{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# From the normal model to regression\n",
"\n",
"##### Keywords: bayesian, normal-normal model, conjugate prior, MCMC engineering, pymc3, regression"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"%matplotlib inline\n",
"import numpy as np\n",
"import scipy as sp\n",
"import matplotlib as mpl\n",
"import matplotlib.cm as cm\n",
"import matplotlib.pyplot as plt\n",
"import pandas as pd\n",
"pd.set_option('display.width', 500)\n",
"pd.set_option('display.max_columns', 100)\n",
"pd.set_option('display.notebook_repr_html', True)\n",
"import seaborn as sns\n",
"sns.set_style(\"whitegrid\")\n",
"sns.set_context(\"poster\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The example we use here is described in McElreath's book, and our discussion mostly follows the one there, in sections 4.3 and 4.4. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Howell's data\n",
"\n",
"These are census data for the Dobe area !Kung San (https://en.wikipedia.org/wiki/%C7%83Kung_people). Nancy Howell conducted detailed quantitative studies of this Kalahari foraging population in the 1960s."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" height | \n",
" weight | \n",
" age | \n",
" male | \n",
"
\n",
" \n",
" \n",
" \n",
" 0 | \n",
" 151.765 | \n",
" 47.825606 | \n",
" 63.0 | \n",
" 1 | \n",
"
\n",
" \n",
" 1 | \n",
" 139.700 | \n",
" 36.485807 | \n",
" 63.0 | \n",
" 0 | \n",
"
\n",
" \n",
" 2 | \n",
" 136.525 | \n",
" 31.864838 | \n",
" 65.0 | \n",
" 0 | \n",
"
\n",
" \n",
" 3 | \n",
" 156.845 | \n",
" 53.041915 | \n",
" 41.0 | \n",
" 1 | \n",
"
\n",
" \n",
" 4 | \n",
" 145.415 | \n",
" 41.276872 | \n",
" 51.0 | \n",
" 0 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" height weight age male\n",
"0 151.765 47.825606 63.0 1\n",
"1 139.700 36.485807 63.0 0\n",
"2 136.525 31.864838 65.0 0\n",
"3 156.845 53.041915 41.0 1\n",
"4 145.415 41.276872 51.0 0"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_csv('data/Howell1.csv', sep=';', header=0)\n",
"df.head()"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"
\n",
" \n",
" \n",
" | \n",
" height | \n",
" weight | \n",
" age | \n",
" male | \n",
"
\n",
" \n",
" \n",
" \n",
" 539 | \n",
" 145.415 | \n",
" 31.127751 | \n",
" 17.0 | \n",
" 1 | \n",
"
\n",
" \n",
" 540 | \n",
" 162.560 | \n",
" 52.163080 | \n",
" 31.0 | \n",
" 1 | \n",
"
\n",
" \n",
" 541 | \n",
" 156.210 | \n",
" 54.062496 | \n",
" 21.0 | \n",
" 0 | \n",
"
\n",
" \n",
" 542 | \n",
" 71.120 | \n",
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" 0.0 | \n",
" 1 | \n",
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\n",
" \n",
" 543 | \n",
" 158.750 | \n",
" 52.531624 | \n",
" 68.0 | \n",
" 1 | \n",
"
\n",
" \n",
"
\n",
"
"
],
"text/plain": [
" height weight age male\n",
"539 145.415 31.127751 17.0 1\n",
"540 162.560 52.163080 31.0 1\n",
"541 156.210 54.062496 21.0 0\n",
"542 71.120 8.051258 0.0 1\n",
"543 158.750 52.531624 68.0 1"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.tail()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(df.height, bins=30);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We get rid of the kids and only look at the heights of the adults."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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YmdPt30PXx+BfRET8FPAO4LWZ+e/zbDZFRyeh2c/sAI4HvpaZ323b/rb9h/Ba4D3UrQ3ACuBBwDWZeVnbdkNErKGpz/uoXZ9Zv0/zOVH/kXzL1qbNnZuBlTT78b8NPBP484jYmZnXs4z6GPyLez3NiWaujIjeeh0QEQe2b8nuoDnpTL9V/OgkNROn3Rf7mTm6PgWcEBEHU7Q2rdkTEH2qr/2zwMaIOIja9ek9fPub5+iuXJtTad5JPz4zb2nbboiIn6X5POB6llEf9/Ev7reBX6VZybOr/VkNvKb9HZrzETy0XXfbaw3NJ+wTKSKOjoiXt6sTej0YmKH5MKpkbVrfaC/7V0KtoJmt7aZ2faBZxnkIc69AqVybI2h2E/Z/R+YfaD5TO5hl1MfgX9yJwOP6fn5As/vnce02W2je0p84e6WIOAr4ZSb7RDS/QLPv+umzDe0SxlOBz2fmHurWBuBzNBOG0/ranwHc0r5brFwfgMfTrFyZ60zilWuzjeaxH9vXfizNks67WEZ93NWziMz8Wn9bRDwAfCczv9huc3tE/A3wjnbZ5w6aE9J8FfjI3hzvXvY5mhnI1e2qg+/S7K89Bvh1KF0bMnNnRFwGbIiIncCNwLOB42jCv3R9Wr8CbGsnCT+meG0205zT5P0RcTHwHZqAfx5wZluvoevjjL87L6L5sO6NNN88/Arw9Mx8YJ+OaoTax3Yy8GHgj2jerv8c8JSelQdQsDazMvNS4JU0X7r5GM2M7ZmZ+cmezcrWh+b58v0F+kvWJjN30axy+iywkSbInwiclplX9mw6VH08EYskFeOMX5KKMfglqRiDX5KKMfglqRiDX5KKMfglqRiDX5KKMfglqRiDX5KK+X8+uxxfcbTlswAAAABJRU5ErkJggg==\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df2 = df[df.age >= 18]\n",
"plt.hist(df2.height, bins=30);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Model for heights\n",
"\n",
"We will now get relatively formal in specifying our models.\n",
"\n",
"We will use a Normal model, $h \\sim N(\\mu, \\sigma)$, and assume that the priors are independent. That is $p(\\mu, \\sigma) = p(\\mu \\vert \\sigma) p(\\sigma) = p(\\mu)p(\\sigma)$.\n",
"\n",
"Our model is:\n",
"\n",
"$$\n",
"h \\sim N(\\mu, \\sigma)\\\\\n",
"\\mu \\sim Normal(148, 20)\\\\\n",
"\\sigma = Std. dev.\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"sigma 7.73132668454 mu 154.597092614 n 352\n"
]
}
],
"source": [
"from scipy.stats import norm\n",
"Y = df2.height.values\n",
"#Data Quantities\n",
"sig = np.std(Y) # assume that is the value of KNOWN sigma (in the likelihood)\n",
"mu_data = np.mean(Y)\n",
"n = len(Y)\n",
"print(\"sigma\", sig, \"mu\", mu_data, \"n\", n)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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Ncm1glvpk5iTwF8DZEXFURBwMvAc4APhUvVnX9XFXD5CZ35utPyKOpfrw5DkzbHIQP30SGuq2QxY2uqU1W20i4heoDs9xGNXMZRtVnT4cEXsy86MMcG1gzufOaqr9spuAa6nOS30KcG1E/F/99nxg6zPX62pKRPwm8DzguLauga0NdFSfS4EXAP9S/70beF1mjtZ/d10fg38OEfEU4IPAJZn5HzNsNkRDJ6HZy2wD1gL3ZOYP6ra/q/8hXAJ8lHJrA7AM2Be4PjMvr9tujYg1VPX5BGXXZ8ofUH1O1H4k32JrU+fOHcByqv343wNeDvxlRGzPzM+xgPoY/HN7F9WJZq6JiNZ67RMR+9VvyR6mOulMuxX85CQ1A6feF3vLNF1fBk6IiAMptDa1qRMQfbmt/SvAVRGxP2XXp/Xw7VdM011ybU6leif9/My8s267NSJ+jurzgM+xgPq4j39uvw38GtVKnl31z0rgnfXvUJ2P4Gn1uttWa6g+YR9IEXF4RLypXp3Q6gBggurDqCJrU/t2fdm+EmoZ1WxtN2XXB6plnAcx/QqUkmtzCNVuwvbvyPwj1WdqB7KA+hj8czsROKrt50dUu3+OqrfZTPWW/sSpK0XEYcCvMNgnovlFqn3XL51qqJcwngp8LTP3UG5tAL5KNWE4ra39ZcCd9bvFkusD8HyqlSvTnUm85NrcR/XYj25rP5pqSedOFlAfd/XMITPvaW+LiCeA72fmXfU2D0TE3wIfrJd9bqM6Ic3dwGcXc7yL7KtUM5Dr6lUHP6DaX3sk8BtQdG3IzO0RcTmwISK2A7cBrwSOoQr/outT+1XgvnqS8CSF12YT1TlNboqIi4HvUwX8q4Gz63p1XR9n/M15PdWHde+h+ubhN4GXZuYTSzqqHqof28nAZ4A/pnq7/vPAi1tWHkCBtZmSmZcBb6H60s3nqWZsL8/ML7VsVmx9qJ4vP5ylv8jaZOYuqlVOXwGuogryFwKnZeY1LZt2VR9PxCJJhXHGL0mFMfglqTAGvyQVxuCXpMIY/JJUGINfkgpj8EtSYQx+SSqMwS9Jhfl/bZCMHKn+AVkAAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(Y, bins=30, alpha=0.5);"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# Prior mean\n",
"mu_prior = 148\n",
"# prior std\n",
"tau = 20"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"mu post 154.594293158 sig_post 0.41199365493\n"
]
}
],
"source": [
"kappa = sig**2 / tau**2\n",
"sig_post =np.sqrt(1./( 1./tau**2 + n/sig**2));\n",
"# posterior mean\n",
"mu_post = kappa / (kappa + n) *mu_prior + n/(kappa+n)* mu_data\n",
"print(\"mu post\", mu_post, \"sig_post\", sig_post)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"#samples\n",
"N = 15000\n",
"theta_prior = np.random.normal(loc=mu_prior, scale=tau, size=N);\n",
"theta_post = np.random.normal(loc=mu_post, scale=sig_post, size=N);"
]
},
{
"cell_type": "code",
"execution_count": 263,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(theta_post, bins=30, alpha=0.9, label=\"posterior\");\n",
"plt.hist(theta_prior, bins=30, alpha=0.2, label=\"prior\");\n",
"#plt.xlim([10, 30])\n",
"plt.legend();"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"Y_postpred = np.random.normal(loc=mu_post, scale=np.sqrt(sig_post**2 + sig**2), size=N);"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"Y_postpred_sample = np.random.normal(loc=theta_post, scale=sig);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(Y_postpred, bins=100, alpha=0.2);\n",
"plt.hist(Y_postpred_sample, bins=100, alpha=0.2);\n",
"plt.hist(np.random.choice(Y, replace=True, size=N), bins=100, alpha=0.5);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Regression: adding a predictor"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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lE1YFzG888mJ29+xXY6cYgSt0rk0L4WOrNSnXolctdZqq7bNdbYQV/guBt7TWa9wnlFKtwB3ACq31A5lj64A9wHLg3hKNteyYWsQ9tfEgN17tbyKoJSrZd9VElPEEmRuiCOT0znF5JppkIjj+vimzs3cuA8kEnN3ZQmum9aITW6A27zjI/Y+9mJPh+50nt2b70D7ydA+XzZ7MnbfOMz6+1GWh3ZgWwlQKkskEqVR1mlSq7bNdTRQi/C97nLsUGAt02Qe01v1KqbXANdSw8Jtr01AVO5q4qETss99rBo0nrEmmUIFMO/7vPurGHX9/+31rSef01PVvpN7eNprWlpPzTEautry8sOVNdu8/bNz5x/159LprWrpI8fgaLSaVGqMQ4R9SSj0PXIxl7/9n4B7g3Mw17kLku4Abogxq+/btUR5WckYGh/MqTzYlYeToAbZv76vcwGLiV1v7eWrjQUZSZM1aV1zQHvrxx44dA6y/n12NsnPCKF+/iN9rhhmP3nvUaJL56drNtIxqynv9FqB3Xx+9+/zfi957NK/+fCoNa9dvRU0ZY3xMC7B521FjI/Xdbw5wTucpnp9t02fNxFM/38JVF0/wvygmrr1kouvvMZELP5Bi2k3THH/r45G+v87PjpBLHHMTKPxKqSbgPOAolklnD3Ad8HXgFOB94LjW+j3XQ48AbSUbaQVobWnmunmTcj7siy8+tW4cvE4GBoez7xNOmLXmTG8t+P2GXUD8XjMNocbT2tJkHMPja3tJp6MtYACdE0YZF/3OCaMiPa6j/WTfx7k/a8kEeQsPwHlTx4ReVEvNFRe0M2d6a95rt7Y0o+rwO1HPhP1rfQx4Q2u9I/P7L5RSY7Gcuf+A1z0wBOxfzMyqIu/prFlw49WZqJ6jB2htaa6q8ZWK7p63GEntyjk2koKmMaeFboe3fft2BgaH+cmm3+UI9k82vc2NV1+cZwJY++LevB2u/ZrWv4PHM9jzFvBG3ljsTbff6wexbLAlzy8QpvKo6XGnjT8O+H+2Z82Cj3zocNaZ+9hqnVMH6PLZk3k33caDT5xoh7ho/pncsnhmzZtX7N1sPX63iiXs3HR3d4d+zkDh11qPAD8znHoa+DOsO4FRSqmTtNbvO863AjUd0WNj21Dr0bxjU6rY5zcPHQ8VDWPVqN+a93j7NfvfPW58fnet+zBRNVEjTaJ0rrIf5/YnbOzeUlAjFrthys2LVfb1x40dxfK7VzuCDdI8/cIe1mzYw7IlF1Q8fl6oHQIzd5VSnUqp/66UmuQ6dUrmZz+W92qa6/x0QBc/RKEcRO3N6qZzwqjAMsDuGvU2zgJmfrXu/cZtJ0z5vX5Yutbt5PP3r+WRp3v4/P1rI/fT7Vq3k689vouVz+zz7Mvr5aQ+dewoli5STOsc59kOcSQFK7u2slsyU4WQhDH1jAK+BYwB7nMc/0PgVeAHmfMfB/4JQCnVDiwE/q6UgxVKT6H9W4NobWkODJ30ErDbb/4gV148BSjsDsS9M9+y8+2ik3eKqffizv1IpxNZe30xjVj87m5SKbj9vrUsX1LazFmpcFmfhDH17FZKPQZ8VSmVArYDn8AS/o9rrd9VSj3oOP8q8EVgAPhOfEMXiiVK/9YwBC0gXqI+5+wTN5WFxN6bTCSr7lpclGBFLYdgyv1wu8C8EsGC8gbsObHLQbhJpUqbOVuN5RiE0hDWubsc+BJwOzAZS/z/UGttx+7fieXIvQMrpv954JO1nrVbz8RdwdAvtjysqIe5A/F7H3NDOqVNeC1Odkcsr7r2XnczTkx3LmHzBuw5eXR1D8+s35MX61+KzNn+gSE27zjIqq6tgS0jS8mRweG8uRXiIZTwa62PYYn7nR7nh7FKNnyhdEMT4iSuGvVhCWtWCkpO8nofm3ccpLXl5MgiErYjFpBzzQ0eO2I7PNO5yDkXjJd3HDTmDZj+Hu1to/mLGy/i2sun8dl7f5Ej/qbs4kJw7vLdxPn5OBECvEvuLsqABN82KNVQwTBqxqlTME3vI5mA+x97iZFUcSaKoI5Yq7q2AemcXfEPf2l2AN/kqtXjFNhkIpHXnAWC/x7jxo4igfu+wP9uw4/d+w6zsmtbTgmGQsYTlb6BoZycjWop9lbPSD3+BqVUUTzlpmvdTpbdvZoVD61n2d2rWbd5X15UDySyNvCwNeq9sJuN9x0ZMpTvSOdFJqVSViVOJ81NiZwELrd5KpVO55lskgk8/x52/Xu/u4RC6Vq3k9vv/4Wv6Mf1+TBVOJX6+fEiO/4GptIVDAuNGPGy5zv70L47+B73PPJizuOKMVHYYxzfNtpYQtm54wfyyhXbJqIHnnyDkRR899n9fGTemYF+ADzuAnIjhhJ5O/5kwrqbK2Rus13CDOmWTckEt9/8QeacPSm2z8f0znF52c7VVOytHhHhb3AqVcHQSuCym5UkWBYiDNHPL2GLhDuG38adWxB2jE77/SXndbDpld4ch3SadJ6T+voF07l6/lk5JiKnGWPNhjcC6/KYInTyI4ZMi0eCZza8nrPwBJm6vBzSyWSC5UsuyIbYxkV72+icchW1cvdZy4jwCyWhf2AIvfdoYC0bsARs5ZPbsqGLI6k0K58Mtul6+SV27H2Hr67cwEgq7VkHc/vr/cw557RQ78MWbPfdxaZXern39oX0DQzl7KRNd01+TdNHUmlOG38KB/qO+Y7FfacSJmIolc6tkx/GXm70kyTh/s8tDJ2tXCxXXNDOjMmncOBYS0FZ0kI0RPiFonEnLC0bbPHdYVq26fwKli/vOMhCn92lKdJm6SLFo8/o7PN5yeL88zs8zpjfh90xy8nwSDor+rv2H2Z6ZkyFdslKJggUfRtniYow5Snc9fHtcfuZuuyexM66QJeeP7ms4uss7GfnYkhUT3yIc1fIodDG2aaEpajO1DDxKEsWzODe2xfyR9fM5N7bF3L6hJa8RcTN5bODRSzP4WowwyQTsGPvO1nn8m1fXc3//v5vfd+rvVg1Zb5pzU0JLlbBdx42e3oHsn8Pk0P+8tmTc36/ZbEi6brtse3+fu/dqydxOfCK6qmW5u31iOz4hSxRMjWj5APMOXtSXtnhZIKczN0wY3xijWbBRWcYr/vEVWfz9jtDXHXJlFAmnjBmlHQaHluts7Z1vyJp7lIYYxMDvLLnKNd9eDYD7x7nNz0H8p7f5Kg1haW6TUvO10oDjz6jXc/k798o5G8YRwkHv6ieem14VGlE+AUgeiZvlHyA9rbRLL/hgmxmaFMSli+ZHanv6y9f2pcnmAngBz/fyUgqzbrf7gu1gIUxo6QxO1Ttuxx7rkxO4Y3b3mQkBc9tXssVF3Uan//KuR9g3W/35dT4cYelLpiTv9A5TU3dPW8ZzWh+Ihr2bxhXCQeJ6ik/IvwCED2T19RzNkxERpRQUnMrzDTXXDaV1ev3kEpbop9ImAXT7zVM78MqruYM3wRnjoATe66mQd7i5LSdD4+k+eWL5vZfc2eexm0fO983LPXR1T08u/ENT/GNuhAHldCIs8SHRPWUHxF+ASguk9cW8bXrt9I5YVSoZiVgDiX1MyV4jXHCuNEkEglIp0lEcG6634f9+us278sTwzRpY5E0e652hYq8gcxwsyQScGZHW3ZO+geGDHkDsGbDG76LmslRO++8jqIX4rhLfNjdvZrGnCa1esqACH8D4SeqhVTDNNHeNtqzF21Y3MlJ7u5SXlE9j685YXc3ZZ5GNRt4ieHsGRP57lOv8JI+kFd/Z3rm9fzE3x6301+QTsPn71+b3cGb3uuieVP56Quv5zyXW3z7BobYsDXXUbt+a2/WOexHodFJpTbHtLY0h+72JhSHCH+DEMY+W8lMXlNykslx6h6j1w7bDsf0W8DcC2GYMtXuxemaS4MXJ6eN35nkNXNqO1/69gvZnb97B+9+rwBrNu7xFd+oobJBFLsxEKoLEf4GoBD7bJyZvH53HH7dpUzmjGxzEvJ32M1NCVZ86lK2v97vmQzkFnlnmQUwz5FpcXp24xvcsnhmznP7tV50Fmlb2bU1sKyy++8RVXyjl27zf19CbSLC3wBUugQzBN9x+EXV+I3Vq3zyiofWZ0M+3a9lWgid2a5er1vIPLoFu7WlGdXSTHvbaN/aOEHmkyDxLSZUNgyVKvEhlBZJ4GoAbFF1Us5wOa87DmeCzolEp/yY8zBiuOquxaz41KXc+9mFbMzU0/F6LZOAp1JW1qv7de3GK342cncDeBNHBofRe4/SPzDkWxunWPOJHSprJ4w1JeFPb5gNUFBinlDfyI6/TojTcVssYXfKzu5SazbsiRTa98ZbA4Gv5eWodDpcm5KWbd7ZeOUj8840vmbfwJBvZrBVkG5XtjrnTYvOjVwbx3quE/kP7sQxMEcnLbt7dcnj74XaRYS/Dqh2x20hESF2d6lbFs8MPVZ3rSB371r7tZyLo7N3bVNmp71l59s5Wbnrt76Z43g1VdUMuhux73ac5QieWPNqNhrJuRCHKSux8smtWTPOSApWPrnV11cTd4tNoTYR4a9xqsVx60eUO46wYzXVCkomLDF3iro7Jv+S8zo44fJM8/Y7x3Ji34E8x6udLOZMoAp6H153O2dPObXghvBejVc27zjoWTq5Gvw7QvUhwl/j1MoXO+wdh9tkFVQbxmivT0PCrtaZTnN06L28iB2nyI+k4Edrd4R6H9dePo1rL5/Ghm29ocoH+93tFLoQe1Xc8avEUw0tNoXqQ4S/xqnEFztqoa4goQtqfGIyYXlFA9m/pdLw6NM6MJzRo+NgHj95fnd2x+9XPjjfrLS16HIEF549Kc+MlUwkuNAnYqfS/h2hOhHhr3HsL3aOwy/GL3ZchbpMJit3jRuTCcstbKZ69GnMdeqdNDclmHPOJLoNVTNtEgSXTADzHN25dHpOHH8UrIidXN/E8iXx1EUS6hsR/rrBrlF5oldrqUvoxukoDFMW2TZhTYec9+UUtt5DR/nmD7bkPXbhB8/IVr70aqN4/YLp7N5/mA3bepk5tZ2vfHt9Xhasu0aPqWSCaY7+9qZpqCljip6nqCIu8feCExH+GudE1MiJaJSHf7yNY0PDOVEjpdiZx+lPmN45Ls+M4cbdZtHZq9dZ3OzbP9ySl8B028fOz1a+9PMfTOscx7TOccbyxqY7B7dZzWuOduwfpGVUEx1nBNfMCUJEXCgWSeCqcbyE5tHV2jeJKQpxJoKlHf+3SUBO5yq7zaJzkVv5ZH4imCmBKdsicebpuaUfHL+736u7b3siAbcsVjkdr9xmNdMcJRPwxC97WfmMFU/ftW5nYZMjCCVGdvwxYpsN4mwe7dUoO2ppYj9K7Sh07rh37z+c52BNA5+7+WLGtpzM9M5xbA5ZgCxqBFHOuSPH88I502mYd34Hi+dP9U2W+8Bprbz+5oBjjGTXNImjF6oBEf6Y+Nq/b8w6Jx95uofLZk/mzlvnlfx1/EoVxxHps2TBDGbPmBi4oAX5F9wO0KWLlDE66cKzJwUKZJQCZF3rdmaToZIJWH5DbgbsRlcPWpsN23pZukh5LqC79h3OEX0T1RhuKzQWIvwxsGvf4bxkoBe2vMnu/YdLsvN3i6pph3vK6OZYdubrNu/LRhA9vrrHWDLAK/LHfp7xraPzHKCPr9E5FTJNY556eptxfFM7co8HRR71DQzxnR9tzQn5/M6PcjNg55/fwSNP9+S91vzzO3znymvBcCJx9EKlEeGPAb/dYrHC7yVqbodfqUL43OUQUqkTO2xTyYCBwWEe/vFref6FwaH3s6Ju18p3MjySZvKEMdx7+0LPu4m+I2YfhbNWTpjIo+e37M+7S0gDL2zZz7UfsrqHTescx2WzJ+cs4JfPnhz49/NaMOyKmRJHL1QDIvwxEHW3GESh4ZTFRn+YyiG4cZcMePPQcaOz2Vn22FSOGOAbj7wImZaEpruJMMlqYSKP3ug9Ynz9Pa7jd946r2A/jdeCcdXsU4qO4xeEUiHCHwNRd4tBlLs8Q5jYesgtGdA5YZTB2WxOnnIfT2f/Z76bCONcDlM6+ayOVuM1Uw3H7fCBkQtwAAAdbUlEQVTOQjAtGNu3b8/W4xeESiPCHxNRdotBlLs8g19zFBt3yYDWlua8Zt8Xq0m82HMgL7b+0x+/gH8zJFvZmAqQBZmwvEJWneagy2Z38s0fbMkx9yQyx0tFlAUDSp90JwgmRPhjJOqX34ty113x6m61YVuvZ8mAgcFhNrl8HC9pUxmEBLOmTQhcWAaPvW8cl19TcFMHKufi2N42mj/9+AU5UT12rH8YSi3O9vPt2PtOqKQ7WRyEYhHhrzHKXXfF9Hom4ekfGELvPcrg8ZE8ITf7BtL0DQzlLCwmxpxyUkHjtZ4lAXn7+eD3FYawtYrCirPz+ZwUUgdImqoIhSLCHyNx7czCOm2jvL7pMe7Xc//uFKNkkrwdt5VFm8ipc9PclKC5KcHg0DArPnUpvzvwrrHGzpkd5hBOL6xEsPwkrzB9cYMI61w3ifM5E4Ofz03YOkCSDCYUigh/TFR6Zxbl9aM8xi1GqZRl929KpnPKEKdJ5zz3B05r5a5vvpB9nplntXs+fyHmskL8IIUujGGc635F2lpbmgOfz0mUiCVBCIMIfwxUYmfmdCSPGzuq4Nf3GzPgKZDmRihp7rjlRKkF+zG2aSWZTPDlb72Q85ie1/vz7hSiOK7D+kGiLHLFhJPuP3Qc5RJ+P+e5Xx0gaaoiFIsIfwzEvTNz71Td5SFmntVufP2XdxzME+OgMT+6uien1aBbIE1VNe1IH69FZvOr5pr3H1Snsfm1g0U7roPs94UszO65DlpUvMS5c8KovHF6lds4e8qpnnWApKmKUApE+GMgzp2Ze6e6ZMGMvPIQpt1zMpHgvsdezJpfTALuHnNT0tx4ZHzbKDZue4urLpnClNPbyK+Wk7+DdY7bq1Xg7185g8/e9MHYHNe2iB8ZfC/Uwux1V+C3qHiJc2vLceOYCnUyS1MVoRSI8MdAXDsz0071hx69Yp2756ZkgnQ6nY2uMe1wTWNeNG8qP33h9ZznHR5J84/f6wbg592/47TxpwQ2AHeP28uqPTySLkmteZNgA47SE4lAs1LQXYHfGE3ivH37ds/rC33PUo9fKBYR/piIY2dmMsd49S1x7p6PDL5nlUNwYNrhuscMsGbjHl8H5IG+Y3nBkwD3Pfoi23Yd4pbFM0NlAJfqjsgk2Ku6tgEnFr6RVNrogHb+jYo110UVZ4nRF8qBCH+MRPny+33xvWvv5z+Pc/fcPzAU2vTkHrPzLiCRMC80Mz5g1dN3xuun0vD0C3tYs+ENbl6cX3I5mYBEwgrxLKWt2iTY7naJ1vjMDmibSjhSTXcqYtYR4kCEv4oIijSJWnu/GNOT8y7g2PH3s2YeJ7d+7DzeOXKce1x3FWCJrlfJ5SvmdJZc1My+CuuexLkwBdX6L7cj1XSnsvLJbdkS2JKsJZQSEf4qIWykSdTa+8WYnpx3AU9Mfi2n0ci0yW3MOec0+geGaEqas3SHR9KcM6WdVXctznv9UptDvATbnUcQRsTL6Uj1CouVzl1CHIjwVwnF2JTDdsUKY3oKsjE/eMeH+dXm3/HT5/fw0cuncsWcD2Sf+7p5k/jPDQfznL2FmEgK7dxl74KdeQxegh1FxMvlSA1TEE+StYRSIcJfJYS1KQdFrDyxRkc2CYRJanJe88ruQ/QNHM9ec8UF7cyZ3sqm3SPZMFB7d71u875Qz72qa1u2ANyyJfmds0x3RS/2HKC7x8oNcLa5DCrRUE2OVPedih2JVWxCmyCYEOEvEcWKSBibcpiIlUJNAva429vy2yG6nycou1fvPUrnhFH8xY0Xccvimdn5SAPL714d+Nwrn9yWTQQbSVk2buc1XndFtujbhGlzWemSGibcdyruxVKStYRSIcJfAkolIkE25bARK2FNArnF1fKbpdjPMx18E5+c2b1NSVg22MKSBTOyr9/d81agGevlHQeNxdVe3nGQhZl8AGNUkyse38avzWU1Fztz3pVIspYQFwUJv1JqFPBbYIPW+tbMsQRwJ/BpYCLwa+AzWuv83oN1SKlFJKjWfNiIlSCTQH5xNXO9mB173+HuVRuy5gcTq9fvyYrvSMoyO82eMZG+gSGmd44LZcZyOoyd7Ok9cdy+K3Kagz6+cAb/8fP8JDa/NpeF+FMqbQ6SZC0hDpIFXv8VYKbr2JeBu4B7gKXAOOA5pVRDGCP9RKTU2MLX3GQJcHOT1Qhl2ZILco6FMQl4JVXZ2t6UzA8VNd1dQP6Oe3gkze33rWXFQ+tZdvdq1m3elzdu9xh73z5qfO79B03H09mf48eN5rLZk3POBrW5tBciJ17+lGV3r86+j651Oz2fUxBqidA7fqXUB4G/BN52HGsF7gBWaK0fyBxbB+wBlgP3lnS0VUi5E31KFbFiNps4c3DTvH34WGDGrZWIlR/GmXLV91l112LfMX708rP49cu5NYfs4zb2XcqJDFyyz33zYhW6zWVUf0q1mIMEoVhC7fiVUs3AKuB/Afscpy4FxgJd9gGtdT+wFrimdMOsXky78LidcO1to5k78/Sc1zAdC3oO57htk5HTZLNmwx5P846TpZnMXDhxx+DEvgPyG+Occ07jrMm5TVfsHAEbv7uraZ3jWLpIha7dv2TBDFbdtZgVn7qUVXct5voF03POl/NOThDKTdgd/98AJwP/E/h9x/FzMz/d98C7gBuKG1rtUKtOOOe4TfV8RlJwzWVnZh23JgdwKk02OWvt+q20tTTxYNfeSHdAD97xYTa/doDnNu3lqkumZBPD7HktdZOVIH9KUO9eQahVAoVfKTUL+CJwldb6PaWU83QbcFxr/Z7rYUcy5yLhV8mwkhw7dgzwHl8L0Luvj959xtNVSwvwzuCQ8dysjjSX3DSN/YeO09bSxANPvpFj1mlKwsjRA/Tu6+PMiUkgzbWXTOSpjQcZSVnnr5s3kd59u0PNy8nARz/YAsOHeOj/7XA9z6RQz/2rrf15j7vignaODA6z/9BxOieMyuuG5WZgcNhYbPq1114LfKwJ02enkPHUO0HfrUYmjrnx/bQppZLAd4CVWusXDJeYCjPaGJL3hWrlyOCI8fjA4AhjT7E+JmNPaea6eZNyRPVj8yfliZadyFWMqA0MDmdfB6y7j6c2HuTOpdN9n9vrccffT/HsS4fyFgMv3jx0PK8gXTqNsZNWFLwWJ0EoB0Gf4M8AZwLXZez8NonM74eBUUqpk7TW7zvOt2bORWLWrFlRHxor9opb7vGFMVuYrikkFLHjjCG+++z+PDPKUGIsX3v81Zxs2oe/dLHxeUs5P909bzGS2pVzbCQFTWNOY+7M0wt+3JqX+rJVTEdS8JNNb3Pj1Rd7zovXfCy8NJr/xjk3fQND/OTh13IWp6Dx1DuV+m7VAmHnprs7v4CiF0HC//vAB4B+1/E5wJ9gxe4ngGnAq47z0wEdehSCJ4WWUTCVcQiTVNbeNppLzuvI6eZ10bmTeOyZV43ZtH7iWwz2YuXlVB4fIIzepavzHbWbdxyk1aMss1/kT7Gx/dI0Xag0QcL/aazdu5NHsET+7zI//xn4OPBPAEqpdmBh5nzVU+kEHT/ChBSayzhsBRJ5LRP9esqObx3Npld6c8692HPA0F0rN5u2lORmEpuv6RsY8o3cCVu6OpmA+x97KVtPyLQwmpz2pcjSlqbpQqXxFX6tdd6uXSl1DDiktf5N5vcHga8qpVJYC8EXgQEs30BVU431WpyE2RmayziA2/Vi2lG6hdbd0MUjX8vo1OkfGMrW6olCfiZx/jVhxTGodHVTEtLpcAujM/KnVLH90jRdqDSlCCW4E8uRewdWTP/zwCe11lUd8FwtCTpBHbeSiURODZtkIlf8vJqkO3f8ENxT1iS0TUlL/J1OzmQC5pw9Kec6q6qm1TAkmYDlmVo9heCZSZwJIS1UHN2hms7F4N3B9/KaxoQxtZTSRFOrIcBCfVCw8GutL3L9Pgx8IfNfzVANdtagVnvm1uS5v0dtPBJWaNOks6LelITlS2bnZbiufHJr9u4glYaVT24teAH1Mn/ce/vCbM2fYsUxSivKMGOMaqKROjxCpWjY4OFK21nNrfa2ZkW0KQmL5k812NgJbJJuC6Rfc5YgoR3fNjoruH47U6uqZv4YN+84yJUuP0CUzlnTOseFzsYNS1RTi5hohHqhYYW/0l9ic6u9E/8eSVnNyt3ZsmGbpDvvJkzNWfyEdsvOt7MVOU2+D6eAHx18HxNHj+UeD+NPKaf5I+priYlGqAcaVvihsl/iMK32gDzRD7M4efkvnKWS29tGG99/kO/DLeALLjrDOIYxp5wUOJ4gZ2oxFFuywQ8x0Qi1TkMLP1TuS+zecXs1FLFJJuHe2xcyrXNcYLKWl//i9vvWZu339o7b/f69HvvMhj3MO78jT8DXvvg743indpyo2FFuf0q1R2sJQqVpeOGvJM4d9/i20dx+79q8LlQ2qZS1c96y8+3AZK2li5TxbsJdKtm04/a6E3nk6R4eW62NRdpMOOPty+lPqZZoLUGoZgptxCKUGLtU8bTOcSy/4XzPjNXmpgTjW/P74q7q2sqqrtxjj6/R3LTo3BOlkg1/Za8Sw+5yzU5MXbq8ijY7H1/O0tVSTlkQgpEdf0TiyPh13gG8trefJ9a8muN47TsyFDpZ65wp7az41KU8t2kv884/nW888mLoHbc9jmc27OGRp/M7aNrJXs1NCS46ZxK/cTU7B9j+en9OLf1y+VMqHa0lCLWACH8ESmlDdi8gts197szTuXr+WTnnTPHnXslaP163i+6MIP+8+3ecNbmN3x04EjqCqb1tNFfPn8pjz/Tk1aS//3NXZp3E77x73Cj8pp635fCnVDpaSxBqARH+AhkYHObhH79WEhty0ALiTDjq7nmL6Z3jQiVr3fBf8huQv/7mAHf/2WUMj6RD77itd+iuvJ3g1LGjsvb79jar562zuFtQz9u4qcaQS7v2fscZQ1UxHqGxEeEvkDcPHS9JhEpYJ6RpcVh112LfnrvPbNhjfM3tr/ezdFFOIx1fk9Xu/YfznM2pdP57vfPWeezef5infr6F86aO4feu+GDoeYiLagq5tEpa7GIkBd99dr9EGQkVR4S/QDonjCqJDTlMiKPf4uAui+wUuvnndxht827ziyVI23Jq7TsFqRB7+bTOcVx18YRCpqAhcDeIlygjoRqQqJ4CaW1p5rbrT0TfNCWj2ZBtUXXiFtWoESrTOsdx2ezJOccunz2ZU8eOorvnLfoHhjI1drZlfQN2rf3+gRMtGEsdjWObrJyvUe9IlJFQjciOPwS2OWRkcNjR6i+d/Zn27D7pTRgnZDERKrb5xa7Vs2Xn2yy7e3VOxq3JjPP8lv10TBjjm90bhbAO8WrujxAFiTISqpG6Ef64BMMpWE1JuOqi8fxsc39O27yot+5BolpshIpd4MxkMvqFR8btt364hXQa3+zeQinGn1HrtnD7b2hXOJUoI6EaqAvhj0sw3II1koJnX+rLy1b1cu6Wol5MKXbcJnNDOg2JBMaG4vZ7KpUtulh/Rq2L5JIFM+hoGWT/oeORe/YKQimpeRu/l2CUwo7sVUEzmfS3zYO1GC27ezUrHlrPsrtX07VuZ+Rx2Nm9zro8hdjKvfwJt1ytMnkA1iLgplS26Dj9GbVCa0szasoYEX2hKqh54Y9TMEyC1ZSEWxYrX4dnnItRlAXFbqTu5JLzOli6aCb3fe5K/uiamXz105d5irN7oQmz8DivCeMkDrM4CIJQGmre1BOn88xtY29KwsfmT+KmRYrF86f6xr/HUY0yqjmkb2Aor5H6pld6eWKNzjYhb25KcMl5HWx6pTfHn7Bu874cM5r7GpNZzcv0Fqc/QxCE8NS88MctGE7BGjl6IBvV42ebL2QxckbeBGW7Rl1Qtuw4aHzco45qm8MjaTa90pvT6jANLM9EAtnXODN0TQtPUGZzKfwZ9Rb5IwjlpuaFH+JP0bcFa/v2vtDXh1mMvvbvG7NC+sjTPVw2ezJ33jrP83mj3N3YjdDdWIXW8heDvoGhbHJYd89bgY1i3AtPsZnNQYtDPUb+CEK5qQvhh+pK0YfgxWjXvsM5u2eAF7a8ye79hz13/oXe3bizRm2aklY9nx/8YkfeY8YH5BG4cS88hWQ2F7pzr+fIH0EoJ3Uj/NWI32K00WVzt9mwrdfX5FPI3Y3JNARw+83etXTe6B3IKcDmXmhMfgDnGOzM5qDFKcrOvdydvAShXhHhrxBh6+mYCHt342UamnP2JDbvOGh8zNFj72crgXpl7gbt1IMWp6g7d8mCFYTSUPPhnLWKVz2dUpYz9gujnHp6m/Ex3/rhlrxQUXcegft3r9f2uiZqCG45O3kJQj0jO/4K4q6nE0cNe6/dd98Rcwx+KobMXTfTO8flNZdPJgi1c6/GWvuCUGuI8FeYU8eO4pwpp3Lq2FGxvYbJNBTGcRuX/dyrwUtYqs2RLwi1hgh/BbFDLUdSVkbwsiUXlLRipd/j8pPTEqTT6ZxdeFz287ANXgRBiAcR/gph1cPfmhXakRSsfHJrySpWhnmc22ziztKNy34uTlpBqCwi/BXi5R0H86p8ptKwecdBrrx4ClBciYawj3OaTcplP5fyDIJQWUT4K4SXRdt5PGrcejHx7qWynxcb8ikIQnyI8BsoRy2YC8+eRDKRyLF1JxMJLjx7UvZ3r9ceHzCmSptSwpqnxEkrCJVB4vhdlLKOvh/tbaNZfkNu794/vSHX3OFV9nhP74BvWeRKxrtbRdriKUktCEJpkB2/g3LXggkyd5h27skE3P/YS4yk/HfTlTKlFFukTRCE+JEdv4NKdIHyy3B179ytblkJRlLhdtNhMmxLjV2kzYlE7AhCdSE7fgeVsI0X4gR9d/A97nnkxZzz1babDlukTRCEyiHC7yDOMEOTwBfqBO0fGKqJ+HeJ2BGE6kaE30UcomUS+CvmnFGwP6GW4t8lYkcQqhcRfgOlFC0vh3HbmJMjOUFlNy0IQrGI8MeMl8P46LH3jdcHxeiD7KYFQSgOieqJGdth7KS5KcGYU04yXt8n8e459A8M+eYsCIJQOLLjjxkvu/ycsyfVhKO2kkhjdUGIh7oR/nKUWYiKl10+bkdtNc9JENJYXRDioy6EvxZ2hu1to5kOlhBnfo/TUVsLc+KHNFYXhPioeeGv5p2hc8ftrnVvC3EcjtpqnpOwVLrQnCDUMzUv/NW6M3TuuJuSkE6fqMQZtxBX65wUQi3lLAhCrVHzwl+NO0P3jnskBbn9ZeMV4mqckyhIzoIgxEPNh3NWsgSxF6YdtxsvIS5F+GI1zklUKlFoThDqnZrf8UP17Qy9yiknEolsOWWTEJfSIVttcyIIQvVQF8IP1ZXN6mWfvmJOp6cQx+GQraY5EQSheggl/Eqpk4EvA/8NmAhsAO7QWr+YOZ8A7gQ+nTn/a+AzWuueOAZdC3jtuL2EuB4csoIg1AZhbfz3AX8JfB34ODAI/FwpNTVz/svAXcA9wFJgHPCcUqq2vIklphD7tFdph1pzyAqCUP0ECn9GvD8FrNBa/5vWeg3wCeAk4L8ppVqBOzLnH9BadwFXA63A8viGXl/Uk0NWEITqJoyp5ygwH3jdcex9rPjEUcClwFigyz6pte5XSq0FrgHuLdVg6x1xyAqCUA4ChV9rPQy8BKCUSgJnASuwhP//AB/JXLrT9dBdwA0lGmfDIA5ZQRDiptConi9hiT7Al7XWWin1B8BxrfV7rmuPAG1RBrV9+/YoD4udY8eOAdU7vkoj8+ONzI0/Mj/exDE3hQr/D4FfAB8GvpyJ9jmGOy31BKnoQxMEQRDioCDh11q/nPnn2oxT96+BvwFGKaVO0lo720q1AoejDGrWrFlRHhY79opbreOrNDI/3sjc+CPz403Yuenu7g79nIHCr5TqAD4KfF9rfcRx6iUs524/kACmAa86zk8HdOiRCIIgCGUhTBz/qcAq4EbX8cXAAeBHwBBWfD8ASql2YCHwXGmGKQiCIJSKRDrtX0wMQCn1feD3gL/Fitb5A+DPgGVa64eVUv8EfBb4Itau/4vAGcD5WuuCzD3d3d3BAxIEQRDymDt3biL4qvA2/j8BvoIl/JOBV4BPaK2/nzl/J5Yj9w6smP7ngU8WKvoQfuCCIAhCNELt+AVBEIT6oebr8QuCIAiFIcIvCILQYIjwC4IgNBgi/IIgCA2GCL8gCEKDIcIvCILQYIjwC4IgNBgi/IIgCA1GoWWZ6x6l1BLgEa11q8f5iViZy/+qtV7hOD4KqyfxzcAY4BngL7XW+2MfdJkwzY1Sai7wG8Pl39Ba35G5pu7nBrw/O0qppVhlTM4B9gIPaK0fdJyv+/lxz41S6lbgYa/rtdaJzHV1Pzfg+d06Bav/yVKsmmndwF9prV9yXBNpfmTH70ApdTlWVzG/shEPAJMMx7+JVdriC8BtwBzgJ0qpplKPsxL4zM0crPacl7n+e8BxTV3PDXjPj1LqJuBR4KfAtcD/BR5QSn3ScVldz4/H3DxF/mdmCXAc+I7jurqeG/D9bt0H/AXwT8B/BUaAnymlPuC4JtL8yI6f7Kr5WeCrWCJ2ssd112NVJR1yHZ+BNfm3aK2fyBzbjFWW+gbgB7ENPmZCzM2FwFat9XqPx9ft3ID//CilEsD/wro7/B+Zwz9TSp0FLAK+W8/z4zc3WuuDwEHX9T/C6u39l5nf63ZuIPCzkwT+GLhXa/2/M8eex5qzpcA9xcyP7PgtPopVgO6vgQdNFyilxgH/BvwV1q7Eye9lfv6nfUBr/RqwDavhfC0TNDcXAi8bjtvU89yA//zMBaYA33Ye1Fr/kdb6jzO/1vP8BH6vbJRSV2OJ1We11scyh+t5bsB/fpJYC8GA49hRLO0Zn/k98vyI8FtsAqZprR/Au43kPcArWuvvGs6dC/RqrY+6ju/KnKtlguZmNjBFKfVbpdR7SqkdLjNGPc8N+M/PhZmfzUqptZn52auU+nPHNfU8P2G+VzZfB1ZrrZ9xHKvnuQGf+dFaDwPfAj6jlLok0+PkH4FTgP/IXBZ5fsTUA2it9/mdV0r9HpbzZLbHJW1YzeXdHMHa8dUsfnOjlOoEJmI5Lf8WqxvbzcC/K6XSWuvvUcdzA4GfnUlYdtku4F+Bv8NqWPSvSqm+zO153c5P0PfKRil1JXAR8BHXqbqdGwg1P38HXApszPyeAm7VWts9FiPPjwh/AEqpFuAh4Cta690elyVozIbz/cDVwBat9ZuZY89mFoSvAN+jcecG4CSgCfi21vprmWM/U0pNx5qfJ2js+bH571h+InfHvoadm4zuPI/V3vZPgH3AHwIrlVIDWusnKWJ+RPiD+QespvH/opRyzldSKdWcuSU7jNVc3k3khvO1QMYWu9pw6mngGqXUWBp0bjK8m/n5tOv4GuAbSqmTaez5QSl1EnAdlhPcTSPPzR9g3UnP01pvyhz7mVJqApY/4EmKmB+x8Qfz+8AHsSJ53s/8Nw74UubfAK8BHZm4Wyd13XBeKXWuUurPM9EJTk4BjmE5oxpybjLsyPx0R0KdhLVbS9HY8wNWGGcb5giURp6bKVhmQneOzK+wfGpjKWJ+RPiDuR64xPXfu1jmn0sy1zyHdUt/vf0gpdQ5wPnUd8P5M7Bs19faBzIhjH8ArNNap2ncuQH4JdaG4ROu49cBmzJ3i408PwDzsCJXthvONfLcvIr13ue7js/HCuk8ShHzI6aeALTWW9zHlFIjwH6t9W8y1+xUSv0/4KFM2Gc/8D+xwhx/VM7xlplfYu1AvpmJOngTy157IfAhaOi5QWs9oJT6GrBCKTUArAVuAhZiiX9Dz0+GC4BXM5uEHBp8brqA3wL/Vyl1F7AfS+D/GPhMZr4iz4/s+EvHbVjOun/EyjzcDFyrtR6p6KhiJPPebgB+CPw91u36acAiR+QBNODc2Gitvwp8Divp5j+xdmx/qLX+qeOyhp0frM/LOz7nG3JutNbvY0U5rQG+gSXklwOf0Fr/i+PSSPMjzdYFQRAaDNnxC4IgNBgi/IIgCA2GCL8gCEKDIcIvCILQYIjwC4IgNBgi/IIgCA2GCL8gCEKDIcIvCILQYIjwC4IgNBj/H30aRjIFzJUuAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(df2.height, df2.weight, '.');"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So lets write our model out now:\n",
"\n",
"$$\n",
"h \\sim N(\\mu, \\sigma)\\\\\n",
"\\mu = intercept + slope \\times weight\\\\\n",
"intercept \\sim N(150, 100)\\\\\n",
"slope \\sim N(0, 10)\\\\\n",
"\\sigma = std. dev,\n",
"$$\n",
"\n",
"Why should you not use a uniform prior on a slope?"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"minweight = df2.weight.min()\n",
"maxweight = df2.weight.max()\n",
"minheight = df2.height.min()\n",
"maxheight = df2.height.max()"
]
},
{
"cell_type": "code",
"execution_count": 160,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.stats import norm\n",
"from scipy.stats import multivariate_normal\n",
"def cplot(f, ax=None, lims=None):\n",
" if not ax:\n",
" plt.figure()\n",
" ax=plt.gca()\n",
" if lims:\n",
" xx,yy=np.mgrid[lims[0]:lims[1]:lims[2], lims[3]:lims[4]:lims[5]]\n",
" else:\n",
" xx,yy=np.mgrid[0:300:1,-15:15:.1]\n",
" pos = np.empty(xx.shape + (2,))\n",
" pos[:, :, 0] = xx\n",
" pos[:, :, 1] = yy\n",
" ax.contourf(xx, yy, f(pos))\n",
" #data = [x, y]\n",
" return ax\n",
"def plotSampleLines(mu, sigma, numberOfLines, dataPoints=None, ax=None):\n",
" #Plot the specified number of lines of the form y = w0 + w1*x in [-1,1]x[-1,1] by\n",
" # drawing w0, w1 from a bivariate normal distribution with specified values\n",
" # for mu = mean and sigma = covariance Matrix. Also plot the data points as\n",
" # blue circles. \n",
" #print \"datap\",dataPoints\n",
" if not ax:\n",
" plt.figure()\n",
" ax=plt.gca()\n",
" for i in range(numberOfLines):\n",
" w = np.random.multivariate_normal(mu,sigma)\n",
" func = lambda x: w[0] + w[1]*x\n",
" xx=np.array([minweight, maxweight])\n",
" ax.plot(xx,func(xx),'r', alpha=0.05)\n",
" if dataPoints:\n",
" ax.scatter(dataPoints[0],dataPoints[1], alpha=0.4, s=10)\n",
" #ax.set_xlim([minweight,maxweight])\n",
" #ax.set_ylim([minheight,maxheight])\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 161,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"5.1409768989960456e-05"
]
},
"execution_count": 161,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"priorMean = np.array([150, 0])\n",
"priorPrecision=2.0\n",
"priorCovariance = np.array([[100*100, 0],[0, 10*10]])\n",
"priorPDF = lambda w: multivariate_normal.pdf(w,mean=priorMean,cov=priorCovariance)\n",
"priorPDF([1,2])"
]
},
{
"cell_type": "code",
"execution_count": 162,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"cplot(priorPDF);"
]
},
{
"cell_type": "code",
"execution_count": 166,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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oOUauSMQMnsyDth2I1/RDH76d9tNo4ymwtMHXqmplmmpb6BJOiv0nMWEI/Tc8r7LMeVnFGqq1zgah/07zHmL/Ed9Oo6vJyIQ8iL4GexW8h76GvaXRn9Drsyn8m3s8rT1TWx+ySdvbzf9dGBOVLty8mT86PSYQOfF0bTlS2wegx6G5oZAPbagW2bZmGDMC2vWI0NtxYzHF9XO7peaSEgf5UIZ6kEnDzY+vleFkMj9GaGS1Vq6hdfLc8lvzHGIdB6oK06tXm32pe2uKRYpDCcMeSzPUeQOGv6LpWWjur9TxeD5D94C2ToYUNzaa+3GzrAyYqHRB9niRXSM1YwTEbwZa1toEZHouBtrDKzsAtPAWokYgVOMPeQ1aWYRqTsC89xd9x4iJA/+tTbjJr1eu066Xl4d2jpjQc9GOlTlHVghinmNf4z3bp6bjUbdWLb9tzsH/X+7Ry+8cQy3Ths7X9Tu0Lna/as+1lobusYjRr2RbpowEhOxADrFjnDtXXFAAE5VuHB42k79xYwKcfOioJ0wOOQIhe5e1EQpJqvbPxSCnW3DqgU8ha/E0qSEXBSlaoWuT5cprZbFr59eXElutPYmnC+0D5AtDF5HIOZbM4+x/q7e3m2WamJCXVSjMG/vm9DH48rttGi1fobxqeQ8Z5ZChb2P0Z2lOtGeFjqPdR/Qdus9ieR8QE5Uu3LqVfgdByGBoYYmYMQrdBCHDSNu69EzqIwypfIW8GbpmANX1683yjRvzvMgHpq5PhpNiIiePoZWvFioktP20hzhWKegiEJpB4d9yHa8RUzkAp3uI8W/xn00onk9lX1IINLqIAP8trztkhEMGmn9rpPbJEZRMg390773N74c8RD/WwCJQGhOVLtx++zxEk2rQjN0cIcMY6p0EtAon9YYfU8sTbx/gD7bcVysHivvzvFMaKX4ydBUTiFyhzhXzmDhohjxUc44ZP4KW29bMu6Tl30DTngU0oqIROr4UNJ6eX49Moz0XWthHo4vBD31rlYbQttSyXJcL9SQdIBS1CNbjKsZmext48IOb5VBtOdQraIxwUgwpCtKDoYdfCkrIMHO0vMfEDzjxMFZHR6i5OADpUBEdI/Qw59RUQ2IoyyXnGLmC07WGn4v2P2jGf0ZFs1pTRUETgZDxP3WwjFr8EN99lo1imKh04eCgqdHRgxgynKWFgR4EEqfQIEaCDIT0JjSjrH3Lmiidh7bFurtq41b4eqXmPqXxKRcv6sZVy5803tKoJ4Qs+s3TD+EJxmjrAWgioPXqC1xrTbVlGtgbSZtdbqHzdqn1mwisDCYqXbh6tXmfdBe4MAC69xLqOca9Cn6sUC2dGxVpYGW8PWR85Ye/YU6ruWrXx5fpLZNyP2AugvxdMPy6NI9KptO8Fy5qMWKikTKgCU8gK02pWnpOfmXWqLGYvkt6ACYC7dAqEqHfbdLK3xsb1vtradjZmRtGIiQOspbL2yJCnkMIHhbi4iD7vksPhfYluMdA2/i6WEhGCh+nrTEUgwIrWfOOfSSxc4Vq9ymkl9bFiLcRgD70qfVXFaY0kv7Spf55WRSljG3b3z2PNaF2LJpIdUwuXOg324GCiUoXqmoe/pLhH/4N6IY55CFonors6sqR3Qsp1ETdmaUAyXyQRxCb90kzRqkR3ClvgS8zb6Wm0dy33Xay/DQRaCMUoQbgtt8laVvTTy13Rd67cszEAo1t699GO0rcPwomKl346EebmXQ1oYgJA31LY8iNq/QeuEDEpvOgc0tyRCJi6E91mQ19U/pQaColDn09gSGJnZPyyv9LbT+5Pcf48ntK26797miIJ6neX0Z/5L06+13Tejm5YyB9clvu75yQcAdMVLpQVU27CoWeyGhIo8w9B9mFtU0ti7wK2QtKa/yWedDSUB7ksejatPPHBKGNwY8YuZraa/hARZ4u12DmGPaUCMh12vmNcehjQEsY31LHDnD8PhX6bkOoQpFa1u7/QpiodOXixdM1yJRR1byEHE8ACI+oDx2f9pG1XplX2sYbx4cMYWjM8lLdvNks37qllxXPtxTCoTyXVRaSFkavJiGnhttFGt8xvM9cYsZZe7Y6LFc0oSR5izJNbP++2CzFS8LOTvPwyfEbXAC45wLoxpDSEiHjuWy15ZCxb7vMv9GzxlaKIWu2qd+lj92CU1OFjEWoFh3aNvbyCJwYI7QGmKh0YWdH73pJ37HPIsgx7G2WQ+fo+bumWrJ8V82YhnwdyTGe1FmDv9Mjd98lN9pLQ8j7oIiHFBWt/VWjqk6HfmPpiZ0dC38tDXVdrjYdCmHRejkeJCRe2nbZVXDIWnMB6p2dZoG+V4VlqFH37Bk1uXWrWdjba7Xf4JQMv4baBEO/OW0Nt5Y+tZyaqaA0Bwfz16EXxESlC5cuzeetkjdCyLCHvBbNczBO0seo5hqZdaptdzG8IU+l7fFShpuTY6iHXl4GxhYTguYtLIyJShf6vE54WVmCGnZF3VmvXx/faJfukNDXELf5zeloYKvptHmVs/ZaAdnupy2ntq0zPcOxx2Ffmvl8rHa4gf4jE5WxWAKjXbymXdjQVvQ2TQrFjGmoY3QxpKll2Ua14Nr28dxfY1WWhmwnS/0ufeyeHId9qZ12xTFR6cLR0cl3frQ13G0M3CJr0Dm/S1FV8+nXeVx/TYx2K0L30ICGtq6qxlPhA/CWvA2uGGPd4yF46HFMaBxdYUxUuvDhDwMf//j896IMcRv6GFvtOHI5J0SSMDTHngr124/low3yGLE4cl9D3adzhPw9dFsbO2516xYqoExD/Qj5XfrjtjjmhMo8ZzaDknmdTJq5vwpfv4lKF/b3T3f/62Koc4zGomrbQ4YXAueqKaZcukvxIlnGCobCqdCjoZP6/zpsr+iFf1evDntuyfZ2IyqFMVHpwsMf3gwSC42o135rvWD6hhOGDI0MZfwixz0e/DjAjb6SDGDAQttqPrXQyOdemWMPBZ9lfOzzTqen5xzriYlKF86fX+yo7yFYggd9SmIiZynOOW9u+1WX7UMdewgj0tUohrzEvsdNYcedN9APYVNi+d3asi7FS0NdNwOH2oY2zloNrCUTevEZb1NZZVJhuMI1xF5Qt9Y1eU/6CTLDr8X3zTz2lN5hc/vt457bZileIvb21maentHIEbWU19H1uF1pe+ychzx3jEmX7YR2jsS+U9onFAaNhUe75jt07NztoeO3uddS6bvck23yAcwrUW0qUyUqkTs7g3hHJipdmE7nU9+HGOom7PqgyeN32Z7a1idvACp68921a+HjD1l7y6Hv/kvqMW5Qd+5Q2RuDMSExGftdNnt7jbBYm8oScPNm2sDJrrva9hjL1INpLOjmHiDOW4yxRaHt+bqmz50pd8j8DF22Q+alx7Er6lLMp77PPbYWgs8dBHz+vLWpLA3b2023YqD7zSf301z4Ujd2yrPoeuyY8HXJO3VrTQ0Ca3NsHnLqEz6KpW3zYLbNu7ZcAjluSb55tM8x224b49ja2zPlfrE3bFZV+g2cfLsMddLzrBj8mvf+Cp1DO5aWD5me3/syHb2+wzyVJeDcufSrfYf2NMbwZEa+hvqOO5qFBz1o2PN2pW2sfojtQx1Dm6YlVAEKGS7t2FrlqO127RxymzTG/HfKAGvk1vZz00U4Hvx4/Xq7Z65NWimiVdVUjE1UloSbN7v3UCrRbjJGT6++xo3y3iKvExr8deVK/Dx9G2ZT20PlLscd9T1Hl/9R3hu5x0ikr6gt5cqVcNpQrTeWb21Z27/LsTXahJVTIeq+x89JD8zHZ128mH+crvng37u7867kBTFR6cLBQSMqIVe19I3aNW0XSuU9ZFgiBqXOHQSWU+6pWqOsueWk70qXmm7u+Qsd+8QM0Ysk5/5rO0hY+51TcQiJjjyGDBnKqexj31WFene3WaauxbE8aNMhafkM7cMZaPJQE5UuyDg0X6+lBeKCE0rTt2bbpQafihsPaHwrakuh9qoYfY2uFmPW0sSOHTtXbgWjRFtDzjkSxvZUbVmmz7nXU+0xMh8pAUi9ajt1jL7pcvfpSU1lzj2VMbCXdC0Rk8nJlxnl1Ho0ZG05RI7RCBm+DINynCYmYjyvIaMbCktp51OOfTz3F39Vs3ZdbR/oNkLXteYbC5/1/d02j7FjaIaxrjG9775m+WEPC6eLLae25aTrYqhLhHoXdXzy0EMeT6HjB9nctN5fS8MDD8xFJeehkAZZW+ZwYxpb7kKsht72OLHfoXWR7RXlhbq1pgx4qOYbq9HmpInlP1VDj+UpFNaI5anvC7Iy75MpjeZe1k4Sa8y6zXlnotKF6bQRllAPk+n0tIEgAUkZDrmtrk/HaGNiFvJMpHjwc+bEaVOvPI0Z8Mzl4xdF7eyMF7oocexcSoi5dv5c8YvsV9HsxNosxQOcr/U6Y2VYWVFxzn0rgO8B8CkA3gPgu7z3fzjKyXd2mhpdrO+71hWylFFpiyYU0uuJ1a65IPL9YmLEy0JbJ/MANOGvum56pITyGbq+2LFT4lBCMMakZCeCGa3as8ZmbBEz0ezFSoqKc+7pAF4P4OUA/gjAMwG8zTn3eO/9nw+egdtua24M8kjaPtRtb6qcUFio+6kUudByKZGr6/QxA4a9IpHmx0iJS0gw5brYMWR5dGkryxW/rvuF/t+cdavOml/nhHre0TRFwLDCRr83NgaZQHTlRMU5VwF4GYA3eO9fNlv3dgAewHMAPGuUjFTVfJbP0AfQRyqnjB2JgbYOSItCm+0abbqltu3CGtqvrucDSqlNZQzD0SbcVTKtti51vXKfNvni6xQRm5Jx2d5u5/nleE0560rutw6MJaQXLxb3nFZOVAB8BoBPA/BmWuG9P3DOvQXAE0fJwbVr8ylF+qLVrmPfwMn2jZSQkfiFzhfKk7yB5bouopLYrg4C63O+PvnsIsYlGEKsMtJO+Jsf2xiZrvlJ3ZNdBRwYVtgGOPaJF6R1PV8XBgrDraKoPGb2/QGx/oMAHu2c2/DeDzsv/fnzjatawuCUDj/FaCtgoXBSyAsLhaBS558tT/nLimRNmSjppfUJA47lwWnbBxC6iiYzlIMfx/LSctLmMJTnSctalCG1nKDe3W0W+kxD30XY7H0qx9BrAe8X6+8HMAFwAUD2/N1333338fLebA4evk7l8LDpLcP/JFaTp7UVGUZqe+G9whTDMJGGJWZ0ltntj4kHT8PW11WF/b091FUFzw0bO0bNf2u90SLnrWWaVD5lCKijcFSJ7aljZT/yPUXs5tERUNe450Mf6pXfQWkb5lOW69g9ydcXEIvjcyaOc3M25dP73v1uNc2J0i0hlAOziqJCpRO6kwd/0XO1v99kQv5Rs9+V+B2b0p3fcNPIMY/TBWrwlTR+csoT0f25EjXeU8avjyHpIHwVgOrgoPkODMhSH4uUgIn1QaOS8tKgGIc2ghaq4SaOdaIEe3ppJ65YpJ3SN3mLfUWua35D54ulbVHhKmpaMz2rKrCd7sXJzZuoq+r0fc/tyRAit7mJemen9f4pVlFUZrMO4hKAj7D1lwAcee9bTV505513Hi+Th8LXqVy7BnzkI42hnkwa0ZhM5p+Njfm6jY3mj0+N8yhJKAylLdPvULiJCD24UsToIeef2H5s+R7vAQCP+czPDJ83tG5o2ghJ3++c83cQqFh6uvc/67GPTecFKBvSK5E2h0WFLGPLAO55//sBAI95xCNiuY/TJiRH35ubzSuMO4yqv3z5cnDbKorK+2ffj8LJdpVHAbhnlBzcd9/cCE+nJ3sracaTh2zIoPNGdL5MgkTp+Xb+iSHj7n0JCRNfx/OopaVyoGXKJ/s+ogn1aAr8lCCFBI1vi+3XdltoXWmGEquIeJ2Yfj03P7nr+LbQZIuJ/CXpa/hLi0iLPNfUhkgj6ocSsdBg7cKsqqj8FYCnAPhNAHDObQF4EoC3jJKD3d3mdcLAaSOqCYgGGcDUBI6hB5OOzT0hOUqee0hcnHh+cxjCkCoCVB0dzYVaK0ttP/4dyu9Q36HlkqLFhZKLZwlYuZ16++AY3lebPHb1zLRtOe1ZjymHAAAgAElEQVRxfWkhAFMKQVGDfc5+HTyiU7SxAS1YOVHx3tfOuVcB+FHn3BUAfwDgOwE8FMDrRsnEhQvAIx7ReChHR/M3tvHffD0ZBvkncy9GeiIhQwmcfOUr79qsHYN7BiHR0x62mEDK7V1rlqI8KrquLt21Q6IT8qyAtFjlMKaAtTl/222Tyfx+1O7XvhWLBXhfvRlC0LT7jY8RGoKQ0Az02u6VExUA8N7/mHNuF8Cz0Qx4fA+Ar/Def3CUDBwdATQKFpjfHHyEqnZDydonCQ4XJDo+iZJ2LD6SPyVGKUJClLNNEytajgmUloe+jORNqcvaOq2bdR8GFq1aqy13zVPbbXxZ88ba/rcrJmAT8g61EfVdRSs3/QCspKgAgPf+NQBes5CTb2w0A/R4jS72Cb16mBvg0HQJUoi0Y2sf7RhS3KRB5HkM3YA8z9pyTIi0a2fnrvb2moFg1F075E1xQaXrGeIh0bzLPnQVKG25cC1zSvH8S5cW733l0FW05PMEnBayXEErJU5UmeSVSPmMDsFkMsjMyCsrKguFd8NLxTg5KYHQPtKA5hI6Ht/GPSUuRKE3MMrrij2omhABugDN1lU3bqCqqqZ3XWrENfcEZPsRLXMB0kJ4HE2gSns/y+ZNpcpiSIMGjCNaJctaHrOrZya79x8cNNtu3gzvN5S3RT1YC2Ki0oWNjfzRr6kbPXc7b5vRlmXbjRSS3LymhCjn+HK/UHlwD66u543FV6+eFKeQ59PGK5LLoeNpHhh1D+dpeBtEyHiHBKqkoSt0vIl8nfAQYiUZS7yA4QWsx39Q85kkkok7CpoWVtzaspd0rSRjPjgaMSHiH7md78+/5bImaqnjc1i5HD9cNPeXPCefkUA7r9wnZvRSQpRLTOwI3jWce1V8P/KmlHJRG9G1ZU08ZTmkKO1NtRWgHDErkY+h6CBGJ175kEqv/dd9ME/FaA2vdbehlNeiEfC0amqnunAhLUZ0baG8V9XJ2hmfKkcTpFg4jH5rAtLXU0h5TnKbFCVt3EfK6Eixrqr5y7lkCEYeW64rsb0tbQQoR7hK0uG4xy+no0pV9o49vSrugRfERKULdT1/CLUBiutA12tpK0Is3fHEejQIMnbczGMGr0saFlnr5+flYiQFKTZ2hBt4zdMLeVhtCXlK0ohzERL3bCXTcA9Kuw94vmODT3OucWjRSm3XhLmvZzUGY3lfLTFR6cLHP376tauyNsmnb5HTuMiBiOtEDzGa8tla+wgHO2bWJ+YN8euiLuMpA07rZR7oN19Phlvr+cOvg7c/pQZBynQyrWLkq/vvb8599WrYSMp7HAgPqk0JHL/2kADJfIo2uF5CrFFStHiZyFdRyOX9/Wb58HAcb2pgTFRKwW/yo4yZ97n4yI8Uo5DhWie4oaJpanJo4w3l1JpLChFdl2ZkQ1PvSDEKHTNlXLVy0X5TchL03d2kAKGum3tcnjfH6ErvJzbLQ0qg+PFSHlJMrELrRmLjvvuahXvvna8MlYNWbjld+rWPTX2/RNx2WzP/F+9frj2sMTGgBzNXgDQR4h6QJkDrLEJEn9pcFyEKGfC2YtTmunIMgzSwWnlo3tQs/XR3t5m5motKSpC6egs8H9ybCnk1XIh4ufB1sgxCU7FIUdPKhXepLyVWbdGEvTRbW8BDH1rcTpiodGF/P9yoJg2I/MRqyyEx4MdLIR+wzc2wNySN0lmj63W3FSHNuKT25Yat7ZxfbWqrs/TVZNJMiS6nCkmJk3a/y/Vdfncl5P3leD0yTCVnx5BCJIWOr6drImT4kl3vlIScvMXU8IBSInNw0FRqC7+n3kSlC9vb81HfEn6T5YRxYuIT6uYbMg50PJ6vw8PwubVab8gDOoteUIghxCi2PfcYXb0iYD7wlNpWEiJ0ylPiFRVKQ0aXG99QbZ7f41rlK+UhlPAO+LXJ65S/c9Jo+1TV3C7Mfh+/Rvv22/PurZwKSc79sbNTXFAAE5VubG01HyD9QMcMBDC/yXIFiD58wko5Mj50HumVtH0ApbCQ2GjekExnlBWj0HrtXssxMDQWRlZg2lxXjghJMeK/ZScI2ldeh7wm+Vtr0G8jSG2vP1Ye2vWLdZMbN5rl69dPX3uueIUmfV0AJipduHVrPvKYBEG+mEt7QID82qVm8Nt4QfK4ckblkJHi55GfNg+bVpMNtQdRGj640ZhTQozkb/GZUo87PvC0zaeLIe4iRJoYxY4Tu/7cdV0FKrNMqtnrhE/MZiDLQCuTWBpexnI9LW9umqeyNFy7Fp+eXRpSTXQ0z0GjzUPNRUgeN3bzaMeS0/fLcRmc2APdoh1o48qV5vfHPqaLEJVb6HzGSVqUzXEIRk4oOcan63WlREhWZmIelXYv5QpPKk0sPTAfSU/PaMkyipXX5mbzf9uI+iXg/PmmVhEKNZEhjfXskiOjKYTExYc/CLndbLs81G0NMxcxLkLTadOGQ2JEZSOPHXqYqbz298PnDhmO2FigXAE3GrjhaUtbMQl5zkOKEV9OCVFIjHK7+mcIT9RLjB1HS6v9Dtmp/X19oHFPTFS6cP58U7uQDYuHhydr+LE/VAqPNKTazUuGkwtQ25tco+1D3UXkZLsP94ZmYx4qKgMKB+TWKGNoRiFHhMwL6kbXMssVEXkPtRGgrmLEr6uNEIXuPVFGx++yCU0oGbuWhGCdul6+jnesKIiJShdu3tR7VVE7Cu8jT0ZYhpQOD0/X+LWaSSx8JG9UzeuR27QBT23dX57f1INN+cw4x/SjH232efCDdQHi3hB/cGSZ8AeX2mlyHp6QQGsdEkKGxejGEGLEt4e69ud6Qn29o4gQVdRA/8ADw9xfISGywY8rQCrsRTX8ra1mnAsXHfqjee2dezya19NHeHg7j7Y99pDzbW17rUXEqK4qVLleUMgQyNc508hvKUJU7l1CGrwM5H5aZ4Su5zDSlBYjvi02zixHiPixIhy/+ZFG1vPrCnlEmneU6rQw0v1motKFc+fmoS5uIFON0rkiQL3HqGbChaeqTooON5paPnLPqYmKNl2M1k6RIvPBry9caAbgxd6qGeq5lkLbT+uMIN/CB5z0uEIPeuz6YvtoHRJitVujDKXESK4LeddthIgfs+t15dxrOzvtpkTKxESlC1U1H6cikcZd+45Bte3U+aXwSHiYLZQP/lDknDMUStM8HpmuDW0f+JxQhrzmnONJYyBDmFRmPBxH+/PraCMSKeGS7UExb8soT18x4suzz/Tee5vl228fV4wmE+ATPqH4vWKiUpqc8M0YwkNGh8JsGjzUJrsNSw+nhPCEemT1je0OIUK53lDMi+LlSst8Hzkup6sIhcIe2ligUHpjWCLlfNxQH3pffKyiFPKKQoIkjzudFvdWTFS6cHjYDIAMxTVT5AhPSnRSwpPTvkP5pw4GEmkcKdSmtfPwtDEiYbTJ9euoJ5OmwTIUkivRGL4oEYp5ULlhE3kNbUQoIiqTq1dRV1XTVT4VgjMhGpdSoTp5n21vW/hrabh1K260Q2LTxiBS2tCfrhn1NsLDt6eEh88QQOvruvmmc2kDJUOiGDhn9cADzcuirl2Lez2h76HCP12OFxLdXBGKpZVtQKlz8PwHRKW6eRNVVTVlz685JESpNiDrkLB4FlT2JipdiE0oCcyNrGastb7sbQUHyKu5xww7N/A5+8fyQcaF2plIdGhZ1sZDHg/tl+tldRGaUiG3FG09q5AH00aEQvuEBJ/tU9FrhGkeKi5CqbBZyJMJ9YoLHctEaC0wUekCTSgZClvEvARKoxHqItg15JMrPGN0LKDr4dOJUy16Vl5T6vVF36EwGy/DnPBeTGRSojOWkWt7npgXkxIhJX19223Nb2oslgN4gZM9DflxUwIjvceQoMj/IRWGG7piYHTCRKUrVLMOzTAci5PHjtlGcEo8VHQNMcYQHh7u29k5fV2a1xUTHSk+oWtPeTs8XUqkxqSUCJGg7+42ZUVThoT200RLm6gU0MOxuV5OSuRDHlBMqMwLGgUTlS7cvDl/R30snEW1LUlJwdEerlKCw88xQseCiq5Rm/uLGwXexsO9HSB87ti6nHfOpIQHyAu5LYqEQa3ppXNdZimWvdpiQhTrhKCtayNCOb3c6P5JpTER6oyJShceeGA+PxVw+obmy3LgIN+mjXXRugbGBEc+2JxQvoaoWbftWKAZ9xhcmHJCXpOJXr4hLyuWrxzhiXkwXExSorMshqywJ9Q6XKfd//we0P4rmfccAUqJUMwL0vYxTFQ6sb192sOIvW9eExvZe0Zu29o6fZOG2m9ighPKV8y7GeLh4A9hgOPZWun1qkN2LCBRp3xxjyckPDHRof8jJD4pb0eWeUp0Fun1aHS5b2KiEhOZ0PaQB0Tnkm1CMu+Uf01EQgNOU79T3tAaYqLShXPn5jcoML85+M2teRkx0Yl5OXK7NpI+FE4LeQBdBGdoQ0YPWurdL2N1LODCk5MPWh8zhEdH5YQn5PEsm9cTgu7xXHI8HPkMxtJKkeFhvJA4Ub552WriTxXGDJGpaCLJmzfj3tCKYKLShf390waWarq8cZcTCmvx5RAx0ZHhNeray4VOCtwqCg4//7J0LOBlPpmc9HaAeLtSSHS456vlMxVm04QnJjqrZLC4IS81kWnIwwm1+cj1/Dx8SiQt31KEZuU/uXatuZ5r19p7OrE0C8JEpQsbG6eNTupP5PNj8X3IgKUEJyQ6/KbSakoyvMZfcxw7VxfB0byqMQWHyBGelOikhCflffL/hTcM07Zc4dFER9ayJSlvR7lXqxs3mu17e/F2hlWibZ5Dno8s9xwRSoX12Pbj1wnTLMUxT0h++PPcVnTsfSpLxM7O/CVdbWr//JuoqtPTpNAyHU9OChmq4WqEjIt8wyRvx6Fad+j6QtcYE79Q+82i2gbovG07Fmg11dT+IaTwcC+XvJ5QGIejpYm1uSnGpqKQ3P5+2BjHPJ5V83o0SooQlbv2CgvxX9XUlkjfWjiVe685nlAomsAjG5ubzXxjhf8zE5WuhGrgIWMcMi6hUAt/UHd35+t4DZeHSmLhtVgoR4oNv+G46PAXVMnzp66Rp9eYHbfa32/mnzo6WryB4uUfIiU8sfKQ+8fywf8TzfDlnDeU19n9UVEX+Rs3Tl9/TEg0YmG2RVYkSlNIhKZ33NH8Hw960OnnuY33Q+eYTuczZ4cqPlXVVCLPnzdRWXrIrdRqwCFDrP3x/EaSDbu81rG1dfIhlcISmoVYGJXo9UjPQnutMeWDatcdBKc6OGjm/qKXFsXc/mWoEecKTyrUFiP1/1A+eDtbB+GpL1xo1tO39H609oKQcOR4oX1Ea1UJXFO9vd0syFmKYx6Q/OTMASc/GxvNPoVF3kRlTEp5N6Ft0gBz70ITFc0912pIud2lZWiNzi9fOKblQyNWk9fEbpkEhyBDHyMUviopPAmDP93aagR9ZyftaWmiU9cna8eU5z7Co+V7Xb0ejS7CGgqDap/t7XhPy46YqHSBHiBuzPoQ8m60mkmsgTYmAFoDHz2csRvx8PDkBJDS4NB3mzE6m5vz8zNPa7q93Ryb2qtShm1ZxuD0Jef+SXk7KeFJ/E/VwcH8XgiJc0j4NLSwDb9/+b4x0aGadG4I96x4PSGWQGxNVLqwt3fyJpdhIVruS+wGIaOaE0oD8r0bYeiPz6WJCgmOPD/PR47ozB78yfXrqDc2gIODk54Ov6aca+0iOMte46X8de1YEAs/Ao2XQpWlYCIRjpQ9CUkE2nhaobyS10P5Tnk7KVHljdkx78fojYlKF7QanGbEuNDwXhel8qC5rm1DaW28GxIc7fpDoTWKxcvtBPtdHRw0Neb7759fo+blyJCadu1nSXCA3h0L6qpClRNmSwmUbN/hFQPuFbcVHi3kJtsRUsJD922bjiuax2PiE8VEpQu7uydr6aGBapoxp4dNejalKNVRIJR/OodmeGO16FBojTcAU8Mh308aMeqlRPmQeSFDxvNCRqCP4Mgw2ioJDhERnvr8edRAM6FkKtQWI6d9J1d45HlTZa218xwcnFwXEhteLjn5D4nOWQu3KZiodIXaBQgejuIhIYkWYuBGSs4xVJKQERzKu+HeWSwcODv/Eb3T40EPmh+fh0Fk+0Gq5hzqQEB54eUrG5glsfIItd+skuAQbToWaEa8lPDwMuReKf1n2nlJkFLnDrVJ0XKqcwEdJxFSTIrOKt4fGZiolEILR3FjKLv1ynRkRA8O5uulcR5oBOwo3k0orEQPGH9zJI3L4ceMeTkyvEakjJd82HnnBa1NKURbwVn1+H2qfQdIezsp459qi5PGmodlubhoopHyekIhOu710Hlink9KdGbHODH3VyjktkKYqAwJN9Z8GnYpNKnwGfdsePiMC85QlPJuckJpNKcahSl4HoCwEZOiw70c2V2al7MUHfkeFy20xh/4lGFMXXcojLhiRkQl9Z9F2neyvIDc9h1NeKSHqp2b0mR42Md54W2IoTzI5bpu2rJkhVISa+dZsnvGRGURkPGQ4TMpNLnhM0BvpxnyRivl3TAvbUIPFY3qzq3l54gOnZ8Eh4sOF6RA3lRk+wqtk/nQ/oeYUZSdE9ZNcIDeHQuKCg8P0fI8xdp3SHhyJjflx6BKIgvhVjQ7MU2Ro3nLKc9NXkvIexrh/jFRWRZCRpqHzXitW7LI8Jkk5t0M1Q06dE6ZH/niLvnA89Ca1l1a5g9Iiw7/SIOhPegxMYt5N+siOESu8KRCbTHatO9owkOE2pf4/xIQoPrcuSbtxsY8P1obXyjc1uZa+L24taW/yK4nJirLjiY0WjuNZnxD4TMpNGM1GGrtTsDxAzjd3m5CAZub8VBabkeBnBp+ynBJ0SEPh8IcslsrJ6chV+ZbXkMJwRnr/10EXToWdG3ficGNvHyPimzf0URP83Al8l7UvLBQuE0eA2juoQGefxOVVaRv+EwzSlo7zVg1X9ZQXwMnG+rbhNJ4eu0cXQxujujw0BqJjewuHRJ9bVkiDYRs3+F5iYltqAzWnVR4FCgnPLkdC5jHMz13rjn+7m5ceHI8N34t0uvh90pVNdO0DPD/m6isC6HwmSY0sfAZR4rMIoxQLJQWEhyNXO9G1jJT8Jry5mYzd1Yon7Ith3eXjhktra2H92KS7TmaBxozepNJE9efTOadJc6K4BAp4RmwfWdC71OhthWtjYdEIRRm4/dPzv/G2nRKVx5NVNYdzTjwto3YmJplC59xSnUU4OklbUNpqXxq8WvpYfL2nNB/o3kowElPSdZu+f/Fu07Prr+i8/HBpaEyyKktrxvL2LFAfhM53taAUQgTlbOI1rYhjRstS0I1fk1oFtVwXMq7KR1K04iJI+WBh9b4t+Z5htoY6rrZb39/vg9rtK1u3GjmXdvfPzmnV6x8SojuOtGxY0FNDfS8/SW2f5uOBbLixyoS9uZHY1hywme0rN34oRr1kFPStKWUd1Oyo0AKHpah925o+ZYdCHh3ae61RK6/OjoCrl8/uQ/9d3z6GxKdmOjGeqmdZRTRr8+daxYuXmy+x+pYoIVrC2CiYsTpEz6j2jFHNjbn9HoZg5R3k+peTIzh3Wj5DrXncAGU3g7PK+VDC9FNp01XdQqN8esjoSGx4aG1VDnIMjnrgkPktu/0FZ79/dMzkhfARMVoTyx8JjsGSLiRE2Nqqlu3mtcJHx6ON6YmRah2P1RHgZJGlnsMofacmfAf/c3foJpOm9fL8u7SsjOAhNLRFCY8tMbfEMpnl97YsDE4fcgY+5IlOgO1h5qoGGUINUhrQhMIn1WHh817Pfb2Th5zWcJnnDE6Cgw97oSM0/Y2sLvbdOe+4475du6lae05R0dpwaEa8a1bJ8uBv4paejva8c7iGJw+5HY/HgATFWNYeHiG4OEzLjiS3PDZsoVOSnUUaOPdaONW+sKFU2vP4fmT7TmHh/FykILFBYdfE/dw+OuxZVmc1TE4S4iJijE+gZH1U5qugl4nrNXuI+GzU+00yyQ0wHjejRxXNJTo0v8YavClSgH3bvhySnjret5bjZcFr6iE2nMIWQYmOINjomIsD2QgqDcM0Cp8dlxLJqSBXdSYmhxKejfahKOLCB9VVXx+KR5G07wdiRQc6iItG6bpPuIejnyXDhBuv1nWe2RFMFExlptQ+EwKTW74DBh/Ruc+jNQN+nhE/cHBeGUSG58DnA6ncfGR/7cUHNqPRqsTfOyG9HR4pWOozhNngOKi4py7BOC9AL7be/8mse2LALwawOcA+GsAr/Te/4xI8xQArwDwGQDuAfC93vtfF2m+FcD3APgUAO8B8F3e+z8sfS3GklJqSppVC59JUt4NeXWxsgDmY1SOjk4a4UU3jlNFItaeo3Ug4FPLA3oPKPJyJKn2HD51igmOSlFRmQnKrwJ4hLLtTgBvBfBrAP4NgK8A8NPOuWskPs65LwHwJgA/DuB5AP4ZgF92zn2R9/5/ztI8HcDrAbwcwB8BeCaAtznnHu+9//OS12OsGJrBk+GzUOgoFD6TQrMKoZFV7gadC2/P0ZC91uQyiY4sA34fyClr+JQ30sOR3o5swzlDglNMVJxzX4zG2H9CIMkLAHwIwDd672sAb3XOPRTAS9AICdCIzdu998+c/X6rc+7TALwIwJOdcxWAlwF4g/f+ZbPzvh2AB/AcAM8qdT3GmtA3fLbsU9K0IRJKm9IMuTs7y90NOhc6Z6o9RxMd7tHIkFpdNx6u9pZGXgmRHQg00VmV+6YlJT2VXwHwdgBPB/AuZfuXAnjjTFD4Pt/snPskAFcAfAFOC8OvAniFc24DwKMAfBqAN9NG7/2Bc+4tAJ5Y6kKMNadv+EwzqLJ776r1MKL8ylDTOnk3nNyu0loHAq0Ni3vEobm5+DUzoamuXm2W9/YWOyN4IUqKyhd579/rnHuk3OCcuwDgkwB8QGz64Oz7MQA+OsuPlmYXwKfO0iGQ5tHOuQ3vfWK2NcMIoD3IbWd05sjwGS2vEmMO8lyWWnxOaI0EJubtaB4PXT9rz9m4cqVZ+PCH5+VNokO953iYbckFJykqzrktAI+OJPmI9/6K9/69kTS3zb7vF+vvZ9tvZaSJHWcC4AKAa5F8nOLuu+8+Xt6bjeTm64zxWJnyZ4ai4t+5u88MB30vQxikaNnz8pHLbQ4DHBvQelXGmIj51qqZZ1NNp6gODk54wNUs7a1Z54j333NP+LhsRul61mmg3tpqljc3m5mOl6TdL8dT+WQAsTvtOQD+feIY9MSE7qppwTSGMSys9k43Yg0cezMVa7PRpKKadXWugOPYfA0cG4R6FYxnDKV8AFZGmuBoh2Hp5XYuMvUyNYiL+dZO3B/Aid5n1eweOdzeRnV42AjE0VGznk8ayT9A01MPQEXTGdF5Z9dfb2w0x5qJTs3bdkYon6SoeO8/BKj/eRvIe7gk1tPvq7NPmzQfEWmOvPfX22bszjvvPF6mWhpfZ4zHWpZ/bvhMY8QZnRde9jJMlOoGHWJZOgq0gMr+MXfeeTK0Rt8HBye/U+1aEvlCr+3t5nPx4smBxi24fPlycNsogx+999edc/8PTUM7h357NCGsaSDNdTTjWnbZug+INBHf0TAWRO6MzpoBjU1JI9tpFl1D78tZ6Aadg9ZbkeA90KjzAAnN/v7JzgW8fOSLvag95777gEc+Mtx21JExR9S/A8BXO+dezBrTnwLgvd77ewHAOffO2bo3sP2+BsDveu+nzrn3A/irWZrfnO2zBeBJAN4yzmUYRk8KzOisdgpY1hmd+7AOs0GXgr/gSxMCunYSlv39efdnObv0gIwpKq9GM1jxF5xzPwngywB8M4BvYGleCeAtzrk3APhlAN8E4PMB/AMA8N7XzrlXAfhR59wVAH8A4DsBPBTA68a6EMMYhNCYmq4zOgOrNSVNW0KG/6x5NwSVBQnP7u58mzYz9M5OcS8FGFFUvPd/4pz7agDfj0Yw/hLAM/hULt7733DOPRXNgMinoQmLPYVPweK9/zHn3C6AZ6PpJPAeAF/hvf8gDGPdCMzorApNnylp1omxu0EvUS++ILwDwUCvESaKi0qsYd97/zYAb0vs/0YAb0ykeQ2A13TMomGsPqHBm23CZ8yzqW7caAzOrVtL0zV1EIb2blYllDYgNkuxYawLPaakOe6+KydZ1F4dsKy18T6MNBv0WRAbExXDWGcyp6SpEQgvhOY+00bAryttvJuQdwgEPZ9jL5FeP7DiZWqiYhhnEWG06gsXUE+nTeNuakyNEj5b2Rmd+1CoG/Sxl6hNUrlKHQVmmKgYhtGgjY+Q4TNalqzbjM59aBlKC3qJPL12jiUNp5moGIYRxmZ0LotyrfWFC6jrGjh/fi26QZuoGIbRHk0IzvqMzn1YxCBPeptlYUxUDMMoQ+6UNBY+a8dQ3aD394ELF4qXp4mKYRjDYVPSDEdf76btZJ2ZmKgYhjE+qSlpYuEzbUoabUbns+jVEDnezUDlY6JiGMZyMNSMzjKEdlaFBoh7N4UwUTEMY3kpFT6TY2q0mQKMIpioGIaxevSYkuZMzug8IiYqhmGsB6HQTukZnU1oopioGIax3uTM6GxT0hTDRMUwjLNH3/CZNqbmrMzonMBExTAMA+g/JY3N6AzARMUwDCOOJgRyuvs+4TMaM7ImmKgYhmG0JTT3WYcZnSd7e836GzfWYkoaExXDMIwSDDGj8wpOSWOiYhiGMSSJGZ3rjY34JJChKWmWdEZnExXDMIyxYVPS1OfONesuXiw3o/MCx9SYqBiGYSwDazKjs4mKYRjGMpOa0bntlDQUPtvaOilehTBRMQzDWDVKzeg8wGwAJiqGYRjrQNvwmb1PxTAMw2hNKHw2UCP+cnd4NgzDMMozYK8wExXDMAyjGCYqhmEYRjFMVAzDMIximKgYhmEYxTBRMQzDMIphomIYhmEUw0TFMAzDKEZVaxOTnREuX758di/eMAyjB3fddZc62OVMi4phGIZRFgt/GabgxWIAAATUSURBVIZhGMUwUTEMwzCKYaJiGIZhFMNExTAMwyiGiYphGIZRDBMVwzAMoxgmKoZhGEYxTFQMwzCMYpioGIZhGMU4k++od85tA3gJgKcCeCiAdwF4rvf+j2fbKwAvAvDts+1/AOCZ3vv3LSbH64lzbgfAewC8y3v/z2frrOwHxDn3EAAfUzb9ovf+6638h8U5948A/DsAjwNwL4D/AODl3vujdSn7s+qpvA7AswC8CsBTADwA4Hecc5822/4SAN8H4NUA/imA2wG8wzl3+wLyus78GwCfJdZZ2Q/L42ffXw7g89nnhbP1Vv4D4Zz7QgD/HcDdAJ4E4EcBPB9NeQNrUvZnzlOZ/UHfCuAF3vsfn637HwD+FsBTnXM/BOC5AF7qvf/h2fbfB/AXAL4FwGsXkvE1wzn3d9AI+8fYukuwsh+axwH4iPf+7XKDlf/gvArAb5JXDuC3Z57jE5xzr8WalP1Z9FRuAPj7AH6WrTsAUAPYAfB5AC4CeDNt9N5fAfB7AJ44XjbXF+fcJoCfAfCDAP6abbKyH57HAfjTwDYr/4Fwzj0MwBcCeANf771/gff+H2KNyv7MeSre+0MA7wYA59wEwCMBvBSNqLwRwJfOkv6Z2PWDAL5mlEyuP88HsA3glQC+lq1/zOzbyn44HgfgpnPunQA+F42n+ENoQi5W/sPxOQAqADecc78G4MsAXAPwYwBejjUq+7PoqXBejOZPfCqA7/feewC3Abjlvd8Xae+fbTN64Jy7E8D3AviXShlb2Q+Ic24DwGMBOAA/gaYG/J/RhGVeDCv/IXnY7PvnALwPwFeiEZTvA/A8rFHZnzlPRfDLAH4XwBMAvGTWK2wPjdeiMR0pX2vJzDP8KQA/7b3/QyVJBSv7ofkqAH/pvf/A7PfvOucuovEe/y2s/Idia/b9Nu/982bLv+OceygaYXkV1qTsz7Sn4r3/U+/973nvXwrgh9HUGG4A2HHObYnklwBcHTmL68YzATwCwIudc5uzthUAqGbLV2FlPxje+yPv/W8zQSHeCuA87N4fkuuz77eK9W9H05ZyH9ak7M+cqDjnPtE594xZTxfOu9E01F9BU2P+dLH9UQD8CFlcZ74WwKegKeOD2efxAJ7GflvZD4Rz7pOcc982azTm7M6+7d4fDhLybbGeRGRt7v0zJyoA7kDT8+jrxfovRzMY6VcA3EQzfgUA4Jx7EIAvBvCOkfK4rnw7gL8rPvcA+PXZ8n+Blf2Q7KBpS/lmsf7r0PwPvwQr/6H4P2h6On6DWP8kAB/GGt37Z/Id9c65NwH4EjQDvj4I4B8D+A4A/8J7/7POuR8A8Gw0Dcr3zL4/GcBne+9XyhVddpxz7wHwHjai3sp+QJxz/wnAk9GU691ojNy3AHiK9/7NVv7D4Zx7GoD/COD1AN6Epqfp8wH8K+/9T6xL2Z/VhvqnoRnN/UIAD0dTi/gG7/2bZttfhKZx7Llo4p3vBPD0VfpjVxgr+2H5FjQ9vf41mnv/bgBf572n8RFW/gPhvf8559wBmjJ+BoC/AvAd3nsau7IWZX8mPRXDMAxjGM5im4phGIYxECYqhmEYRjFMVAzDMIximKgYhmEYxTBRMQzDMIphomIYhmEUw0TFMAzDKIaJimEYhlEMExXDMAyjGP8fq15S1DOOwB4AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plotSampleLines(priorMean,priorCovariance,50)"
]
},
{
"cell_type": "code",
"execution_count": 167,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"likelihoodPrecision = 1./(sig*sig)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Posterior\n",
"We can now continue with the standard Bayesian formalism \n",
"\n",
"$$\n",
"\\begin{eqnarray}\n",
" p(\\bf w| \\bf y,X) &\\propto& p(\\bf y | X, \\bf w) \\, p(\\bf w) \\nonumber \\\\\n",
" &\\propto& \\exp{ \\left(- \\frac{1}{2 \\sigma_n^2}(\\bf y-X^T \\bf w)^T(\\bf y - X^T \\bf w) \\right)}\n",
" \\exp{\\left( -\\frac{1}{2} \\bf w^T \\Sigma^{-1} \\bf w \\right)} \\nonumber \\\\ \n",
"\\end{eqnarray}\n",
"$$\n",
" \n",
"In the next step we `complete the square' and obtain \n",
"\n",
"\\begin{equation}\n",
"p(\\bf w| \\bf y,X) \\propto \\exp \\left( -\\frac{1}{2} (\\bf w - \\bar{\\bf w})^T (\\frac{1}{\\sigma_n^2} X X^T + \\Sigma^{-1})(\\bf w - \\bar{\\bf w} ) \\right)\n",
"\\end{equation}\n",
"\n",
"This is a Gaussian with inverse-covariance\n",
"\n",
"$$A= \\sigma_n^{-2}XX^T +\\Sigma^{-1}$$\n",
"\n",
"where the new mean is\n",
"\n",
"$$\\bar{\\bf w} = A^{-1}\\Sigma^{-1}{\\bf w_0} + \\sigma_n^{-2}( A^{-1} X^T \\bf y )$$\n",
"\n",
"\n",
"\n",
"To make predictions for a test case we average over all possible parameter predictive distribution\n",
"values, weighted by their posterior probability. This is in contrast to non Bayesian schemes, where a single parameter is typically chosen by some criterion. "
]
},
{
"cell_type": "code",
"execution_count": 168,
"metadata": {},
"outputs": [],
"source": [
"# Given the mean = priorMu and covarianceMatrix = priorSigma of a prior\n",
"# Gaussian distribution over regression parameters; observed data, x\n",
"# and y; and the likelihood precision, generate the posterior\n",
"# distribution, postW via Bayesian updating and return the updated values\n",
"# for mu and sigma. xtrain is a design matrix whose first column is the all\n",
"# ones vector.\n",
"def update(x,y,likelihoodPrecision,priorMu,priorCovariance): \n",
" postCovInv = np.linalg.inv(priorCovariance) + likelihoodPrecision*np.dot(x.T,x)\n",
" postCovariance = np.linalg.inv(postCovInv)\n",
" postMu = np.dot(np.dot(postCovariance,np.linalg.inv(priorCovariance)),priorMu) + likelihoodPrecision*np.dot(postCovariance,np.dot(x.T,y))\n",
" postW = lambda w: multivariate_normal.pdf(w,postMu,postCovariance)\n",
" return postW, postMu, postCovariance"
]
},
{
"cell_type": "code",
"execution_count": 169,
"metadata": {},
"outputs": [],
"source": [
"design = np.concatenate([np.ones(n).reshape(-1,1), df2.weight.values.reshape(-1,1)], axis=1)\n",
"response = df2.height.values"
]
},
{
"cell_type": "code",
"execution_count": 171,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# For each iteration plot the\n",
"# posterior over the first i data points and sample lines whose\n",
"# parameters are drawn from the corresponding posterior. \n",
"fig, axes=plt.subplots(figsize=(12,6), nrows=1, ncols=2);\n",
"mu = priorMean\n",
"cov = priorCovariance\n",
"postW,mu,cov = update(design,response,likelihoodPrecision,mu,cov)\n",
"cplot(postW, axes[0], lims=[107, 122, 0.1, 0.7, 1.1, 0.01])\n",
"plotSampleLines(mu, cov,50, (df2.weight.values,df2.height.values), axes[1])\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets get the posteriors \"at each point\""
]
},
{
"cell_type": "code",
"execution_count": 245,
"metadata": {},
"outputs": [],
"source": [
"weightgrid = np.arange(-20, 100)\n",
"test_design = np.concatenate([np.ones(len(weightgrid)).reshape(-1,1), weightgrid.reshape(-1,1)], axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 255,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(1000,)"
]
},
"execution_count": 255,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"w = np.random.multivariate_normal(mu,cov, 1000) #1000 samples\n",
"w[:,0].shape"
]
},
{
"cell_type": "code",
"execution_count": 264,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 264,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sns.distplot(w[:,0] + w[:,1] * 55) # the weight=55 posterior"
]
},
{
"cell_type": "code",
"execution_count": 257,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(120,)"
]
},
"execution_count": 257,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mu_pred = np.zeros((len(weightgrid), 1000))\n",
"for i, weight in enumerate(weightgrid):\n",
" mu_pred[i, :] = w[:,0] + w[:,1] * weight\n",
"\n",
"post_means = np.mean(mu_pred, axis=1)\n",
"post_stds = np.std(mu_pred, axis=1)"
]
},
{
"cell_type": "code",
"execution_count": 258,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with sns.plotting_context('poster'):\n",
" plt.scatter(df2.weight, df2.height, c='b', alpha=0.9, s=10)\n",
" plt.plot(weightgrid, post_means, 'r')\n",
" #plt.fill_between(weightgrid, mu_hpd[:,0], mu_hpd[:,1], color='r', alpha=0.5)\n",
" plt.fill_between(weightgrid, post_means - 1.96*post_stds, ppmeans + 1.96*post_stds, color='red', alpha=0.4)\n",
"\n",
"\n",
" plt.xlabel('weight')\n",
" plt.ylabel('height')\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Oops, what happened here? Our correlations in parameters are huge! But the regression lines do make some sense. Lets look at the posterior predictive.\n",
"\n",
"### Posterior Predictive Distribution\n",
"\n",
"Thus the predictive distribution at some $x^{*}$ is given by averaging the output of all possible linear models w.r.t. the posterior\n",
"\n",
"$$\n",
"\\begin{eqnarray} \n",
"p(y^{*} | x^{*}, {\\bf x,y}) &=& \\int p({\\bf y}^{*}| {\\bf x}^{*}, {\\bf w} ) p(\\bf w| X, y)dw \\nonumber \\\\\n",
" &=& {\\cal N} \\left(y \\vert \\bar{\\bf w}^{T}x^{*}, \\sigma_n^2 + x^{*^T}A^{-1}x^{*} \\right),\n",
"\\end{eqnarray}\n",
"$$\n",
"\n",
"\n",
"which is again Gaussian, with a mean given by the posterior mean multiplied by the test input\n",
"and the variance is a quadratic\n",
"form of the test input with the posterior covariance matrix, showing that the\n",
"predictive uncertainties grow with the magnitude of the test input, as one would\n",
"expect for a linear model. "
]
},
{
"cell_type": "code",
"execution_count": 259,
"metadata": {},
"outputs": [],
"source": [
"ppmeans = np.empty(len(weightgrid))\n",
"ppsigs = np.empty(len(weightgrid))\n",
"t2 = np.empty(len(weightgrid))\n",
"\n",
"\n",
"\n",
"for i, tp in enumerate(test_design):\n",
" ppmeans[i] = mu @ tp\n",
" ppsigs[i] = np.sqrt(sig*sig + tp@cov@tp)\n",
" t2[i] = np.sqrt(tp@cov@tp)"
]
},
{
"cell_type": "code",
"execution_count": 268,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"55"
]
},
"execution_count": 268,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"weightgrid[75]"
]
},
{
"cell_type": "code",
"execution_count": 270,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(array([ 6., 18., 62., 125., 263., 239., 176., 92., 16., 3.]),\n",
" array([ 136.32163732, 141.63972751, 146.9578177 , 152.27590789,\n",
" 157.59399808, 162.91208827, 168.23017846, 173.54826866,\n",
" 178.86635885, 184.18444904, 189.50253923]),\n",
" )"
]
},
"execution_count": 270,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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xu9zVXsdm/3e98D85XhMRYydHBkcDv8rMX5Q//2NEzKKYMP46MNxiux0d7IMkqYKOJIPM3A7c3aTqTuCTFCOGGRExPTO31tXPBiqtJFq4cGGVzTqulpmnSn+a6cRZw7VPknPmzh33vqaqqjFOXz9Y6fm68bvc1V7HZv93vfA/OV5VY+zv729Z16nDRPtSjAx+kJn148+Z5eNmoA/YH3isrn4ekJ3ogySpuk6tJpoB/AXwkYbyD1K8+d8CvAAcX6uIiL2BdwOrO9QHqaesWrNx55fUbZ06TPTLiPhfwIqI2AEMAB+mSAbHZ+bzEXFlXf1jwBeA54DrOtEHSVJ1nZxA/hjwJeBPgTdRJIQPZmbt3ILzKSaLl1Gcc3A/8FHPPpak7utYMsjMIYo3/PNb1G+juBzFuZ16TklSZ3jVUkmSyUCSZDKQJGEykCRhMpAkYTKQJGEykCRhMpAkYTKQJGEykCRhMpAkYTKQJGEykCRhMpAkYTKQJGEykCRhMpAkYTKQJNHZeyBrFCsfub3bXZCkphwZSJIcGUjqXc1G289s2gTA2u3rJ+x5Tzjo6Anbd7eYDKQKVq3Z2O0uSB1lMpCmgPrkcuRhb+1aP/Ta5ZyBJMlkIEnyMJHUNucJtCtzZCBJmvyRQUR8HPgc8BbgZ8DZmfnTye6HJOllk5oMIuKjwDXA14AHgDOBVRFxSGb+cjL60OmzgCdjTbMkTbRJSwYR0Qd8FfhOZn61LPsRkMBngLMmqy/SVOYyU3XDZI4Mfg/4T8BttYLM3BoRfw8smcR+SNK4dPM6YxN19vNkTiAvKB9/0VC+ATggIqZNYl8kSXUmc2SwZ/m4paF8C0VS2gN4rt2dDQwMVOpE7Rh/p2zdtm1C9jvVvBbiHC3GWv1k8u917Hb1GAcGBhgaGtr5fadMZjLoKx+HW9TvGMvOfvvb31bqxKF7Lqq0nXTo27vdA+mV731V3webmcxk8Gz5OBv4l7ry2cD2zHy+3R0tXry4b/RWkqR2TeacwbrycV5D+TzgsUnshySpwWQng18Dx9cKImI68H5g9ST2Q5LUoG94uNUh/M6LiP8OXAVcCNwHfBr4L8DvZ+aGSeuIJOkVJjUZAETEOcBSYA7F5SjO8XIUktRdk54MJElTj1ctlSSZDCRJJgNJEiYDSRLe9rItEXEs8P3MnN2ifg7wT8DVmbm8rnwGcBFwEsW1l1YBZ2XmkxPe6TFqFmNELAYebNL80sxcVrbp6RjL8hOBLwDzKc6FuSIzr6yr79kYI+I04K9atc/MvrJdz8QILf9eZwLLgROB3wH6KVYr/r+6Nj0TZ4sY3whcRnF+Vh9wF7AsMzfWtakUoyODUUTEO4Hv8fK1lZq5ApjbpPwa4FTgXOB04BDgjql2hdYRYjwEGATe0fB1RV2bno4xIv4Y+J/APwBHASuBK8obMdX0cox/z6tfv2OBF4Hr6tr1RIww4t/r5cD/AP4MOAHYDtwdEW+pa9MTcTaLMSJ2pzhB90jg8xRJ7/XAfRHxhrrNK8XoyKCFMrsuBVZQvCHu3qLdMcB7gRcayg+geEFOzsybyrKHKG7mcxxwy4R1vk1txLgIeCQz17TYvqdjLG+49A2KEd3nyuK7I+KtwBHADb0eY2ZuAjY1tL8V2Eh5Q6leiBFGfS13Az4CXJaZ3y7L7qeI/UTgkl6Ic5T/yWOAg4AlmbmqbP+/Kfr/eeBz44nRkUFr7wPOAz4LXNmsQUTsBfw5cA7FJ616h5ePO++CkZnrgEeZOjfzGS3GRcDDI2zf6zEuBvYDvlNfmJmnZOZHyh97PcZXiIgjKd4UlmbmUFncCzHCyHHuRvHGWX8Z/EGK/8v/WP7cC3GOFOMCitHOzsv3ZOaLFLcQrvW/cowmg9YeAPbPzCtofdntS4B/yswbmtQtAJ7OzMGG8g28fKOfbhstxoOB/SLiZxHxUkT8ouHwSa/HWLue+esi4p4yxl9HxKfq2vR6jI0uAn5Y+2RZ6oUYYYQ4M3Mb8BfAmRHx9ojYG7gYmAn8bdmsF+Ic6bX8NTAN2LehfH/greX3lWP0MFELmfnESPURcTjFBM3BLZrsyatv5ENZtt/4etcZI8UYEftSXDJkPsUnlc0U8V4fEcOZeSM9HiPFPM92iluxXk1xj+7jgasj4jflMLvXY9wpIv4I+H3gPQ1VUz5GaCvOrwKHAf+n/HkHcFpm9pc/T/k4R4nxTuDfgO9GxCeBfwXOpDh0NL1sUzlGk0EFEfF64FrgK5n5yxbN+ujQjXy6ZDPFRNXazHyqLLurTBJfAW6k92OcTvFJ6zuZeUFZdndEzKOI8SZ6P8Z6Z1DMATVeJbjnYyz/J+8HZlAcM38C+CDwlxHxXGb+HT0eZ2Y+ExHHA9+lWL0IxeGga4HTyp8rx2gyqObrFDfruSoi6n+Hu0XE68oh67MUN+5pNJuXb/QzZZXHk3/YpOpOYElEzKLHYwRqN1S6s6H8R8Cl5eqNXo8ReMXl4r/RpHpXiPEDFKPYP8zMB8qyu8tVNlcCf8cuEGdm/qT8sLI/8GJmPhERfwX8pmxSOUbnDKr5b8B/plhBtLX82gv4Uvk9FPdv2Kdc+1xvHsXM/pQWEQsi4lPl6oZ6M4Ehism5no4R+EX52LiKajrFJ6wd9H6MNe+gOITQbDXJrhDjfhSH/BrPi/kJxbzXLHo8zoiYU543skdmbqg7pLSI4grQMI4YTQbVHAO8veHreYrhWu1OuaspDkEcU9soIuYDB9IbN/N5M8Vx9KNqBeVSzA8A92bmML0f448pEvqHG8rfDzxQjvB6PcaaP6RYadPsDuq7QoyPUcRwaEP5oRTLSwfp/Th3pziB8L21goh4B/AHvLx6qHKMHiaqIDPXNpZFxHbgycx8sGyzPiJuBq4tl6Bupripz8PArZPZ34p+TPGp6ppyZcZTFMecFwHvgt6PMTOfi4gLgOUR8RxwD/DHwLspEkLPx1jnIOCxMom/wi4S420Un45XRsQXgScp3hA/ApxZxt3TcWbmkxFxG8UhzGGK5PBN4CHghrJN5RgdGUys0ykmIS+mONvzIeCozNze1V61oezjccAPgK9RHF54I3BE3eoM6OEYATJzBfAZihOTbqf4JPnBzPyHumY9HWPpjcC/j1Df0zFm5laKVVI/Ai6leON7J/DhzLyqrmlPx0nR/3sp+n4VxXzXEZn5UkObMcfozW0kSY4MJEkmA0kSJgNJEiYDSRImA0kSJgNJEiYDSRImA0kSJgNJEvD/ARfthEMoJEOUAAAAAElFTkSuQmCC\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.hist(w[:,0] + w[:,1] * 55, alpha=0.8)\n",
"plt.hist(norm.rvs(ppmeans[75], ppsigs[75], 1000), alpha=0.5)"
]
},
{
"cell_type": "code",
"execution_count": 249,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"with sns.plotting_context('poster'):\n",
" plt.scatter(df2.weight, df2.height, c='b', alpha=0.9, s=10)\n",
" plt.plot(weightgrid, ppmeans, 'r')\n",
" #plt.fill_between(weightgrid, mu_hpd[:,0], mu_hpd[:,1], color='r', alpha=0.5)\n",
" plt.fill_between(weightgrid, ppmeans - 1.96*ppsigs, ppmeans + 1.96*ppsigs, color='green', alpha=0.4)\n",
"\n",
"\n",
" plt.xlabel('weight')\n",
" plt.ylabel('height')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"However, by including the $\\mu$ as a deterministic in our traces we only get to see the traces at existing data points. If we want the traces on a grid of weights, we'll have to explivitly plug in the intercept and slope traces in the regression formula"
]
}
],
"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": "3.6.1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}