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@mamacneil
Last active November 24, 2017 17:45
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Code to support Thinking Bayesian lecture
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
},
"source": [
"# Intro to Bayes - lecture notes\n",
"\n",
"Aaron MacNeil \n",
"Dalhousie University \n",
"a.macneil@dal.ca"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/Users/aaronmacneil/anaconda/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
" from pandas.core import datetools\n"
]
}
],
"source": [
"# Import packages\n",
"%matplotlib inline\n",
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"from mpl_toolkits.basemap import Basemap as bm\n",
"from scipy.stats import gaussian_kde\n",
"import scipy as sp\n",
"import pymc3 as pm\n",
"import matplotlib.image as mpimg\n",
"import matplotlib as mp\n",
"import matplotlib.image as image\n",
"from collections import Counter\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"import statsmodels.api as sm\n",
"import sqlite3\n",
"import os\n",
"\n",
"\n",
"# Return list of unique items and an index of their position in L\n",
"def indexall(L):\n",
" poo = []\n",
" for p in L:\n",
" if not p in poo:\n",
" poo.append(p)\n",
" Ix = np.array([poo.index(p) for p in L])\n",
" return poo,Ix\n",
"\n",
"# Return list of unique items and an index of their position in long, relative to short\n",
"def subindexall(short,long):\n",
" poo = []\n",
" out = []\n",
" for s,l in zip(short,long):\n",
" if not l in poo:\n",
" poo.append(l)\n",
" out.append(s)\n",
" return indexall(out)\n",
"\n",
"# Function to standardize covariates\n",
"def stdize(x):\n",
" return (x-np.mean(x))/(2*np.std(x))\n",
"\n",
"# Find most common element in a list\n",
"def most_common(lst):\n",
" return max(set(lst), key=lst.count)"
]
},
{
"cell_type": "markdown",
"metadata": {
},
"source": [
"## Coin flip example"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [
],
"source": [
"# Prior shape\n",
"a = 3.4\n",
"# Prior scale\n",
"b = 7.4\n",
"# Probability range\n",
"p = np.linspace(0,1,500)\n",
"# Successes\n",
"s = 10\n",
"# Failures\n",
"f = 15"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [
],
"source": [
"# Prior\n",
"prior = sp.stats.beta.pdf(p, a, b)\n",
"like = sp.stats.beta.pdf(p,s+1,f+1)\n",
"posterior = sp.stats.beta.pdf(p,a+s,b+f)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
},
"outputs": [
{
"data": {
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RwxUalbyICApuxWHSsVONky2AWc/eNOnWHaM2bbUQnSA0HD4+7XFwcOTECd315Cvj5Mnj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hAAAI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\nEDho0sdMmqRT3gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10e31fb70>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"plt.plot(p,prior, label=\"Where I think it is (Prior)\")\n",
"plt.plot(p,like,\":\", label=\"New information (Likelihood)\")\n",
"plt.plot(p,posterior,\"--\", label=\"Where I think it is (Posterior)\")\n",
"plt.xticks(fontsize=15)\n",
"plt.yticks(fontsize=15)\n",
"plt.legend(fontsize=14)\n",
"plt.savefig('betaprior.jpg', dpi=300);"
]
},
{
"cell_type": "markdown",
"metadata": {
},
"source": [
"## Frequentist coin-flipping"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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lypTMmjUrCxcubGmeV+vUOZzU1alSnnb3qqZOjSZPO3tVe6cSvRpNFteqejo1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\nBAAAUPD/AD/QyiILgUw4AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11721edd8>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig=plt.figure(figsize=(12, 7))\n",
"pflips = []\n",
"nflips = 3\n",
"for i in range(15):\n",
" newflips = sum(sp.stats.bernoulli.rvs(.5, size=nflips))/nflips\n",
" pflips += [newflips]\n",
" ax=fig.add_subplot(4,4,i+1)\n",
" ax.hist(newflips)\n",
" ax.set_xlim(0,1)\n",
" ax.set_yticklabels(\"\")\n",
" \n",
"ax=fig.add_subplot(4,4,16) \n",
"ax.hist(pflips)\n",
"ax.set_title('P(Heads)='+str((sum(pflips)/len(pflips)))[:4])\n",
"plt.tight_layout()\n",
"plt.savefig('freqflip.jpg', dpi=300);"
]
},
{
"cell_type": "markdown",
"metadata": {
},
"source": [
"## Bayesian coin flipping"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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6XJ+dmGaiKArfeKIIgHeP1MnDiSLg2B1ODle0EWo28NASbSYojAYdO9ZkY7E5+Oy83J0S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\nQulq+zi0GhF7gnjOzUZMMVrsLk7B0MQ8BifmQv7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SOPvK05GTGosLTaMYmpxXOg7RbU7V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\nB2xMERERERER+eD/A3+8zCrmCsDbAAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119338828>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig=plt.figure(figsize=(12, 7))\n",
"# Prior shape\n",
"a = 7\n",
"# Prior scale\n",
"b = 7\n",
"prior = sp.stats.beta.pdf(p, a, b)\n",
"for i in range(15):\n",
" ax=fig.add_subplot(4,4,i+1)\n",
" newflips = pflips[i-1]\n",
" ax.plot(p,prior/max(prior)*2)\n",
" a += nflips*newflips\n",
" b += nflips-nflips*newflips\n",
" prior = sp.stats.beta.pdf(p, a, b)\n",
" ax.hist(newflips)\n",
" ax.set_xlim(-0.05,1.05)\n",
" ax.set_yticklabels(\"\")\n",
" \n",
"ax=fig.add_subplot(4,4,16)\n",
"ax.plot(p,prior/max(prior)*2*Counter(pflips)[most_common(pflips)])\n",
"ax.hist(pflips)\n",
"ax.set_title('P(Heads)='+str(p[list(prior).index(max(prior))])[:4])\n",
"plt.tight_layout()\n",
"plt.savefig('bayesflip.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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PvY1z01nUajJEi8+qol2erf0zKnJt2Q9LNgmy3C6GVjnY4nkr/h7F6hrHtQrb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\nOceeeOkYfvo074kDgL4OBy49tw+bP7AW4Qbtrrfn7QB++6fjODQYQZ5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C2/WRD66d8TUR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\nADDAMgUAAAAABn4DDsRldNx8+V0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11995d5c0>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig=plt.figure(figsize=(12, 7))\n",
"# Prior shape\n",
"a = 100\n",
"# Prior scale\n",
"b = 100\n",
"prior = sp.stats.beta.pdf(p, a, b)\n",
"for i in range(15):\n",
" ax=fig.add_subplot(4,4,i+1)\n",
" newflips = pflips[i-1]\n",
" ax.plot(p,prior/max(prior)*2)\n",
" a += nflips*newflips\n",
" b += nflips-nflips*newflips\n",
" prior = sp.stats.beta.pdf(p, a, b)\n",
" ax.hist(newflips)\n",
" ax.set_xlim(-0.05,1.05)\n",
" ax.set_yticklabels(\"\")\n",
" \n",
"ax=fig.add_subplot(4,4,16)\n",
"ax.plot(p,prior/max(prior)*2*Counter(pflips)[most_common(pflips)])\n",
"ax.hist(pflips)\n",
"ax.set_title('P(Heads)='+str(p[list(prior).index(max(prior))])[:4])\n",
"plt.tight_layout()\n",
"plt.savefig('bayesflip2.jpg', dpi=300);"
]
},
{
"cell_type": "markdown",
"metadata": {
},
"source": [
"## PyMC3 Regression example"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [
],
"source": [
"# Number of observations\n",
"nobs = 35 \n",
"\n",
"# Intercept\n",
"β0 = -3.5\n",
"# Slope\n",
"β1 = 2.8\n",
"# Standard deviation\n",
"σ = .5\n",
"\n",
"# Covariate\n",
"x = np.random.RandomState(42).uniform(0,1,size=nobs)\n",
"\n",
"# Observations\n",
"y = β0 + β1*x + np.random.RandomState(42).normal(0,σ,size=nobs)\n",
"\n",
"# Export data\n",
"pd.DataFrame({'x':x,'y':y}).to_csv('linear.csv')"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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7JoXHUwFhHAAAAJbkdDi0pNSnsnmF6ug2lJPlSZkr4oMI4wAAALA0j8up/NxMs8uIC9aM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\nrkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119485208>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"plt.scatter(x,y)\n",
"plt.xlabel('X',fontsize=17)\n",
"plt.ylabel('Y',fontsize=17)\n",
"plt.xticks(fontsize=15)\n",
"plt.yticks(fontsize=15)\n",
"plt.savefig('regdata.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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Lz+OaMwvr1s8ACAy7OLpT5gUXHvROmfEiLcVBZk8H1e0E8oxUJ2kpjnaelZgS62vSj5hM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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1196cef98>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"plt.scatter(x,y)\n",
"plt.xlabel('X',fontsize=17)\n",
"plt.ylabel('Y',fontsize=17)\n",
"xnew = np.linspace(0,1,100)\n",
"lcol = 'red'\n",
"plt.plot(xnew,β0 + β1*xnew, c=lcol)\n",
"plt.xticks(fontsize=15)\n",
"plt.yticks(fontsize=15)\n",
"plt.savefig('regline.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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NM3zUGsWUCQ1FA2/OZW22+96XkqZx6LqeU/vuBqQis2/3Un/u0lXu/+fWq9KE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\nIiLXYlglIiIiItdiWCUiIiIi1/p/uP/GBfNRz08AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11d755390>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol)\n",
"ax.view_init(70, 90)\n",
"plt.savefig('3drot0.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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NxLBRZitBPCxIrBLEA6E6TZVFMemMjiadp4oBuiKmndttgLu75ejbqyLirrIsw+3tctIj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+3XXdVTsnw6luFpvM9Iw1+VJEj09nAI81Rbv3eNhYfzfqLDu9/2xR77KxY26KYGWENQrDrM1q1b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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ba230b8>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol)\n",
"ax.view_init(70, 38.9)\n",
"plt.savefig('3drot1.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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X1biAamIjuhSlwmK1QqRnqYYwHL7hjI7OzHu2+yLURVApiox3dFu51/MHTgvz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D79AEyffkBrF+cA1gJRIBBAPp+HKLLwmF122RUA8MADK5FOp3HggQe5tVSiSkisOsD99z+s/f/8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\nsUoQBEEQBEF4lv8PJ8y5b5Mef2sAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11ba23e48>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol)\n",
"ax.view_init(30, 38.9)\n",
"plt.savefig('3drot2.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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oGiCE1ha2QaELoKuYjdtGZgch5ndJtx9kNSTI2q55g2JVMhTSqgqiTo8z79eB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\nWv8PeMpit2QqzrUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1192db3c8>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol)\n",
"ax.view_init(10, 38.9)\n",
"plt.savefig('3drot3.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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43WXK2QNxve/wvbTmhS1a//awXNfVnP6YjnjHbO05qxYyDz1gll7fnNZjz27U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\nqqwSVjEl8vm8Xnjhd4rHa1XnSgU6Eok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"text/plain": [
"<matplotlib.figure.Figure at 0x11b9796d8>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y, s=50)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol, linewidth=8)\n",
"ax.view_init(0.2, 38.9)\n",
"plt.savefig('3drot4.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
},
"outputs": [
{
"data": {
"text/html": [
"<table class=\"simpletable\">\n",
"<caption>OLS Regression Results</caption>\n",
"<tr>\n",
" <th>Dep. Variable:</th> <td>y</td> <th> R-squared: </th> <td> 0.806</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Model:</th> <td>OLS</td> <th> Adj. R-squared: </th> <td> 0.801</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Method:</th> <td>Least Squares</td> <th> F-statistic: </th> <td> 137.5</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Date:</th> <td>Fri, 24 Nov 2017</td> <th> Prob (F-statistic):</th> <td>2.61e-13</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Time:</th> <td>13:41:54</td> <th> Log-Likelihood: </th> <td> -21.760</td>\n",
"</tr>\n",
"<tr>\n",
" <th>No. Observations:</th> <td> 35</td> <th> AIC: </th> <td> 47.52</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Residuals:</th> <td> 33</td> <th> BIC: </th> <td> 50.63</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Df Model:</th> <td> 1</td> <th> </th> <td> </td> \n",
"</tr>\n",
"<tr>\n",
" <th>Covariance Type:</th> <td>nonrobust</td> <th> </th> <td> </td> \n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <td></td> <th>coef</th> <th>std err</th> <th>t</th> <th>P>|t|</th> <th>[0.025</th> <th>0.975]</th> \n",
"</tr>\n",
"<tr>\n",
" <th>const</th> <td> -3.7023</td> <td> 0.144</td> <td> -25.796</td> <td> 0.000</td> <td> -3.994</td> <td> -3.410</td>\n",
"</tr>\n",
"<tr>\n",
" <th>x1</th> <td> 3.0990</td> <td> 0.264</td> <td> 11.724</td> <td> 0.000</td> <td> 2.561</td> <td> 3.637</td>\n",
"</tr>\n",
"</table>\n",
"<table class=\"simpletable\">\n",
"<tr>\n",
" <th>Omnibus:</th> <td> 1.532</td> <th> Durbin-Watson: </th> <td> 1.931</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Prob(Omnibus):</th> <td> 0.465</td> <th> Jarque-Bera (JB): </th> <td> 1.106</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Skew:</th> <td> 0.434</td> <th> Prob(JB): </th> <td> 0.575</td>\n",
"</tr>\n",
"<tr>\n",
" <th>Kurtosis:</th> <td> 2.931</td> <th> Cond. No. </th> <td> 4.12</td>\n",
"</tr>\n",
"</table>"
],
"text/plain": [
"<class 'statsmodels.iolib.summary.Summary'>\n",
"\"\"\"\n",
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: y R-squared: 0.806\n",
"Model: OLS Adj. R-squared: 0.801\n",
"Method: Least Squares F-statistic: 137.5\n",
"Date: Fri, 24 Nov 2017 Prob (F-statistic): 2.61e-13\n",
"Time: 13:41:54 Log-Likelihood: -21.760\n",
"No. Observations: 35 AIC: 47.52\n",
"Df Residuals: 33 BIC: 50.63\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"const -3.7023 0.144 -25.796 0.000 -3.994 -3.410\n",
"x1 3.0990 0.264 11.724 0.000 2.561 3.637\n",
"==============================================================================\n",
"Omnibus: 1.532 Durbin-Watson: 1.931\n",
"Prob(Omnibus): 0.465 Jarque-Bera (JB): 1.106\n",
"Skew: 0.434 Prob(JB): 0.575\n",
"Kurtosis: 2.931 Cond. No. 4.12\n",
"==============================================================================\n",
"\n",
"Warnings:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"\"\"\""
]
},
"execution_count": 16,
"metadata": {
},
"output_type": "execute_result"
}
],
"source": [
"# Frequentist linear model\n",
"X = x\n",
"X = sm.add_constant(X)\n",
"M1 = sm.OLS(y,X)\n",
"M1results = M1.fit()\n",
"M1results.summary()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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am5vjyiuvjHHjxg3GbAAA8IFVfQX34Ycfjl27dsUvf/nLWLBgQVxzzTWDMRcAAOyXqoH7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\nBQAgFYELAEAqAhcAgFQELgAAqfx/HZUkLlTV1kUAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11958e668>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"plt.hist(M1results.resid)\n",
"plt.scatter(0,0,s=200,c='red')\n",
"plt.savefig('resid.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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RJC8lV1fMvUQDgUE91fhb0zlAzGLgAsfpibqnNR4e143lVykjId10DoAoc2nx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\npno3fwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x119920da0>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"plt.hist(M1results.resid)\n",
"xtmp = np.linspace(-1,1)\n",
"ntmp = len(xtmp)\n",
"ytmp = sp.stats.norm.pdf(xtmp,0,np.std(M1results.resid))\n",
"plt.plot(xtmp,ytmp/max(ytmp)*7)\n",
"plt.scatter(0,0,s=200,c='red')\n",
"plt.savefig('resid2.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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CtuLUrKgqLNFNKBNGiO1UcerzVYDnOUQi0V7iVFGMe0/N+GWaDeWusZ99+kl0AfAOHwa1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aX6sWBHntfWZJErZDy4UKunxwmPJ1CoZTBoodGockZtz0cUPKtZRXpeIooi/b7T4Cf2nh57v3hn\nMoVgA5DnBbUvo6tIkvAfd9F7KvTKTr0gKpvKqug9FYlqroBlOfT2urF27Vro9UWYMGEiaJqGVqvx\n54syjAdeL4vly98BANx4o2ABcDqduPPO22G1WvHSS3/G8OHDE/690RcZoNcIOaQGnRIlBnVS8yRJ\n0u89pWna54vzoKfHhS6rC1+fsoLjBDI8YlBRwvGCyer3v39LUnMIBsfxsPV6oKRJaFTCLWHkyJEY\nMmQItmzZDI7joH51GajWVrivvQ6OBQug8Hh8PmI1OI6Hx+Px57rGQnFxMSoqKrB1azu6u7thNptT\nmqegugLhXtdRoy7G7NlzUF+/EXv37kF5+fgYn5ee9ER6XUl/gWPA6yp4HrNFuBK1kJU7ctHmIBx3\nj/+6HHzcKYr057p6PGxaSSu5tr+5gIKymgMQvWlCxygziotNUCqFzjLnznX74lZ6ZUlUgXywAWRv\nfFE9LSkxorQ0Uj1NN6BfqoxfAf2rnqaCw4cP48iRb1BXVweeF2wSor8TAPR6LfR6DT744J8oKSnB\nVVctAs/zeOyxR7F37x7827/dHjOzMxoGmLUYNdiQkKiKpNlkMsBkKgJNU3C53OjutqCnR2gf6Wa8\n2H24Ew4Xi16GxTff2vFtpzPhHK644gro9Xq0tbUlPW8RjIdF24Gz2PbFebTsPYPDp4TUAoIgUFNT\ni+7ubnyxbh10v/sNuJIS2H//R/+NWvxubTYHOI6HVitEYxUV6aBSRVe0Fy5cBJZlsX79upTnGomA\n6vrDHwrq6quvLutXfz7Lcn2uuuaK8pgtyGH/go+71WqH2+0BRZEoKtLAaNRBqxXSWWR6G8wJFMhq\nFhGPLIiFUeISr6BQcLBYekIKowT/lnyVSSB3fJ+5ACFySAWjMTROzGaL7j1NH+nZAKK1Nc2G9zRb\n2LhxAwBgzpw5Ia97vSycThcsFhvee++fOHfuHG699VYMHFiGF198Du+/vxyTJ0/G73//R0nmEfwA\nGqs4SkgzCHyml/HC4w28QFEErPZERUOCz3Xq1Gk4dOggzp8/D0CwJSRzg1/Tdgy7D3Wiu0doJvDN\nt3Z4fMkFNTU1AICtv3gcRG+vQFSjFKzFKoATiblWq/YTtMWLhS5hn376r4RzSwXz58/HyJGj8P77\ny/Htt6cSel37ApFeV5c/JklKr2suKo9SQg5kNRiBQi03rFYHbLZAoZbRqA9qAVygX6mgYAPoIwQv\n8Qa3tnQ4Im9a4ZCzMgnI2wYABMh2uhdMhYL2R0tRlNg1ivEpUtnJuE3WBhB4kCAg2A9Tb2uaSxAV\nuzlz5sXc5u23/w4AuPnm7+JXv3oKv//97zF69GisXLkKgwaV+Zf3Ul3JECO2lErhOItL43a7M6lz\nR6OkQQV97xzLQa9J7hJdWVmF+vqNaG1tweAxVbDYGFAUgcuGGTG4VBf1M2tajuHAESu8HI8z3S4w\nHg4DizVgOR4KADU1MwEADUeO4IGrl4C57vqE8xAL4MRoLLHVq16vBUmSmDx5EsaMGYP6+o3o7e2F\nRqNJMGJyoCgKDzzwIB599GEsW/ZXPPnkUyHdtIQoKrrfVVeWZfzdtBQKyrd0rATH8X7LQOrFsfke\nXSUvshoOoVArsqOWVqvuM6tIPqBA7bMEhmGwc+cOvPHGa7jvvruxb9/usMIosXgiPlEFhJNdrtFP\nQH6Q7VTmH0s97elxSKyepge5q6ex4HA4sGXLZowbNw5Dhw6Nus23357Cxo0bMGWKUO3+618/hYsu\nuggffLACGo0OPT3Rl7RjfSciEYtXHJXsDYimSIwbZYaCIkECGFyiw9AB+qQ+W1Ul+FY/29AIm9MD\n2teM4MAxqz9CKxxHzzpQpFX4Hya/7XLCpFdCpRCuNcNZFhcTBBoAWH77+7RM0MGKtsUiqK7XXnst\nnE4ntm1rj4gdywTf/e73MHDgILz55puwWCy+FptaFBcbUFSkBc9zcDh6c1B1dWSkuua/sppf+ycW\nakVaRbT+Qq2C6hqJgrIqIY4fP4b29ha0tbVg166dGDlyJKZPn44HH/wJLr30clgstrTGzRdlUq5I\nZv79oZ4mgqiuBj8sBIL55auexkJTUyPcbjfmz18Yc5t33nkHHMfhlltuxfDhI/Czn/0nbrrpOxg2\nbBgAcUlbWNYmCMKvlOp0GrAs51dbaZryF0cxjAdOpzQta0tNapSakivUCsbkyVOgUCiwc3s7broj\ncFy9LA8vyyOaTZIiAYqkUFykgothYdIrMenSUuG84Hnof/oTzOF5vAZg99kzmDRkSAZ7FmhIMHfu\nfDz33HP46KOPcNVVV6GoSOdvciAo2okf4KNBo9HgwQcfxM9//gTeffdtPPLoY7A73aB6eyNIabDq\nGrDL9F/BYDzVled5v/IWTXWVu/KYCPm8f7EK9PLs0iwJ8o6schyH55//Aw4dOgiFQoH/+q9fYOjQ\nYf73169fi/fffxc0TWH06EvwyCP/JYlqefr0aTz22E9w5ZUTsXDhYjzxxK9QVKQHx3kzJgUC2ZDv\nk1Y+ktWArUMgqGLlvvik3N8Qvc5arQYMw4Bl5f3AkwzWrfsMALBgwYKo73s8Hrz11psoKirCDTfc\nCK1Wi8cei92hSlzS5jjO7znTaFS+7xZwuxn/Un9/Q6PRYOLEidixYwccdjt0ekGR1alpKBXRrx0V\nl5ahZd8ZEASBIq0CV1UN9Z8jqr//L5RNjZg5/kq8tmc3Nm/ejEmTJksy18mTp2DAgIFYs+ZT9PTY\nQVGUPyFBrVZBr9eBZQNdyuK1gw61XpC455578Nxzz+H551/A4LFzodLoYdAqUDluAOgoapWY6woI\nxDWQ/pF6Ny2pkAsJA7mEfCar4RAfWvpJ38hpyJcBxUBT0yYwDINly97Evfc+iJdfftH/ntvtwmuv\nvYK//GUZXnnlDdjtdjQ3N0nydwcNGoTly1fg8cefxNy5C2A0miBV/p1gA5A30ZAzYeV54aYVqNw3\nBVXuMyGV+/1FVIMv5mLVvs1mh0JBw2QyorjYCK1Wk7c5gDzPY926dSgpKfEH2ofjk08+xunT3+KW\nW26FXh87Eiq8OEqr1YDnedhsDnR2WtDVZYXVagPLCt2eiotNMBj0UKtV/WrXqaqaLijDnYdg0ilR\nbFChYmxpzIzXSZeV4pb5F2PB1CG4/aoxGFIqEFzyxAnonvwlOKMRFX/+MwCgsbFBsnmSJImrrroK\nnZ2daGlpBhDakKCrywKn0wWSJGEw6GE2G6DTaaFUKgDAt7yviWK9sAIg8e/3PwCr1YJPP3oLKgUF\nF8Piy2PWhPMiCB6Rua4cku2mlS1ESxig6cCysaDEyfPamgwuJLIq4gLb3aSQd2R19+5dqKysBgCU\nl4/HF18c8L+nUCjxP//zBtRqYZmNZVkolaoszka6rj0Fstr3IEnC7x8ymYqCvKf2HPaeUn7vqdfL\nwm53orvbCrvdAYD3NxnQ67U+T1y/TF1y7N69G2fOnMbcufNieiBfe20ZCILAj350d8R7oZ2jDFAq\nFWAYj78NaW9vaOeoYHLV3W2By+UGTVMwmYpgMhWBpGhs+/I86neewtYDZ8F4st9RrqpKuO59tX8H\nJowpwfjRxVAp4j+cmIrUuGSoEWqlb5HNt/xP2u1wPP0blJVfibFjx6KtrRUul0uyuV7nK9ZauXJF\n1PeDmz3YbA6QJPwPioJtgITN5kB3d09ErN8PfnAXzMVl+NeKv6O78xwIggCbxm9UUF058DznU9eT\nbwObLYiqq9gS1OEQjonwUNr/3bSygXzzrBaQHvKOrDocDuh0gaIEcdlE/O/iYqHX9wcfLEdvby+m\nTq3M2lyk8gVyHCdrGwAgH8Idrp6qVEpwHOdX1XJNPRX/SZR7Gl7oIvaAN5uDVcHcPz6xsH69YAGY\nPz+6BWDHju3Ytm0bFixYiFGjRoEgAsVRYiFVsEKXSnEUzyMkd9Rud2LHl+fg9gIqlRouL4EDR3uy\nTiAqKytBEARaW9PvZKX6x9tQbqoHM2cu3L4GA7NmzUZvby+2bm2XaKZCh6yysgFYvfoTeDyRNgqK\nIv0PD8JDIuEjr1Z/uoLQYtcAnU4DhSLgaDMa9Pj+Dx4A43bhw3deAcvzGFSizWi+4aprLhRpAYLq\nynFCMwyrNVJ1zYeuSgVltQAgD8mqTqeD0xkI0uZ5HjQduJBxHIeXX34JW7e24be/fUYWT6AcJw+i\nFw+5mgggqqeRlfsB9TT1KBnpEE09DQ7mT+c75Tg+hioYmYspF6xZswY0TWP27DlR33/llb8CAO6/\n/37f0rIJarUKXi/rJ/BSNd7well023rR2+tGb68LLMuCYXmYzUYYjfqsVfsajUZcccUV2LFjO9xu\nd8qfJ0+dhO6XPwen18P+wov+6v+6ulkAhNarUoGiKCxdei06OzvR1NQIIHh53wCDQR/14YHjQhsS\nhKY3CKqrWq3Czx+9D8NGjMKGtR9Cw57BAJM0EVkBJG4D29eIprryPA+NRhWiusr9XpLvKBDV6Mg7\nsjp+/AS0tm4BAOzduwejR18S8v6zz/4ODOPG73//vN8OkC1IRc4EVVLehyqXbADh6qlSKXpPu6Oq\np30592TUUynnEk0VBAjo9boQu0Au49ixY9i9uwMzZ9bCaDSGvKdQ0Dhx4hhWrVqJiRMnYt68eXC5\n3OjqEjpHuVzZsXHo1MJ3JlRye0ERXJAXk4LBUBRVFcwUlZXVcLlc6OjYldoHeR76Rx4GabPB8fSv\nwQ0JRH9VV0+HUqlEQ8MmyeYJADfccAMAYPXqT/zeYI7jfQ9RyT08hDYksIJhGCgUNAYOKMFfX/4z\nOJbFH37986xadcQirf5SXWMpj6FdlRxgGEF1LSqSj+p6IaqqBURH3qUB1NbOxtatbbj33h+C53k8\n/viTWLduLXp7nRg79gqsXr0KEyZMwkMP3QsAuPnm76OubnY/zzo+BBtAbhC9dNGfNgCSFApmxKYM\ngcp9e1JKWrbJqjg+QYjROQQIQrqHnVTg9bLwenvhdPZGVGiLle9CE4vcuYGI3ZCuvnpJSNyUQkGD\nZTk888wz4Hke//EfD8Ph6O2TOU28pBh7DnfB6WKh09C48uJiAPD1C/fC4RDURZKicKrLDZoiMaRM\nB9YXhZXu91tdXY033ngdLS0tmDYteYuT6v33oPx8PZi6Orhvuz3kPZ1Oh2nTKrF5cxPOnz+P0tLS\ntOYGCMv7wvFRYsGC+RgyZChWrVqJ06efgVKpTHtcQExv8PjD12tqanHddddh5cqVWL16FW699bY+\nOn9DEwYEiI03pP9NJ0PoxIcm8XoX3ste7GPv9Xr7VR0OR8GvWoAIgo9zlp87l14uaAEBsCyDTLuL\nkCSJkhIjzp3rlmZS/QCDQQ+Px4Pe3tSXJ9NBIPdUaGvndnvAMIx/KTEV6PWC303sLy8lxJuXQE5z\nVz0Xsh+F71QkgYFoof6zSQDA0qVL0NragqNHj2HIkIvg8QRij77++mtUV0/D2LFjUV/fmFMrFF6W\nQ2PHabgYLwACpiI15k0bAbXvgSqd7/f06dMYP/4KzJ07D8uXv5/UZ4jTp2GeOR0E40F30xZww4dH\nbPOnP72E3/zmabz66mu4/vobk54PIPwWxQcIgADDMP4OYU8++Qv89a//jbfe+j9cffWSlMZNBidP\nnsD06dXQaNT44ouvUFSk95+/4sNX39p8xJUR6aKxioq0cDpdcSO+4s6IIPxdlRQKKmGua1+Cokho\ntWrYbNJfe3MVHIcLOrqqrCx6UkvuXLkLiAmel3cHK0BUD7O3DyRJ+rxZ0b2nQkW3Oy3VQPDbZja/\nYO8pSRJRvKe5fXwFP5wHNpvQ215QXomYRS7ZxP9n77zDnCjXNn5PS99soYjUFalKF6UXKYqioogo\nlk9FrMfGsSGK4BE92FHxHHsXRVFROBZU6tJFVlgEBEQR6WzJpmcy8/0xmUkmZTebnSST3fd3XVy6\nm2zyZjLlmafcd+RwVCDgxfr169C/f3/Y7fkxw1Fz5z4HQRAwdeo9ujuG/jzshJGeFMQAACAASURB\nVNfPh7LqQIXDg12/H1Vt37w8KwoLk2/HaNGiBdq3PxUbNqxXBktrRBRhu/9e0JWVcM2cFTdQBYDh\nw4cDSK5vNZ70l1Ted6GiokpV3p8wYSIA4OOPP6p9rSnQqlVrPPnkU+jYsRPcbo9q/43X7pL+aob2\nva71LZXLWdfEva7mrPW6kjYAgkyDawNoiDSEYzUdbQDxsqdyeV/LUlZ9A211aV9fAVOqhMvZHqW0\na7GYlZKi1uVWqWwpZecinaMWLPgUoihizJjzYlo6tm/fjgULPkaXLl1w4YUXabKOTBEu2ca2Y8if\n3e8PxO3FHDRoEN5//z2UlW1Dr169a3wfwxefw/jN1wgMHATvddcnfF737j1QVFSElStXxG2LCZf3\nOTAMq2Qt5cn9xK/bHd2798D33y/F0aNH0bx585o3TApcccUkXHHFJNXv5O2rbncxRBkS8GmtGki9\nroBceQsGU8u6al0qV7tpASzLJu2mpTUkWCXINIwrp47R6k5dUgTI3a9Li77bdGZPaya5ntXwSVXO\nnlI5lT1NlWBQls6pRkWF5P9uMHCh6fe8lKff1dPheWAYJmY4asmSxQCA889Xl5BFUcQjj0iDNY8+\n+phm/vPRBHgBP+08htW/HMK238vrdGFt18IGk4GFKIoQRBF5Fg6tmlljnlezpqs9xuxh4MBBAIA1\na0pqfH/q2DHYHnwAosWC6rkvAjWcX2iaxvDhZ+PgwYPYsUPSro7+fmiagdvtRXl5ZZ2kvyZNuhLB\nYBALFybXtqA14e3rijIkkLLakYYE6SW1rKt0bkpPQCeKqDXrajSmL+tKelYJMg3z6tkAkVoBcnfI\nKtUhJfXkfgEMBgO83sST++kgGdmtyMCUZesnLZXLyBalUrm1UslcJTP9Lg/CSeXjgjjlY7fK2rS8\nvBwrV65A9+49UFxcrHqtpUu/w6pVKzFixEiMGDEybZ93w69HceiEG1WuAPYdrEbZvuT7ylmGxtCe\nLdClbSFOLy7E4O4taj3GY9UbYs0ehg0bBgBYu3Ztja9le+A+0OXlcE1/GMIpp9S63lGjRgOQ3Kzi\nl/dTOxYvvXQCDAYD5s//UBdZtEhDAocjO05ldVUYyNRmUysMOOH3B8Aw6VMYIJlVggxpA0g72mVW\ncznwSVYrlqZpGI1caHqfQzAYhM8XSHpyPx1EBtrh/6eURJRW5g8NEXW7AKNqF5DKrDwoiobBwIKm\nwy0EtZWPAWDJkq/A87wigSTj8XjwyCMzwDAM/vWvx9L58VDp8ivfPU1TqHDUbYCQZWi0b5nY+rU2\nJPWGYCgbKCkhtG9/Ck499VSsX78OBgMbKuuq2wUMX30J4+KvEOjXH94bb0r4+nKJ3GDgcOml4/GP\nf9yKb775H2677TbNKhhFRUU499wxWLz4K2zZ8nNCu9xsIG07H7xeHygKSiuK2WwCICrtGOk/N8VX\nGMhmtUbOuiZWGJDUBQKB1BUGSLBKkCGZ1RxBEHJ7yKqmzKo8LBM/e1qVVdcoQFo7wzAwmQwke1oP\ngsEgvF5JKD8Q4JWLvtlshCgCbrcXLpcn6fLx559/DgC4+GJ1sPr000/i99/34oYbpqBz5y5p+Swy\nZoP6ft9oyN79v2T2IGW1+/cfAIfDgbKyspisNnXiBKz33wfBaEL5M3Njyv8sy8JiMaOgwI78/Dyw\nrNR+QdMszjjjDGzYsAHl5doqk1x55VUAgPfee1fT19WSyKx2RUWkIYEplHW1wmQypP08zTAUTCYD\n7HYLCgps8Hr9unHTSpx1taaUdSXBKkEmd6OfnEGbgy1X7EoTERmsRvee5uVJ0lCRvaeSWHt2TlLR\nvadSkOWF1WpG06ZFyM+3wWg0kCA1SSTrTCPy820oLMyHyWREIMCjstKB8vIqnDhRCY/HG9WHWbOL\n1uHDh7B27RqcdVY/tG4dFrD/+efNePnleSguLsb06Q+n/bOd0akJTAZJ7ifPwqF3x6K0v2cyyH2r\ny5YtCwVWTsXpyTjtQTAnjmPTFbfhf8eNOFbpUVnP2mxmACKcTpdibyq3X4wadQ6CwSCWL1+m6XrP\nPnsEiouL8dlnC1FRUf9A+FilB+u3H8GGX4+iyuXXYIWxhA0JnKioqILX6wfLsqpeYq0UMliWgcVi\nUlzmIvuDXS63Dt20ontdPaFeV0Odel0bY89qY/u8yUKC1RxBagPI3a+LYRiwLBORPeV0lz0F1Lam\nkdlTr9evXJTUA0SZ6WHLNeIP3yR2jortw4SqDzN6wGXRokUQRRHjx4c1P91uN+6883YIgoC5c1+E\n1Ro7rKQ1BXlGjOrbChcOaodhvU6GgdOHI1B4yEpy85OG4LzwfPQxbIsW4ljn7th72fUwm034/YgP\nFosZwaCAykoHKiur4XZ74057y32rP/zwvabrZRgG118/GV6vF/Pnf1Cv16py+bFm2xEcLvfi0AkP\nVpUeCmnZpg9Z2i26l1iygc1HXp61zje4cr++dAxI+7LTKUlvJeoPjux1FQQh425aiQhnXT11yrqS\nzCpBhpgCpBlBECCKgdqfWAtWqxkURaVFmD4dxPaeCmAYGhUVjqwGpTJa9Z5yHAejUepjk3zL/VkQ\nGs8+NE0p/Xwcx0XI/wRSFiuXXjfcMxmWrPJj2LBhKC3dgrKyHWjWrBlEUcTtt9+GTz5ZgBtuuBFz\n5jyp4afLTc48sw8qKiqwa9ceMAwDrroK9v79IVRU4JuXP0dFq2IEg0FYTSzGDmqv6IxGOpVFI4oi\nunc/HTwfwPbtOzVVWaisrESPHqejWbNm2Lhxc8qv/esfFfjtL4fysyiK6NmhCO1b2rVaap2I56oW\nz5BA/bzwMeTzxZcoqyuiGOmglR43rVSQe105jgHDMOD5oNILa7GY4PX6G9X5NBl55IYMMQXIElqV\ninOhDSC29zScPS0vrwJA6Tp7msp3FQhEZ1MkoXFJ8iZzQvnZIFyalMqeHMfC7/ejoqIKVVVOeDy+\negWqQHzZpr179+Lnnzdj5MiRaNeuDViWwVtvvYlPPlmAPn364NFH/6XRJ8xtBg0ajKqqKuzdu1vK\n7s14GNTRI9h/01042OTk0GBQECcXmeF2e1BZ6UBVVTV4PvH0O0VRGDVqFE6cOIHNm3/SdL0FBQWY\nMOEy7N+/v16ZW4uJVQV3UotG/axc64NaIaMqZPkbNiTIz5eOn8LCfBgMHPz+gOoY0iJQBeSsq6D7\nrKvPF866siwTulHVR8Ui3ZAkcmJIsJojSDql+vq6ontPZVvScO+pU+k9lTKZmV1fZNFAlpaS/0kB\nqrYLkqaywxd9QRCiyoCZcMhJH3LmJ7I8DyAiWHfD50uf77o84PLmm28CAK644koAFNauLcHDD09H\ns2bN8P77H8JoNKbl/XMBmqZhMhlht9swZswYAFLfquuThaA//BCBnr2Q9/B96N2pCdqdZMMZnZui\nS7sC5e+T0XQdO/ZCAMA333yt+fpvuOFGAMB///uflF+juEUe2jS3ISgICAoiOrS2o1mBSaslaoAI\ntS6qFEQCUG6cMyGNFavrKuiu11WqTIowmaReV5stvbquBP1C2gAyQDBYNzmbeBgMHKxWMyoqHLU/\nOY0YDHLZW3aN8ivOUbUFKc2bF+HYsYq09iDJ5X3ZwlIP5a7o8l7Ygcif1QtDMkQ7E/F8uEScjbUH\nAgH07NkdPB/Atm2/4qeffsIVV1wGAPjyy69w9tnDVQ5KWrpo6RU5+2QwGEDTlPK5Dxw4gNNP74oR\nQ4Zi6e7doE8cR+WPyxHselq93kcQgmjRogVatGiBn3/egkAgqOk2njhxApYvX4avv/4WZ555Vsqv\nwwclIxJGB4ENx7HKdyT3t/r9seXt8PM4SJUoWRorkLGsmyjKbnt1d9PSmvx8KxwOt5LskN20OI5R\nSWc1lDYBUQTSaJqWEyRqA2i4NcoGRrI6pVoj9Z4alL5Mng/C709N91QOJLW8sKlVBmRbU33pnspl\nQJ9PmkqWL0YWix2CIMDnk3s79XGWUl8wpWym2+3VRa/xjz/+gGPHjmLKlJtw+PBhXHXVJASDQbz7\n7gfo06cvqqqcqpsDq1UaHJKDg/q2JegF+fNF9ko7nS7VRbt585PQuXNnrF+7RlK0mPZgyoEqENZ0\nBYCRI0fhq6++xJ49e9CrVy/NepQB4K67pmL58mV44YW5+OCD+Sm/DpuCa5pWSPsgC4PBoPSp+v3+\nkMlA4u0TqUscz2ZXDl7TuR9LWddwZUrSdc1Or2vk9SKRrqvJZADLqntd9Z4EINQdEqxmhPrb4Yli\n5toA4mVP5Wn4+gSacsBd3xasyOypHKBmO3taFyKHV1iWhdHIwW63qh7LZGAoi8lLvWHhwQ6Hw6m7\n4G7+/A8BSLqcPp8Xbdq0xrRp0zF69GjlOdE3B3LwLdvzZnobC4KIPw5LVariFnkp7avSd2SIGjST\nbiJq6mkcdkp7vLZrF9ae0h7d7rw75c8Qzfnnj8VXX32JTz/9FG3bFmu6jQcOHIgzzzwL3333LbZv\n347TTz9ds3Wnk9jvSBqOSsbgIh5yS4bXK1Xm5MqM3Z5ZQwJZYQCQAldRDGdds3nelQwb/KE1yllX\nBiaTJWezrg28CFQvSBtABpAOqPrthRRFoVmzQhw9Wq7NoiKIlz31+fyanwiLivJRXe1KOSMrrVX6\nr96yp1ogldwNoZI7HXEx0r4EGC4dc6BpWnXh02vZ/PDhw+jVqztOO+10LFu2IqXXiN7GsmNWutoF\nBEHE0k1/o7JaCjgK8ow458xWSV3kE39Hye0PVLUDK/v2waXl5Xjg2utx7zPP1vfjKDgcDnTp0hFd\nunSN+S7CrSMGMAyTUkvG0qVLcdVVV+CSS8bjtdfe0GzdWsMwjHLejPyO4ikpaPu+0e054f1Yq4Gs\n5KDS1i5AUUB+vg2Vlc46/y3D0ErwmktZV0FAvZM5uQ5pA8giWpS+a3KASgUpe2oIDf3Q8Pu1yZ7W\nRF0+Q7zsabiPqmGiaGF6wtaZkSVAWRYrlZOtXJbkOAMMBmlaWtaFzJXMw7vvvo1gMIhrr70u5deI\n3MbqdgGLpqVsmb0HHah0+pSLeKXThz1/O9CpTX7c58eW91P/jiyzZmJEeTloisLKXTtxb70+iRq7\n3Y7Bg4dg+fJl2L9/P9q2bas8Jm1jHzweX9yWjHiyTdGMHj0a3bv3wKJFX+COO+5C9+7dNVx9/YjX\nJuN0esBnUHMoehvLa7JYTMp+EwhkzwZWi6xrfa6bctbV52s4WdfGDglWc4j69Hwmyp5WVjozdpKt\nqe82F3pPM4lsnen1+lWe5LJ4ezI9mAzDRGRfwhkut9ut6+xCPHw+H959913k5+djwoTLNHnN+O0C\nBtjtpoghmEC9jg9BDHf7AaGGoIhNH27BMNSpvF8b3KqVML/3LrjTTkMPjsPmzT/B5XJpapRwwQUX\nYPnyZViy5CvcdtvtcZ8TvY1Zlg0pSlhVw2DR2WKKojBjxiOYOHECZs/+FxYs+FSzddeV8PEn3ejJ\nx59e2mQi91VAyshznHSuiKweBALpHYqU2gUAuYoYDNYv66rVfIO619WnZF1Jr2tuoS8tpAaLNgFX\nXYesDAYOeXlWNG1agCZNCmAwsPB6/Th2rELR+8tkNiA6sxpP9zQsK5Wa7mlDJNKTvLy8Cm63BzRN\nwW63KZ7vLCvdd3KclCUsLMyH3S4FBG63B+XllaiudsHn078CQTy++upLHDt2FFdffU3anKmkwRbJ\n9726WnIgstnMKhetuu6Sp7bMg9XMhVyFRFhMLDq3K1Dp07IsC6/Xp9iiRrt71RmnE7apd0FkGFS/\nOA9Dhg5HIBDA+vXrUn/NOJx//gVgGAZffPFF0n/D87wi71ZZGdZ0LSyM1XQdPvxsDB06DMuW/YiS\nktWarr02aJqCyWQIHWMFMJmM4PmAIkvn8Xh1EajGg+dlG9hqVFQ4FMc92aq1Nitj7YiWxqqbDWy6\n3KuCQQE+nx9OpweVlbKuK12rmxYhu5Ce1QwgCDxEsf7lhtp6PuV+vOjsqc9Xv+yQVuTlWSGKIpxO\nd0TvKXSnH5tLSNOwRnAcC4qiIAgiAoGAri+mdUUURZxzzihs3foLNm36WVVyzgSJsp/J9gfyQQH7\nDrvAsiy6d2gOlqE0ydomwvrA/TC/9Qbcd02F++EZWL16FcaPvxg333wLZs9+IuHfVTp92Lm/CjQF\ndG9fBLOx9sLb5ZdfhmXLfsSGDT+hffv2Ka85snoQ2QKxYcMGjBgxHL1798G33y5Nq/5oJnvGs0Vs\nH3RYYSCzveq1Z105joHRaIDT6cnYqrLd60p6VknPapahNOk5jfca8XtPfWntPa0Lkbamfr8feXk2\nmM1GxUZQD0F0riGXUqULDqVkXYNBPtSTyiE/395gtEY3btyA0tItOP/8sRkPVAF1SwYQKT0m9wfG\nWuxGa+sWFdql8r7LFRPg/nGoGnsPVoNhKPTu2AT51tTdlti1a2F+6w3wnTrBfe99AICzzuoHi8WC\nFSuWJ/y7Kpcf3244gGDIwOPAUTcuGty2Vvmn8eMvxbJlP+KLLz7HPfek3hUrVw8iS9kGA4chQwbh\n8ssvx4IFC/DJJx9j0qSrNN2X48u0eXQh05YOZPkxt9urskiWeraDET3b6e7lrL3XNV2Z1ZqI7HUF\noGi6Rva6ShJipNc105DMagaQyh+Beger+fm20LQ2YDRK/VN6y55Gkih7GpkBlidofT4pg0GIJdpb\nXB6OqmlIJZHOo1Y+45lEzt4tXvw1+vfvn+3lqIgW5A8GBdC0lDUKBHj4fP4aFRb+PubCsp8Pgg6d\nGwwGGpcMKU5NI9TtRuGwIaD3/4mqr78Ff0Zf5aFJky7HDz98j9LSrWjVqnXMn27ZfQK//lGh/CwI\nIgb3aIFTTo6f5ZCprnaga9fOKC4uxurVa9PSunP48CEMGNAPBoMBO3bsRGFhQb0G4dRDbPrTOc4W\ncuDOcVyN/cTphwLDMLBYjBBFwOOpv6mOFtA0rQSv6qxrULNzajBI5KsSZVZJ/TUj1O8ELveeGo2G\nUO8cC6/Xm7Xe02jCF2Lprli2Ng33nqp3M3kiu7KyWulbs1iMii1pKr2BDQ2GYWA2m5Cfn6fyDJd7\n/dxub42TrNJgS0DxI5f6XGnFh9xiMedEX9aWLT9j2bIfMWjQYN0FqoAsoUYrWSBRlH3Ww0oWNe3L\nfx1zKYEqALjcPModqV2crU/MBvPHPnhuvU0VqAJS/ycALF8eP7tqZGlVmVMQRVhNtRfe8vLsGDVq\nNHbt2oUdO3aktO7aaNHiZDzwwIMoLy/H1KlTQ1lBWtWzzXGJ10pRFIxGqf+0qEjuPw0qx5LUMtO4\nA1VA7tlO3E9sNhvBpNFoQQpQpV7u/HwrBEEMDRrWrdc1XUg3NvF6Xc1KryvH6f+cmquQzGoGkC5g\n/qSfzzB0KHOqzp4yDI1gUIDLlbkentoI9xppI1UiGxKwrGxL6k+r37yeiCwbp1P0O549p5wB1BtX\nX30lvvvuW3z++SIMGTI028uJKe8nkruK7cGMn8Er+70cW347oRw7QVHEpUOLYTVzdVoXu2E98i8c\ni2D7U1G5fCVgNqse3737Nwwc2B/jxl2MN954K+bvBUHE9z/9jUMn3KAAdGyTj4HdTkrqvb/8chGm\nTJmMO+64C488MrNO604WnucxatQIbN9ehrKyHTjpJGlt0XqjYYenoLL95Yl4aR9vOP2nmUTalqyq\nXULud60PsimK/LrSMRJrQxsmfbqu9UHKujLgOLZeWVedFUezQqLMKglWM0AywWq83lO5vC9/RRaL\nCQzDhCaVM0tk76k845BOaSn5Ym805n4ZOxGynWK0K1Emhb3lNRiN6ou9Hvpct23bhhEjhuHMM8/C\n//73TdbUIdQSYKkZCch9xkaj5PkuS4/5/AGs3HIIB465wTAU+nQsQpd2hXVboMeDgrOHgfl9L6qW\nfA3+rH4xTxFFEX369ITT6cTOnbvBMLEZIFEUUenyg6Up5FmS75v1eDzo1q0rLBYrtmz5RVGm0Jp9\n+/bhu+++wU033RJ30Irj2NAkt1SZkSWdvF4f0dPUEPkGgeNSO29xHBtKxtSvDUMU5WtR9t20opHb\nBTiOTbrXVRSlNoDGDglWs0wwqC7tJcqe+nyJ7ypNJiOMRg5VVXV39KgPWmZPU0XWwDQaOaVn0+fL\nvT4z6SSmHo7Sy8RxvKyhfCHJ9A2CKIq47LLxWLlyJRYs+BQjRozM6PvHG7zRKssdLxvo8fgQ4PmU\nGoYsj86EZd5L8Nx8C1w1TPtPnXoXPvjgfXz77VKcEdUmUF/uv/9evP32W5g/f4HK+jbdRPefRp4X\n4g0i6uVYayjEU3GQb3jlYyVziYfczrqSYFWCBKtZxu12YPv2bdizZzduueVmMAwbN3taE0ajAWaz\nCZWVjrSsMdPZ01SRytiGUJYKulYWiB6OStbBRw9IF5hIKaHYqfd08f333+PKKy/H8OFn45NPFqZ9\nH4z3PcmfN50SYPHft3bDBxl280/IP38MhLbtULFiFVCDBu1XX32JG264Hvff/wDuu+8BLT8GSku3\nYPTokbjgggvx9tvvavrakUTfUCWb1dNDFaMxEG1EIoqSNrjchpGpik0uZV2ljCsPvz9IglWQYDUr\n/P33Aaxfvwbr16/F1q2l6NSpE4YOHYYJEyam1CzOcSzy8qwoL6/SbI2RtqZSPKCvA7s25JOjWlkg\nu/2XWpSN9YZ8gyANv1FKIJeO7RwIBDBs2GDs3bsXy5evwmmnnab5ewCxupp6+J7qlNH1elEwcjjY\n335D5aLF4AcNqvG1q6qq0LlzB/Ts2RPfffeDpusWRRHDhw/B7t27sXXrdjRt2lSz15bc96Qeay2+\np0SarunSvW0sxGspEgRBucFIRsUkHYhipFW3frOuoghUVelnHiVbNEqdVUEQ8Oyzc7Bnz25wHIdp\n02agdes2yuMlJavwzjtvgGEYjB17ES666BJN3nfduhK88MJz8Hhc6NdvIMaMuQAPPTQDeXl5oXWl\ndiGsq4NVPGKzp7ltaxoMBuHxSI4t8slS7u3N1FBF5MWP4yS3okCgYek1SvqMHrjdHqWMHWnnWJtE\nU1145523sXv3bvzf/12reaCqd11NWYDc5fIoNz3RtplykGZ55mmwv/0Gz+QptQaqAJCfn4/+/Qdg\nzZoSHD16FM2bN9ds3RRF4corr8bDD0/HwoWf4pZbbq3X68XeHGn3PSXSdLVa429nQmLiyRB6PD74\n/bGtavJ2ttksoOnMbWeKkvVcI3Vds9/aBsgKA0KoJSJry8gJGnRmdeXKZSgpWYWHHpqFsrJt+OCD\ntzFnznMApNT7VVdNwOuvvwez2Yxbb70BTz31PIqKmtT7fY8dO4qKinJ06NBJGQQQhABEsX57I01T\naNKkEMeOldfp73I9e5oKYWWBsOuQlmUoUlaUiK/gIJWxU7kp279/P4YMGQSOY7F27YZ6B1T1LbPr\nhejyt7BxA5jBgyG0aoWKlSWAzZbU6/znP/Mwc+YjePHFeZg06UpN13jixAl0734a2rdvn5Lmajbb\nTmRi+7aDObm/pBN1G1ZqVZZIQ4LI4zIQaLxZV+JeJdEoM6tbt5aiX78BAIBu3bpj586wDuAff+xD\nq1ZtYLfbAQA9evREaekWjBgxqt7v26xZczRrpl3WQibZzGqk05X0/NzOnqaCpDMq9QRHNvhbreaU\nG/wjRbMl0Xdp0jgQcDbagY3I7QxEujvZ6zzpK4oipk69C263C/Pm/SflQDU8wGQIZdgDistXrmbK\nVNvZ50PhDTeACgaB199AQeuWSZexR48+BzNnPoKlS7/TPFht0qQJLrpoHD77bCFKSlbXKjWWaKBP\n0tbMzlU7en+Wj3m7XboZSJecnN4JVyQMIZUFP6qrXSkHloIQu505joPNZo0ahtOmWpMIPWddCWoa\ndLDqcrlgtYYzDjRNg+d5sCwLl8sFW0Q2wmKxwuXK7JR9KohifBu6yOypHKCSA00iuuwnS6cUFJhq\nVBZIlJWrrnblnApBplCXVyUNRbvdqnos0YX+vffexapVKzFq1GhMnHh5nd5XXd6Xsj16Ku9riWXu\nc2B+/RWea6+Dq09fsE5XqLxqVkqxiabeO3ToiOLiU7BixXL4/X4YDKlbu8ZjypQb8dlnC/H666/F\nDVYTSaXp9UZC3ZYR2WYUXrvUm6m/tdeXSKUF+Qbf4ahOS4ZZ3s6yeYnBwMFkMsJmsybUMk4HFKW2\ngZWvt9nOuhIaeLBqtVrhdruVn0VRVDQApcfCeqVutzp41R5tdnJRlBrW5cZ1oPFmT1NFPjECUklL\ncrexKo8B0pBUZP+aXi+meobnJW3B8IXeoPRfRgdUW7duxcMPT4fdbsezzz5X636c6EbC4WjYNxLM\ntm0wz30ewVat4J45C0Cs37vBYFAu9NHtKRRF4ZxzzsFrr72K9evXYejQYZqu74wz+qJXr9747rtv\nsX//frRt2zauCUWivkY9Iznv+eDx+EBRlHKDZLWaszY8pCWJlBbcbk9Gg3FBEOD1+uD1SnKP6uw2\npZw35JvidEGyrvqiQdutdu/eE+vXrwEAlJVtQ/v2HZTHiotPwYEDf8HhqEIgEEBp6RZ069Yjreup\nb7AjWzlareaQdiANlmUibE3JwVNXgsGgErxGnqzlgMrr9cHn85NAtZ7IFrtVVdWorHSA53nFyjEQ\n8GHy5Gvh9Xrx3/++hpYtW8V9DYahYTYbkZ9vU1nQVlQ4UFXVCGwzAwHk3Xk7KJ6H87m5EPPsMU8R\nBBFerw8OhxMVFZXwen1gWQYFBXkoKMiDxWLCmDFjAABLl36n+RIpisKUKTdCEAR88MF7KCzMh81m\nBUDB6ZSsf51Od9oDjXQjGw44ne7QZ/IAoGCzWVFUlB+yxda/bTRNUzCZjCHr2shjqgoOhxNery/r\nWWM5s11R4YDDUQ1BkGxgi4okG1iTyRjXJEJrpKyrAFEUIAgCgkF92MA2AF8S/wAAIABJREFUFhr0\ngJWsBrB37x6Ioojp02di166d8HjcGDduvKIGIAgCxo69CJdeOjGNawlCEAJ1Cihje0+l0qrZbFT1\nDuWiOH42SWY4Kp5cDrFr1B6/34crr5yElStXYObMmXjooYdVAy2x5X3psYZY3q8N87PPwDrnCXiv\nvArOF15K+DxBELHlt+PwBoLo0MqOk4osAMKDMaIo4OSTW6BJkyYoLd2qybaMvNEThCCKi4sRCATw\nyy/bYDZb6v36uYTehy+jz23y2nLtBiJahSWdFtVJrKbe7QLBIMi1BURnNeskG6zGm9wPTyuqiS+O\nX5OvcuMlXtCTbCkp3coCjZVAIIDJk6/Dt99+g/POOx/vvPNeyPjCCJZlQ+0uYcvMXLkhO1rhwZ6/\nHbAYGfTo0AS0Buk1ZsevKBh5NoQmTVFZshZifr7qcVEU8dOu49h3yIF9h5wwsjSMBhYMDYwd0Bat\nmqnNAm6++UZ8/vln2LRpE/r0OQM8L/Vt16X/Mjooi7TqffrpJ/Hkk3Pw6KP/wm233V7vz5/LqF22\nROXck8mAimEYJUClaSo0+NiwbvqiDQmkbSzfJGTuPJ2qIQEJViVIsJplpBK+P+7vo7OnqfSeRp6M\n0i3anguopVEiJWjql4WOtQ4MZs2SNNe5445/4OOPP8KwYcOxcOFnsNvzQjcD8sCbAIOBVVpeciED\n9PcxF5as3Y+gKGU4i1vYMHZAm/q16PA88s87F1zpFlR9+BEC55wb85Rte8ux8pdDEERg36FqGFga\n7U6ygaIodGqTj5FntFQ9/8svF2HKlMm49977MG3adMXO2GCIlPeKPVbC55mav5OKigr07t0TVqsV\nmzdvgclkSv3zNyAyaRgiDzjKmsJygNoYkhmRPcXZN35ILutK/CgkGqV0lV6JN7mfKHuaLMFgEG63\nNGQRb5gl265OmSA8yMGpRKe1HI5KpCxgsZjqLNXUmGEYBqWlW3D22Wfjyy+/BMcZ4PXGDt3wPB8a\nHFJPCEdm8fSS3RYEEYvX7MdfR13gOBpNC0z47a8qFNkNaNXUinYt4p+Ea8P88jxwpVvgnXhF3EAV\nAA6dcIOmaYhBARSAAC8gKIhgaCBeO9/IkaNgNBrxv/8twQMPPBizT0sDLVKvqXxxl4ZTRfh8ATid\nnhov+oWFhZg8eTJeeulFfPzxR7juuutT+uwNjUgTk8jWCavVoskNtXw+kh2jfL4AHA5no9OIlXuK\n9WH8IEYNaQHRWVednMJ0DcmsZpBg0K9cOKTgNP1N4WGpmNzuT4qH3mwTG3MmozZivysBbrcHwaBQ\n5wtpfCWAuuvmas2ynw9ixc8H4fRK2pAGlgEfFNCuRR4oCjjrtGbo17Vu2rHMrp0oGDEcYkEhKkrW\nQiwsjPu89duP4qddx0HTFE5UeVFV7UPbFjYU2U24ZGg7WE1czN9cc81V+Pbbb7B+/Uacemp4+DT8\nXUlBj2xmImkLJ3+RP3r0KM44oxeaN2+O9es3hfoKCYmIJ79WW3WMVHrqTrzzh3zzm/lzdbjdTxAa\n9Lx70iTKrDKzZs2aleiP3O7YsjUhdWiaAkXRSklAksZI77ioKIrg+SB8Pj+8Xn+oud4Aq9UClmUA\nIKdOagxDw2SSssZWa9i2z+XywOPxIhDgs/Z5BEFAIMCHjAJ4sCwNs9kEi8UMmmYAiDm1reuLvK+p\nv6tA6LvyIRgUUs5qyFkoj8cHQRDAslLWRJ4MlpUzMsnasiMQATg9AQgi4PbxaGo3wWqWTCROVHnR\np3PT5F8wGIT9mqvAHDiA6v++imD3xGolLZtaUOn0w+3l0TTfhHPObIVeHZtiQLfmMBniF9D8fj++\n+eZrnHxySwwYMABGo1H1Xfn9Abhcbng8vpCUUNj4wWq1hCoYkuZzvO/RarXi6NGjWLFiOVq2bIme\nPXsl/9kbIerzRwA0TcNkMsJqtYDjGEWyEKAUgxP1d+WB1yvdHOul2qBXos8fDMOEztWSVTeQui16\ncoiKFJas55ruWCBXsFqNcX9PMqtZQw5aRABiRgLXSGKHhgLKHbneTnTxJ8Kl5vlcIHb6lleyJg2N\nSE/3SCeaTH3WeJqemWqB+WL1Hzh4zA1BEOH28XD7eDQvMCuPGzgaN17YJenXM7/8EqyzZsI7/lI4\nX31d8/U6HFXo1KkDevfujQ0bNtRoJhCPSFejRJPYhw8fRr9+fZGXZ8eGDZtgtVoTvyAhLvK52mQy\nKgkGKYPqh9frIyVkDZEqkWxoaFC7WQeJcIAavtaTbGo0JLOqO+QdloZ650XGAtfwCc8LADAYDKG7\neBYUhaz1OcnC5haLCTabFSzLhETPPXC7vaGJ5dzJUMZmtwGjMZwxkUpAufN5IqEoKdNmNptgs1mU\nUqTH44XL5cmI60wkgiAq2SmfT1LfMJuNSiUhnJ3SnpObmPH3MTd8gSCa5ZswtEcLHDzhhigCgiji\njM5NY6byE0Hv3QP7lBsgFhTA8eHHgEUb+SeOk6TvbDYLCgrysXr1aqxZswbjxo2H2Wyp03cVXUkI\nZwLNYBgpm2uxWOF2e/DDD9/DbLZgwICBmnyOxoBURZK2p9FoUPq3JbF8SumVD2cCc/McoifC5+oA\nPB5vqGrDwGIxwWw2pVCNjAxQ5Ws9g+hrPiEMyazmDKLqX6YzrgCUbIk0GRxUei/TWRaJHo4KS0ul\n1xs6m+Rqv5nedSTjkcidJx1rFgRRGZw4XunF/iNONMk3Jj9gJQjIv3AsuI0b4HjzbfgvGpfyWqJ7\nhaMn/T/44H1MnXoXHn74Edx1190pv08kshKH0Shlp8rLy9GlSxf4fD789NPPaNKkiSbv0xCJL0eY\nuAc/F4/FXCXetnY4qnHo0CG0aHFyxIB0dAaVBKZ1gUhX5STZD1wjp0u1HGSJlRbJfbvC+iJf4CMn\neWVx/GwT72aiLiVjvaHWvtTXvmd69RXYHp4O34UXofqtd+r89xRFKW0n6gAm9oazsrISp5/eBR06\ndMDKlSUafQI1BgOH119/Dffeew9uuulmPP/8XDJ4GEFYNoyrt9FL5A2ZKIrK4FBDV4LJBgYDh927\nd+Of/7wbHMehf/8B6NdvIHr37gOj0QwSoKYGCVZzHjHqHzJu5ScHl0ajQbnA+3zJB1OSpJasMSj1\nyYazADkY8aQRPSgLxIqZ+3UT0GlJZJ9ttjWK6X37UDh8CESTCRUl6yA2a5bU38lydWGrYD4k+l77\nzcS1116Dr7/+H1auLMFpp52mwaeIxe/3Y8SIYfjtt9+wYsUKDBw4sEHc9KRK5LGVLjWLTGq6Nk5E\nZTjqjz/2Yc2aNVi3bg127/4NvXr1xsCBg3HBBReHJN8IyUKC1QZF9gNXlmWUjCsAxdEpOpBRD0ch\n4uJE7vSTJVPuM3KvcGMuKYZvqKJtdjPQjiIIyL9kHLi1a+B49XX4x19a49NZVr55TF7qKB6LFn2B\nG2+8AXfdNRUPPzyjHh+gZtauXYtx4y5A9+49sHTpD8q+Fru/pbflKBskbkPJzGeNfn9tB4caE7WX\n+B0OBzZt2oAtWzbjhhtuQmFhURbWmbuQYLXBoo/AVc64AtJgFkUBDMMiGOQjToqNI+BJJ1r7eje0\n8r6WhBUzpN7LdAcYprfehO2B++A773xUv/t+3AM5XvtCqiVjGbfbjdNO64KiokJs3lxaP7etWpBd\ny+bMeQo33DBF+X08HV49tWakQvTNn56MLHJdYSWThL8q0oOaCYiDVYMl8sCRAlbpRJj5wFUURdA0\nHdKTpQCI4HkBPB8kgapGCIIAj8cHj8en9CbW1dUpnle50+nO2aAgXYiiCJ/PD58vrC9qMHCwWOya\nu5XRf/4J66OzIBQUwPnUM8qBmygj53Z7Nct2WywWjB07Fp98sgAbN25Av379NXndeMyc+ShWr16F\nAwf+Uv0+2hlObs2w2awhMwIpKNd7MBWdmff7A3Gd2bJNIMAr+tTymi0WIxjGStqzQAJUPUIyqw2W\n9GVcpQsoq2RCEmVB4mUBc+GCk4vElvl4pV0ACAda6gxh4ynva010T3G92ltEEfYJ42FYtRLVL/8X\n/KRJMa0I6c7IrVixHJdddimuuupqzJ37YlreQyYYDCpyS8kQduGTet31lKEE1G062e55ri+NefCV\nBKj6gLQBNGrqH7iqMwZMxJRpcnffcklMuuAwDVoYXw+YTEaYTAYlKAgGg/B6pSyhHi7wDYnY4aa6\ntVIY33sHeff8E8Fzx0BcvBiU0o6RGTMDQMrY9+3bGydOlGP79l9hsyUps5Vh5Btlg8GAsNVu5nsv\no3vxG6q1ckNvEyIBqv4gwSohguTcsyJ7yBI51KRCtLROOFPibxAnwGwR+X1JEjjSdpWF+2WnoYZ6\nYdUD0k1ZtGyUNOkdfao1GDgYDh+Cse8ZAEXB+9NP8DU7KWvfy9NPP4mnnnoSzz//Aq6++pqsrKGu\nZHKAU8/ScpmgoWi6kgBV35BglZCAcOB6+PBBbNq0HmvXroUoivjvf19RAsl0nZDjDbHIygIkA1gz\n8Ur/cqtFootHQypZ6p14gvyCIICiKLAsiyAfADV2LNgffkD13Bfhu+rqrK73wIED6NOnJ/r27Yuv\nv/4uq2tJhegMd33bJ3LVtCNTyOcdrZMZ2kNsTnMJEqwSYuB5HmVlW7F2bQnWrStBRUUFBg0ahEGD\nBqNPn77Iy7Mik3ec6otDuLeSlK7DaKmdqLWyACGWyH5LlmWVYFUURfCvvwnjrTfDP/xsOD5ZmHkZ\njzhcdtmlWLFiOdasWYdOnTpnezkpk+hGrrYb7/DNczgzTm6ea0d/mq4kQM1VSLBKiOHVV1/Ghg1r\nMWDAYAwcOARdunSNGHxIrlUgnUQLZ8sXjcaW1QiXOqUyfjoyGHqW2ck1wn1+ki5uvMFC9sgR5A/q\nDwgCxK1b4W9xsi5uFGTN1VtuuRWPPfZ4VteiJZEuUfIxJNuYqge4mAht3YbRl5lp1DcKmewrJgFq\nQ4AEq4R6kP3ANdL2taH3i6WaFUrX+zdksXatiLXMrKEvWBRhv/pKGJZ+h+pnn0PgusmqXsBs3ij4\n/X707t0TXq8Hv/xSBpvNFvd5xyu9WLJuPxyuAJoXmnDxkHYwGXJDCVFqhZGGPWlaCmYCAR5erxd+\nv95K2LlPPE1XeR+vPyRAbWiQYJWgEfoIXOXMVX29tPWC/spoYWKtIRvujUKyxM8eJWeZafz0E+Td\ndgv8Q4bC8dkXqvJ/fV5XK+RBq6eeegbXXz9Z9djqXw5j1/5K7D1YDZahYTIwEEURp7cvxCVDijOy\nvlSRtVslxy8oQZOUWTXk9NBQriCrynAcpxpArJumKwlQGzIkWCWkAbUkVjYC11jb19yZdM9FK9rY\nG4Xc2d71JXoaOpUMKHXkCAoHDwDlD6BiVQmEdu1qfH5sxja+rbGWHDlyBL1790BxcTHWrFmvOFqV\n7j6BJWv3AxSFQ8ddEAGcXGQBTVNo3cyCa8/rlLY1pYq8/YxG2QCj5hvbWMOM9G/vxkoiTVeHoxoU\nRUdp8ZIAtbFAHKwIaUDtnhV2zspc4MrzQfC8J+TEIk26y6438oWJ5/UR/CXKmjkczpzJUkY638i9\nmZHbW+/Bdl0JqyeEdSZTdiQSRdjuvxd0ZSWcc56qNVAFIrc3VNs73AurvRbrSSedhIsvvgSffvoJ\nVq5cgeHDzwYAHDzuVrLALEvD6+PBBwVwFI1mBSZN11AfYisBflRWJuf4Feuipd7eeugrbihEyusB\n4e39zjtvYdGiRRg0aBDOPLM/zjqrP/Ly7CASU40bklklpIHsZ1xlGRu5L03OuGY6kEpkpqCH8r6W\nxLOZzNULe/RAm1bZesMXn8N+0xQEBgxE1aKvALpumSFRFFHtDoChKeRZjUoQLQ8FablfbdnyM845\nZxRGjRqNjz5aAAD4aecxfLPhACiKgiAIqHb50aF1Plo1s2JMv9ZgmexkujLRYx1fY7Su5WtC7UgZ\n1KNHj2LjxvVYtWoVSku3oHPnLhg4cAiGDTsbLVu2yvYiCWmEtAEQskT6bF+TJdMSTblY3teSXFMW\niNXT1L4vlzp+XCr/u92oWLEaQvv2dfp7QRDx8Y+/Y9dflWBoCmd1bY4x/VqH1p8oWKtf3+XYsedh\n48YNWL58Fbp16wZRFPHDTwex+0AVOJbGsF4no1Ob/JRfvz5kcx+L1s+Vy9e53jefPaJL/OoMqtfr\nxebNm7BuXQl4nse0aTOytM76IQgCnn12Dvbs2Q2O4zBt2gy0bt1GebykZBXeeecNMAyDsWMvwkUX\nXZLF1WYPEqwSdIAeAle17assU1OfwDV7Ui36R6/KAtHBTrr1NPOmTIbxy0VwPvY4vLfcWue/X7/9\nCL7ZcAB06IARRWDKBZ3QunnstL667zL1QOqHH77HpEmXY9y4i/HGG2/Vec1ak8jWNtvZe5YN35xK\n7TDZqeLkFjUHqA2RlSuXoaRkFR56aBbKyrbhgw/expw5zwGQNM+vumoCXn/9PZjNZtx66w146qnn\nUVTUJMurzjykZ5WgA9Q9ruo+18wEroIgwuv1wev1KYGUyWSEzWatU3YmXPbmwDDhzI7T6dZl9jBb\niKIIn88Pn88PIBxIWSz2jCsLyIoLcmtIvfpP64Bh8VcwfrkIgTPPgvfGm1J6DZeXVwJVABAhosoV\nQOs4z43tAzQgL6/ufcUjR45Cjx498dVXX2L37t/QsWPmB6giNWvl9bvdHl0FgjzPg+d5uN0e5bxg\nsZhU5wW9VhUyidrmlEZjCFAj2bq1FP36DQAAdOvWHTt37lAe++OPfWjVqg3sdjsAoEePnigt3YIR\nI0ZlZa16hASrhCyR/cA1MpCKzABarZa4mbZ4eoFut1dXF069ExlIydvTbs9L26R7vJYMlytzwQ51\n4gRsD9wH0WSC88WXANWEc/Kcfkohftp5HB5fEC5PAHarAe1bxs9ARCIPIKoDKbMij1aT+D1FUZg6\n9Z+4/vpr8cILL2DevJdTWntdidcz7HS6cmIiPxgU4PH44PH4os4p5kYp+6YOUBtHBjURLpcLVmu4\nEkLTNHieB8uycLlcKk1ji8UKlyu9N9G5BglWCTpAb4FruIfRarVAFEXQNKV4gzscrkZf3teCdCgL\nRPcTygFCthQXrA89CPrYMbhmzkKwQ8eUX6dFkQUTzy7GG//7DX5egNsbwEc/7MV153UCTSd3gMQL\npEwmA2w2a8L2jPPPH4vOnTtj4cJPMHXqP3Hqqaem/BlqIrp1QTrOqnM6qIuuKoRvzqSgpKH2spMA\nNT5WqxVut1v5WRRFsCwb8ZhLecztdiU05GisEKEygs6QS0RM6B8NUaQgioib/dEamqZhMhlhNhvB\ncVyojCddcMITwazifEPQBp4Pwu32orLSAYejGoIgwmIxo6goHzabRcmMxoOmKZhMBtjtNhQWFsBk\nMoLng6isdKCqqhoejzcrQY/h229g+mwh3D164fNeF2LpxgPw+FIPTA4c84ACBbvVAJZlsPdgNbb9\nXp7Sa8mBlMPhQnl5JbxeH1iWQUGBHQUFeTCbTWAYBjRN4777HkAwGMQTT8xOee3RUBRgNHLIy7Oi\nqKgAZrP8nVWjsjJ731k6kW/MKioccDicqn08L88Ko9GgaNrmGvL5WepDVZ+/SaAq0b17T6xfvwYA\nUFa2De3bd1AeKy4+BQcO/AWHowqBQAClpVvQrVuPbC1Vl5ABK0IOkR73rPgDEmovd5nGZPuqBxJN\nfQeDQSWDKg3b8KGhFn34uVOVlSgYPBBUeTmevedV7LW3giiKaNnUgpsu6gqOrfvNzqpfDmPpxgNK\nQCOKIiYML0avjk01XXt064TP58fQoUOwefNmfPvtUpxxRt+UXlfO5hqNsltUIHT8NO5+zkT2ypl0\nLUsFkkGtG7IawN69eyCKIqZPn4ldu3bC43Fj3LjxihqAIAgYO/YiXHrpxGwvOSsQNQBCAyP1wDWR\nc0pdJ6Ybou2rnuE4FmazCRwnlc7k783j8epO69L2j9tg+uRjlF57J17pfIHye0EQce15ndC5bd0l\nn7w+Hq8v2YUj5R4AQNuTbJg8tlNa9U3lCfz169dh1KiRGDx4MJYs+Ro8zyd1UxAtG1dbnywhnmtZ\nINTLne12AeIiRUg/RA2gEfLnn3/gppuuxVdfLYXRaMz2cjQm8iQphC58NQeuJpMxQqooEBqQ8qQc\n6MT2XBpgt1sB5Jbtq56JJ8PkcnkQDAaV3xcU2BWnIinrmt1sFLd0KUyffAy+R0/smXg9xNKjSjaU\nogGrObXTrsnI4sYLOmPzb8dBUxTO7Nos7UL8Up+rFz179sa5556L7777Dt9/vxTjx49PKPcVz/VL\nbxP8eibStSzsymdWtqVc9clMsB8ZoMr7GglQCZmHZFYbKC6XE7NmPYQdO37FZ58taYDBaiKkQIXn\nA9i+fRs2blyH1atXo2vXrnjiiX9nRJcxfLE21GtYqDESLhVzYNnkBe7jZbmz4elOORwoGDwA9PHj\nqPx+Gbydu+Kdb37D7wcdoGkaZ3ZuiouHFmd0TVrx22+7MGzYELRo0QJr1qxDQUFBKAPIQhCE0CCi\nFMjIlYrsZwMbDlJLjLSPh1206m/+EAvJoBKyB2kDaESIoohZs6bj6quvx4MP3oMPP1zYKIJVl8uJ\nDRvWY82alVi/fi2aNz8Jw4YNx8CBg9ChQ0cwTOZ7qqJtX9Pl557LRFu1Stahfvj9fEq9jHKWO9yD\nnLmbBdvdd8L04QdwPTANnnvvByCV/v8+7oKRY9C80Jz2NaST2bMfwwsvPI877rgTjz02W9m3RVGE\nIMjBqnYWtYTExKs6pH6DRgJUgj4gwWoDZcmSRViwYL7qdy1anIyRI8/BmDFjMWHChY0mWJ0z5zEc\nO3YMgwYNwcCBUgYoTHqGs+pCpm1f9UymAspMuh5xy5chf+IE8Kd3Q+X3PwJcYgWDXIXnA+jf/yz8\n/fff2LBhIzp37hwzCBSvDaCx7ueZItI8gaapJLc5CVAJ+oMEq42Iyy+/GM2aNQcA/PprGbp2PR0v\nv/x6llelJ9S2r9kJXGOn3Bv64Ik6E5T5Un06/eQpZzUKhgwCfegQKpf+iGCPsOzM1r0nsPPPKlhM\nLM45sxUMXGrGANkgnl3u4sWLMWHCpbjuuuvx9NPP1vj3Ybk37bc5IT6R25xhGMyc+Qg6duyIfv0G\noGnTpiRAJegaEqw2UhpTZjU1sh+4Rkv6NJQLejxJHlmqKNuSPPGCMDl4TmXgznrfPTC/8zbc/7wH\n7gcfUn5fuvsEFiz7HXxQ6uns2KYAN13YWdd6mskE9f/73xJ06dK1TiYB6m3OIhgM5oREUy5DURTW\nri3BsmU/oqSkBCef3BKDBg3F4MFD0bGjvvdDQuOEBKuNFBKs1gX9BK6RQVS8iWu9Em514HLKGz0y\n6ysrCyQbRHElq5F/yTjwXbqg8oflQMSx9uH3e1C6+4TyM8vSmPF/vWEx6UuIJZPtEjKyRJPRmJ1M\ne8MmusRPgeeD2Lq1FGvWrMaaNavg9/tx1133Ytiws7O81tSRtUv37NkNjuMwbdoMtG7dRnn8+++/\nxSeffASWZdC+fQfcc880Yuiic0iwSiDUCTHqX2ZsX6ORM65yJkoeXNGTrmi8frl0DJFVOv34YdPf\nCASD6N2pKbq0LdD09WVidS5r0M91uVA4bDDoAwdQ9c134Hv3UT28cMU+rN9+RMlgWc0cHv6/XmmX\nnEqGyO8t26oV0fuQvJ+TQcS6EBugJrrZFkUR+/f/CYvForSM5SIrVy5DSckqPPTQLJSVbcMHH7yN\nOXOeAwD4fF5cc83leO+9BTCZTJg5czpGjz4XgwcPy/KqCTVBdFYJhDoReaKXAlbpvi6zgWtkdkvO\n/Fks9jpn/7QmXkDndLrSlhUL8AJeX7wTB4+7QFEUyvZVYvL5nXBqK7v27xWhcxmtnxvt526d/RiY\nP/+E+867YwJVABjTrzUOHnfjr6NOWIwsxpzVKquBajyJr3R+b8nC80HFclfOzlsskuWrpA6h/+x8\nNlC7SMnWprWfnCiKQrt2xWlbV6bYurUU/foNAAB069YdO3fuUB7jOANeeeUtmEwmAAhpM5MKY65C\nglUCoVb0F7jKwWJBgSkjtq+J+g2rqrwZCZb/OurE38dcoGlpY3t8PMr2VaQlWI1ECqI8cLs9Sqnc\napUE2gPLlsPw5uvgO3WC+7774/69zczh9vGnocrlh9nIwmTI/HBVbItDAA5HddbNExIhCAI8Hh88\nHp9qv7NaLWnUFs0diM1pGJfLBavVpvxM0zR4ngfLsqBpGkVFTQAACxd+DI/HgzPP7JetpRLqCQlW\nCYQ6oY/AVZ39Y2E0crDb8zS1fU00ye10ujOe4cq3GWDgGPChAEsURVgz3Pcpuzl5PF7QXi8KbrkZ\nAEC//Q7ymjVJmP2jaQqFeZnL6MQfHqufW1u2EEURPp8fPp8fQGR1wZSyTXIuQgLU+FitVrjdbuVn\nURTBsuHzgiAI+M9/XsRff/2Jxx9/igyU5TAkWCUQUkYfgSvP8+D5+Lavcv9osmXeeBqZXq8Pfr8z\nnR+hVprYTRjdtyVWbDmEQFBE5zb5OLtPy6ytx/zEbNB798Jz621wd+4Kgz8AozEy+yfdMGQqqKco\nStHwle2Efb7s3Fikk8jqgnpfb3hOcSRArZ3u3XtizZrVGDlyNMrKtqF9+w6qx59++glwHId///tZ\nMliV45ABKwJBc9SDWZKyQOZXkazta2Qfo97dh7z+IAK8AJuZzVqWhN20Efljz4NwSntUrFgFmNWu\nVPVRFqgLsSYTfGgoqeFq9SYingtaLuoWkwC1bshqAHv37oEoipg+fSZ27doJj8eNLl1Ow5Qp16Bn\nz97K8y+7bFJOqx80BogaAIGQNbLvnhUtTSQHoizLKAGV3x/QbR+jbvB4UDBiOJi9e1D15RLwAwbU\n+PR48kw1la0FUcTiNX9i30EnrGYWlwwtRtN8k/J4vMw3se9VE9baT9wyAAAVf0lEQVQt5sCyXESf\nq75UNGRIgEoghCFqAARC1ogsPwmhi1NmA1dRFJV/FEWpSmLBYBDBoEAC1SSwPP0k2D274bnxploD\nVaB2ZQGfLwCeDwea3204gO83HVQy8Q5XAA9c3QtGo3SjIf+d0+nWZeZbDyTuc7UrA2bSjVm2th+x\nOSUQ6goJVgmEjJK5wJVhGCXDFNl/6nCE+09ltyKTyQibzdogbV9FUcS3Gw/gt7+qYDIwGDeoHVo0\nsSR8/rFKD/484kT7k+0osocHo9gtP8P88jwEi4vhemhGndcRT1nAZjNHZEgD+Pu4KxSoUqAo4FiV\nF5zRCFEU4HC4GvwgUTqIVdHgEkqRpY/IAFU+B5AAlUBIFhKsEghZQ/vANdx/Gs7CuVyehBdjQRDh\n9frg9YZlguTAVR7SyXV9y5Wlh7Fk7V/Kz+UOH+6/sicYOnb7/rTzGBYs/x0uD498qwFXjj4V3dsX\nAT4fbHf8A5QgwDn3RcBqrdeaVMoCIdUFq9WEls3z8cueCiWzmm/l4Ha6yBSzRoQz3eEbBovFnCbX\nLhKgEghaQYJVgu7xeDx49NGHUF1dDZbl8PDDs3LadSU+qQWuFAVwXDwdTWedy/qR5VOKgtLjmq0J\nd63Yf0StZHDohBvVbj8KbLFyUst+PgS3NwiKouBwB/DjTwfRvX0RLM8+A3bXLniun4zAoMGarCte\nb+VFA9vieIULfx11wW41YOLIDjCbjTm53fWO+oZBXWFI3eaYBKgEQjogwSpB9yxe/AU6d+6K66+/\nEV9/vRgffvge7r773mwvK41EXtwi5bCkwPXEiRNYt24tduz4FbNnP65oq2qpoymKiNP3J2Wh9Gr7\nmogiu1Hp1QWAwjwjrCYu7nP5qACfF0Qwv/wC84tzEWzTBu5HZtZrLXJQFKld6/MFUF0dlpj6v3Ml\n+R35RoTjuNB2z65rWUNGXWGQtrvRKBlA1D6ASAJUAiHdkGCVoHsmTrxS6dU7cuQw8vLiTws2TCiI\nIrBv3+9YvXolSkpW4u+/D2Dw4MEYMWIkHI7qjPSWqvv+uJAdZvZtX5PhvP5tUF7tw54DDlhNLC4c\n1BYcGz+Y6NOpCQ6f8CAoiuBYGn1PsSPvrqtBBYNwPv8CRFvd971oJYZktWtFsWbXssYiiJ9p4m93\nDvv3/4kHH5yGQYMGY+DAgejatRsYhgUJUAmE9EOkqwi6YsmSRViwYL7qd9Onz0TXrqfjzjtvwe+/\n78Hzz7+Mjh07Z2mFmWXdujWYO/dp8DyPIUOGYfDgYejVqw9YlkGknms25LCAaGmm9Nu+ZoKffzuO\nv4+50K5FHvp/9hosTz8F7zX/B+dzc5N+DWnyv3aN21SRlQWMxnBvcrSyAEFbRFHAnj17sWZNCZYv\nX4bjx49j4MDBGDp0OPr27ad40BMIhNQhOquEBsGff/6B++67C5988mW2l5IRjh49gqqqSnTo0KmG\nIRsReghcWZZRJJak7JQUoOWqxBJTVoaC0SMgNG+OytVrIdrtNT4/0lxBbs3IxOePp/pAtFe1Ilpm\nKiw3dfDg3ygpWYWSkpXYtWsH3nzzA7Ru3SaLa60/ssj+nj27wXEcpk2bEfczPfnk47Db7bj11juy\nsEpCQ4borBJylvfffxvNmjXHmDFjYTabQdNMtpeUMZo3PwnNm59Uy7PUtq+RPa5AJm1fJWmmsO0r\nh7y81Gxfs04ggLw7bwfF83A+NzdhoBrrVhWAw1Gd0cxyMBiExxNUKQtYLCYwDJOzTk7ZJboHNb5I\nf8uWrTBx4iRMnDgJPp8XBkPswF6usXr1Cvj9frz66tsoK9uGefOex5w5z6mes2jRZ/j99z3o1atP\nllZJaIyQYJWge8aOvQizZ8/CkiVfQhAETJ/+SLaXpGPUgas6eM104BqE2+0Fw9AwGg2w2SygaVqZ\nstZz5s/80otgt22F94pJCIwcpfxenuA3GKTBJ9kdScvhtvogCEINUmSpTrg3fNQuUokD1EQYjQ2j\nBWDr1lL06yeZXXTr1h07d+5QPb5t2y/49dcyjBs3Hn/++UcWVkhorJBglaB7ioqa4LnnXsr2MnIQ\nfQSuwaAAt9sLt9ur+NlHalvqrWTN7PgVlmeeQvCkFnA99jgoigpZnBqUCX7ZRUrPQV+0FFm8CXc9\nD8alG2JzGovL5YLValN+pmkaPM+DZVkcP34cb7/9Op544hksW/Z9FldJaIyQYJVAaBToI3AVBAEe\njw8ejy+mZK29KHtqmOZ/CCoQQOCll2Bv16ZOE/x6Jd6Eu9HY+JQFSIBaM1arFW63W/lZFEWwrBQm\nLF/+AyorK3HvvXeivPwEvF4v2rUrxvnnX5it5RIaESRYJRAaHfoJXCNL1kYjp7J9lQeUMpW8ZBgG\nRiMHbvp0CBMuhThwMNzuxO5f9eGvoy4sWv0HvP4gTmtXgLED22r+HjUhOzkB4cG4SAvSnOovrgUS\noCZP9+49sWbNaowcORplZdvQvn0H5bHLLrsCl112BQDg668X488//yCBKiFjkGCVQGjUJApcpZ8z\npSwgiiK8Xj+8Xn+Es5MBVmt6ey1Zlg2V+CUJKJ8vAGeeHXzPPoDLXctfpwYfFPD64p3466gLALBr\nfyVsFg7Dep2clverdT0Rg3FywC73F+uxTSMZSICaGkOHno1NmzbgllsmQxRFTJ8+E0uXfguPx41x\n48Zne3mERgyRriIQCAmQexmzJ4kV2WsZOdDk8/lTDlzlErjBEKkNm7kS+NEKDx58dRMi57GG9WqB\n687rlJH3Txa5v9hgMIBhaN0rC5AAlUDIfYh0FYFAqCORjjxCKBjIbOAa3WspT+LL7llyxrWmISF1\nwMsqw0WVld6sDBfl2wxomm/C0Uqv8rtm+fqbJo/sL9anskC0BipAXKQIhIYJObIJjYannnocgwf3\nxQ8/fBf38SNHDuOcc4bhllsmN/hBk7pDh/4xAGiIIgNRpCIC2MwgT+GXl1fB7Zb0XAsK8pCfnwez\n2QSalk5pUg+s1IdZWFgAk8kIvz+AigoHqqqq4fH4sjYFb+QYXDnqVJxysg0nF5kxtGcLnNdf32Ly\nsrKAw+FERUUlvF4fDAYOhYV25OfbYDIZlW2f5pVAFBHa96R9Ud4nyeUslhMnjuOCC0bjiisuUQ1O\nyZSW/oxhw/rhlVfmZWF1BELykDYAQqPB7Xbh2msnweNx4/33P0VhYaHq8X/+8w5s2/YL3nlnPlq1\nap2lVeYa2W8VAOTSftjeFECobO3L6JBWYyT9bRUkg1of1q4twf33343zz78Q06fPVH5/4sRxTJ58\nFdq0aYcXXvgvGKbxmK0Q9EuiNgByxBMaDRaLFQ8++Aiqqqowd+5TqseWLPkSGzeuw1133UMC1TqR\n3Ywrw9Awm02wWs0wGAzw+wNwuTzwen1gGBoWixlmsxksSy7E6SIQ4JVst9PpAU1ToYy2HRZLqtue\nZFC1YuDAwZgw4Qp8/fViLFv2AwDJ9WzmzOkQBBGzZj1BAlWC7iE9q4RGRZ8+fXHppZdj4cKPMXLk\nuRg6dDiOHz+GefOex9ChZ+OCC8Zle4k5TGQQobZ91TLjKlm5GmA0cgAo+P1+uFyxElPq6XYrKIpS\nhPB5Prem23MFnufB83xcZQEp41qTskC0zSlAAlNtuO22O7Fly2Y89dTjOP30bli06DNs3VqK556b\nh6ZNm2Z7eQRCrZA2AEKjw+v14rrrrkQg4MeHHy7E7NmPYNu2rXj33Y9RUFCQ7eU1QETVv1QCV45j\nQ8NVBoiiqGiw1kULlGFoJchNLngiaEWkssBbb72JHTt2YOjQYejb90yYzVaQEn/6+eOPfZgy5Rq0\nadMWe/fuwXXXTcHkyTdle1kEgopEbQAkWCU0SsrKtuK226agZ8/eKC39GU8//QL69x+Ysfd3Op34\n179mwO12IRAI4I47pqJbtx4Ze//skXzgKk/+GwxcaIJfCi6DwfoPRkXLMunFPasx4HBUYdWqlVi5\nciVKS0vRq1dvDB06HIMGDYvpIydoy8cff4B58+bi1FM74O2352doKI5ASB4SrBIIUfznPy9i/vz3\nMH78ZfjnPx/I6Hu/+earyMvLw8SJV2L//j8wa9ZDeOutDzO6huyjDlyrq6uwceMGrFq1Em3atME9\n99yrBKiCkL7+V5qmlIwrwzCKnigJXLUkekhK+ud0OrF2bQlWrVqOTZvWo3//QXj00Seyu1SNEAQB\nzz47B3v27AbHcZg2bQZatw6rPuzYsR0vvfQ8RFFEkyZNMGPGYzAajWlbD8/zuOOOm1FWthUUReHF\nF19Br1590vZ+BEIqEJ1VAiGK/v0HYv789zBw4JCMv/fEiVcqrkk8H4TBkL6LlH6hcPz4caxatQKr\nVi3Hr79ux1lnnYVhw4ajf/+BcDicGVmFIIi12L4GsqwnmqtE96DGivTbbDacc84YnHPOGPh8Xhw5\nciQL60wPq1evgN/vx6uvvo2ysm2YN+95zJnzHABJCuzJJx/H7NlPonXrNli8eBGOHDmEtm2L07ae\n1177D7Zt+wWPPvoEXnzxOfzrXzPwzjvzYbfnp+09CQStIMEqgZBmlixZhAUL5qt+N336THTtejpO\nnDiOxx6bgTvvvCdLq8seTzzxKFavXokBAwbh4osvxb///SzMZjPUtq9SgEhlSA0rnu2rwcDBarXo\nRAhf36hdpOIHqIkwGk1o27ZdehaWBbZuLUW/fgMAAN26dcfOnTuUx/7660/k5+djwYL52LdvLwYM\nGJTWQHXt2hJ89NH7mDhxEkaOPAc2Wx7uvfdO/Pvfj+Hf/34mbe9LIGgFCVYJhDRzwQUX44ILLo75\n/d69ezBz5nT84x93oXfvM7Kwsuxy00234b77poPjuKhHIgOc7AauPp8fPp9f5YIlB66ZaFHIBYjN\naXxcLhesVpvyM03T4HkeLMuisrIS27ZtxdSp96N16za4//670aXLaTjjjDM1X8eRI4cxe/ZMdOzY\nCbfeeicAoF+/AZg4cRIWLJiPzz//FOPHX6b5+xIIWkK6qwmELLBv3++YMeMBzJw5GwMGDMr2crJC\n06bN4gSq0cgZOgZhLVcqpMGZ9iUqyLav1dUulJdLDk6Se5Y95J6VKQcnfSBvf6nMr/5+SKAqYbVa\nVa5RoiiCZaX8UH5+AVq3bo3i4lPAsiz69RuAnTt/1XwNPM9j5szpCAT8mDXrCdXxdvPNt6NDh06Y\nN28ufv99j+bvTSBoSeM5uxIIOuLVV+fB7/fjhReewe2334Rp0/6Z7SXlAPoIXIFY21eGkWxfCwok\n21eGaXinVhKg1o3u3Xti/fo1AICysm1o376D8ljLlq3g8Xhw4MBfAIBffinFKaecqvkaXnllHsrK\ntuLuu++LabEwGAyYNetxUBQwc+Z0+Hxezd+fQNAKogZAIBBynEhVAennbNq+RuvB+nxaWo9mFlLi\nTx1ZDWDv3j0QRRHTp8/Erl074fG4MW7ceGzevAmvvPISRBHo1q0H7r773mwvmUDIOkS6ikAgNBJk\nHVbt3bPqgtppC4oJQV2MDLIBCVAJBEK2INJVBAKhkRBZghdCwVfmA1eeD4LnPUqbgH5tX6M1UAHS\nIUYgEPQECVYJBEIDRh+BazAYhNsdhNvtVWxfbTYzaFpyz/L5Mm37Gq2BCpAAlUAg6BUSrBIIhEaC\nXgJXAR6PFx6PV7F9tVjMGbB9JQEqgUDITUiwSiAQGiH6CFwFQYDH44PH41NsX81mI2w2i0a2ryRA\nJRAIuQ8JVgkEQiMnMniLNCDIdOCqtn01GFK1fSUBKoFAaFiQMxiBQCAoqDVERZFRtFzD0ljpR3bP\ncjicqKiogt8fgMHA/X979xdS9RnHcfzj+cPpeI5n6lAGRyFzeqV2Zwl2sMk2UOcp2e7aYDPWH9zF\nootmjPRCFmxE0KUXY2WjJmNLYisJ/5QipZ2kjAUJC9ZdMJl6jrQO/nYRnvlLLdLj+f30vF9wkOd5\nPPi90o/P7znfRzk5bygry6eRkWFNTU0tfkeiB6phLPQ+XfjKr3kAGxs7qwCwLPO1r1btuC6+9lWS\nHA5pYGBA7e1tKi0t1a5dNQqFapSf/1bKagKAVKLPKgC8FsP0Sm0f1/8f8T99+q9u3x5Vf3+fhodv\nqKCgUDU176iurlHZ2dkpqmd9LTTWn5x8KLfbrWPHvlZBQWFivbf3d1240CWHw6n6+kbt3fuhhdUC\nWCsuBQCApDNeeEkZSc+tL/ZBXdqkPx6PKxIZ0+Bgn6qqqlVdHUp2EZYYHOzT0NB1HT/epomJe+rq\n+l4nT55KrIfD7+vcuZ/k9WZq376P1Nl5VoFAwMKKAawFlwIASKnBwX71919TW1uH1aWsI/NRAfNx\ngdUHV/MtUg696hYpl8ulysqdqqzcubofaFN3745rx44qSVJZWbkePPjDtF5cXKLZ2Vk5nU4ZhqGM\n5P+nAMAGCKsAku706e9069aISkpKrS4lhdYWXLnmdKloNCqfz58YOxwOxeNxuVzP/3QVFRWruflj\neb1ehUK7lZW1/K4MgI2Nj4kCSLry8godPfqV1WVYyNxVQHIkugosPni1MH7+mN/8/ekeVCXJ5/Mp\nFoslxoZhJILq5ORDjYwMqbu7R93dPZqa+lt9fdesKhXAOmJnFcCqXb78qy5e/NE019p6QrW17ykS\nGbOoKrtZacd18RrBdDnl5ds1PHxDtbXvamLinrZtezux5vf75fF45PF45HQ6lZOTq5mZaQurBbBe\nCKsAVq2hYY8aGvZYXcYGQjB9HaHQbo2O3tTBg5/JMAy1tp5Qb+8Vzc3FFA43KRxu0uHDzXK53AoG\nC1RX94HVJQNYB3QDALAuIpExXbr0s9rbv7G6FADABrBSNwDOrAIAAMC22FkFAACA5dhZBQAAwIZD\nWAUAAIBtEVYBAABgW4RVAAAA2BZhFQAAALZFWAUAAIBtEVYBIA3cvz+hlpbPl8wPDV3X/v2f6MCB\nT9XT84sFlQHAy3HdKgBscufP/6CrV3/Tli1e03w8HteZM6fU2XlWXq9Xhw41q7o6pNzcNy2qFACW\nYmcVADa5YLBAHR3fLpl/9OhPBYOFCgQCcrvdqqjYrvHxOxZUCAArI6wCwCZXU1Mrl2vpg7RoNCq/\n358YZ2b6FI3OprI0AHglwioApCmfz6dYLJoYx2Lm8AoAdkBYBYA0tXVrkR4//kvT0//o2bNnGh+/\no7KyCqvLAgATPmAFAGmmt/eK5uZiCoeb1NLypY4c+ULz8/Oqr29UXl6+1eUBgEmGYRjGSotPnsyk\nshYAAACkqby8rGXnOQYAAAAA2yKsAgAAwLZeegwAAAAAsBI7qwAAALAtwioAAABsi7AKAAAA2yKs\nAgAAwLYIqwAAALAtwioAAABs6z/Oh9S5kGMlFwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11e645358>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol)\n",
"[ax.plot([i]*ntmp, xtmp+(β0+β1*i), ytmp, c='black') for i in (.8,.6,.4,.2,0)]\n",
"ax.plot(xnew,β0 + β1*xnew, np.array([max(ytmp)]*len(xnew)), c=lcol, linestyle=':')\n",
"ax.view_init(30, 45)\n",
"plt.savefig('normals.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": true
},
"outputs": [
],
"source": [
"# R estimates\n",
"rβ0 = -3.7023\n",
"rβ1 = 3.0990\n",
"rσ = 0.4571544\n",
"\n",
"# True error distribution\n",
"ytmp0 = sp.stats.norm.pdf(xtmp,0,σ)"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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MZWW4zzyLouTU8qbMuvV8eTlSCymMi4iISKXcHg+rN+xgy7YscgtcREdaiI+L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\nAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11e869cc0>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"plt.scatter(x,y)\n",
"plt.xlabel('X',fontsize=17)\n",
"plt.ylabel('Y',fontsize=17)\n",
"xnew = np.linspace(0,1,100)\n",
"lcol = 'red'\n",
"plt.plot(xnew,β0 + β1*xnew, c=lcol, label=\"True\")\n",
"plt.plot(xnew,rβ0 + rβ1*xnew, c='black', label=\"R\")\n",
"plt.xticks(fontsize=15)\n",
"plt.yticks(fontsize=15)\n",
"plt.legend(fontsize=15)\n",
"plt.savefig('regline_R.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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oLHZaGULFb06nfhVgrRQWIygqN0MCEskrQAYV5BsiqxYk33IaTardAOLJqcfj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\nIYkqnL0MQBAErFYzra1OurraaG93YTbLJBIpnj/fYWtrl/39aLbyfPB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7tSErvUUt58hp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\nQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11d970780>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"ax.scatter(x, y)\n",
"ax.set_xlabel('X',fontsize=17)\n",
"ax.set_ylabel('Y',fontsize=17)\n",
"ax.plot(xnew,β0 + β1*xnew, c=lcol, alpha=0.5, label=\"True\")\n",
"ax.plot(xnew,rβ0 + rβ1*xnew, c='black', label=\"R\")\n",
"[ax.plot([i]*ntmp, xtmp+(β0+β1*i), ytmp0, c=lcol, alpha=0.5) for i in (.8,.6,.4,.2,0)]\n",
"[ax.plot([i]*ntmp, xtmp+(rβ0+rβ1*i), ytmp0, c='black', alpha=0.5) for i in np.array([.8,.6,.4,.2,0])+0.05]\n",
"ax.view_init(30, 45)\n",
"plt.legend(fontsize=15)\n",
"plt.savefig('normals_R.jpg', dpi=300);"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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EhTd74GPJ5qakIvdXpFI9chauxJUzuzny64q7ri98pSW7CpTj2RM78R070g0J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\nERFZFA5cIiIiIrIo/w+SRa+pnLX9jwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11e853940>"
]
},
"metadata": {
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(12, 7))\n",
"plt.hist(M1results.resid)\n",
"xtmp = np.linspace(-1,1)\n",
"ntmp = len(xtmp)\n",
"ytmp = sp.stats.norm.pdf(xtmp,0,σ)\n",
"ytmp2 = sp.stats.norm.pdf(xtmp,0,rσ)\n",
"plt.plot(xtmp,ytmp/max(ytmp)*7, label=\"True\", c=lcol)\n",
"plt.plot(xtmp,ytmp2/max(ytmp2)*7,'black', label=\"R\")\n",
"plt.scatter(0,0,s=200,c=lcol)\n",
"plt.legend(fontsize=15)\n",
"plt.savefig('R_resid.jpg', dpi=300);"
]
},
{
"cell_type": "markdown",
"metadata": {
},
"source": [
"## PyMC3 Version"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": true
},
"outputs": [
],
"source": [
"# Specify model object\n",
"Model = pm.Model()\n",
"\n",
"# Define model\n",
"with Model:\n",
" # Priors\n",
" β0 = pm.Normal('Intercept', 0, 100)\n",
" β1 = pm.Normal('Slope', 0, 100)\n",
" σ = pm.Uniform('SD', 0, 100)\n",
" \n",
" # Linear model\n",
" μ = β0+β1*x\n",
" \n",
" # Likelihood\n",
" Y = pm.Normal('Y', μ, σ, observed=y)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Auto-assigning NUTS sampler...\n",
"Initializing NUTS using jitter+adapt_diag...\n",
"100%|█████████▉| 5489/5500 [00:05<00:00, 1006.74it/s]/Users/aaronmacneil/anaconda/lib/python3.6/site-packages/pymc3/step_methods/hmc/nuts.py:452: UserWarning: The acceptance probability in chain 0 does not match the target. It is 0.884705959287, but should be close to 0.8. Try to increase the number of tuning steps.\n",
" % (self._chain_id, mean_accept, target_accept))\n",
"100%|██████████| 5500/5500 [00:05<00:00, 1005.28it/s]\n"
]
}
],
"source": [
"# Sampling\n",
"with Model:\n",
" trace = pm.sample(5000, njobs=2) "
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
},
"outputs": [
{
"data": {
"image/png": 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ipiNj8Io+WPWD98MMiQq8shuCIqPHEURIUtDU5cUpM/oNn4ZAHQp9Icyyzkhz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