Pb34DnJM0FPdKXolhdFQiC66QripJiHsLx6vk3TioH1loI8iSbLQh6Tk88u5c64h3lzVRQdXOSeB5SSeA4fikhHW4l/OdeKiLSqwCtkg6CJzrBVteAJZLasXHpN7phf8Mrp5stCFpqaRf8Jb1t5IGYjj7/kQ22gDewqPxfiXpsKTsZ/yGN/MaSLNxPkyDmo04/hk8XEJVkabAYU1mtqSv7Qr6nTamAivMbFa1tEHPCW30nGhB9Q9+B3aXXrirhKRleOjqi3WxKsiBWrUxBx/7uFAXq4Ic6PfaiBZUEARBkCXRggqCIAiyJCqoIAiCIEuiggqCIAiyJCqoIAiCIEuiggqCIAiy5D+x9wpqqBGMtgAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 3 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "Aecd7EoDV0Ut",
"colab_type": "code",
"colab": {}
},
"source": [
"# posterior predictive\n",
"\n",
"def posterior_predictive(x, model, chain):\n",
" return [model(x, c) for c in chain]"
],
"execution_count": 39,
"outputs": []
},
{
"cell_type": "code",
"metadata": {
"id": "yeFCHgCQjBGH",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 297
},
"outputId": "8f172e44-1323-44d3-ba5c-d4238cc43842"
},
"source": [
"# some test points close and far away from training data\n",
"x_test = np.array([-10, 0, 10, 100])\n",
"\n",
"y_ppds = []\n",
"fig, ax = plt.subplots(1, len(x_test), figsize=(10,4))\n",
"for i in range(len(x_test)):\n",
" y_ppd = posterior_predictive(x_test[i], model, chain[burn_in:])\n",
" y_ppds.append([np.mean(y_ppd), np.std(y_ppd)])\n",
" sns.distplot(y_ppd, ax=ax[i])\n",
" ax[i].set_title(f'std(x={x_test[i]}) = {y_ppds[-1][1]:.2f}')\n",
"fig.tight_layout()\n",
"y_ppds = np.array(y_ppds)"
],
"execution_count": 86,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x288 with 4 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "--8tBizJjUq5",
"colab_type": "code",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 295
},
"outputId": "671e3173-8772-41bd-8072-2561eb76de93"
},
"source": [
"plt.plot(x_test, y_ppds[:,0], label='mean')\n",
"plt.fill_between(x_test,\n",
" y_ppds[:,0]+2*y_ppds[:,1], y_ppds[:,0]-2*y_ppds[:,1],\n",
" alpha=0.5, label='2std')\n",
"plt.plot(x_test, model(x_test, params_true), label='true')\n",
"plt.scatter(x, y, label='train data', s=1, color='purple')\n",
"plt.legend()\n",
"plt.title('predictive')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y');"
],
"execution_count": 87,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"tags": [],
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"metadata": {
"id": "CbCxdOQTmFPk",
"colab_type": "code",
"colab": {}
},
"source": [
""
],
"execution_count": null,
"outputs": []
}
]
}
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