{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pymc3 as pm\n", "import numpy as np\n", "import pandas as pd\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "%config InlineBackend.figure_format = 'retina'\n", "%qtconsole --colors=linux\n", "plt.style.use('ggplot')\n", "\n", "from matplotlib import gridspec\n", "from theano import tensor as tt\n", "from scipy import stats" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 13 - Extrasensory perception\n", "\n", "## 13.1 Evidence for optional stopping\n", "The negative relation between the number of subjects and effect size suggests that the results are contaminated by optional stopping. Here we inferred on the correlation coefficient (same as in chapter 5): \n", "\n", "$$ \\mu_{1},\\mu_{2} \\sim \\text{Gaussian}(0, .001) $$\n", "$$ \\sigma_{1},\\sigma_{2} \\sim \\text{InvSqrtGamma} (.001, .001) $$\n", "$$ r \\sim \\text{Uniform} (-1, 1) $$ \n", "$$ x_{i} \\sim \\text{MvGaussian} ((\\mu_{1},\\mu_{2}), \\begin{bmatrix}\\sigma_{1}^2 & r\\sigma_{1}\\sigma_{2}\\\\r\\sigma_{1}\\sigma_{2} & \\sigma_{2}^2\\end{bmatrix}^{-1}) $$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", " 95%|█████████▌| 3335/3500.0 [00:21<00:01, 121.74it/s]/home/laoj/Documents/Github/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 1 contains 9 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n", " % (self._chain_id, n_diverging))\n", "100%|█████████▉| 3493/3500.0 [00:22<00:00, 172.20it/s]/home/laoj/Documents/Github/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 0 contains 2 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n", " % (self._chain_id, n_diverging))\n", "100%|██████████| 3500/3500.0 [00:22<00:00, 152.69it/s]\n" ] }, { "data": { "image/png": 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rB/jlN8xV9rNv6L1+YyRJlVaM/vfNz/Sz+WOY/woAAABd8vvf/z7UIQB+UeJ0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\noe2ahnqptFiKjJQZHB/U8nAnq3V5VVr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leUDBMHl+LlNz3K0BY7Ootsxinq2karCtJ8CV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ZYlWbtKVaXal6ys3PeXb42480e8zLe/fC/z5ar7OadOvYz1xo2IGxG/72/BkqvR24JlWyuo4VUq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\n7Nu3D5s2bcLs2bPR1taG/fv3Q6vVYtWqVX6nMZTOxUIpLeQfl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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 136, "width": 855 } }, "output_type": "display_data" } ], "source": [ "# Sample size N and effect size E in the Bem experiments\n", "N = np.array([100, 150, 97, 99, 100, 150, 200, 100, 50])\n", "E = np.array([.25, .20, .25, .20, .22, .15, .09, .19, .42])\n", "\n", "y = np.vstack([N, E]).T\n", "n,n2 = np.shape(y) # number of experiments\n", "\n", "with pm.Model() as model1:\n", " # r∼Uniform(−1,1)\n", " r = pm.Uniform('r', lower=-1, upper=1)\n", " \n", " # μ1,μ2∼Gaussian(0,.001)\n", " mu = pm.Normal('mu', mu=0, tau=.001, shape=n2)\n", " \n", " # σ1,σ2∼InvSqrtGamma(.001,.001)\n", " lambda1 = pm.Gamma('lambda1', alpha=.001, beta=.001)\n", " lambda2 = pm.Gamma('lambda2', alpha=.001, beta=.001)\n", " sigma1 = pm.Deterministic('sigma1', 1/np.sqrt(lambda1))\n", " sigma2 = pm.Deterministic('sigma2', 1/np.sqrt(lambda2))\n", " \n", " cov = pm.Deterministic('cov', tt.stacklists([[lambda1**-1, r*sigma1*sigma2],\n", " [r*sigma1*sigma2, lambda2**-1]]))\n", " \n", " tau1 = pm.Deterministic('tau1', tt.nlinalg.matrix_inverse(cov))\n", " \n", " yd = pm.MvNormal('yd', mu=mu, tau=tau1, observed=y)\n", "\n", " trace1=pm.sample(3e3, njobs=2)\n", "\n", "pm.traceplot(trace1, varnames=['r']);" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the Bayes Factor is 16.44719\n", "the approximation Jeffreys Bayes Factor is 16.19579\n", "the exact Jeffreys Bayes Factor is 21.53765\n" ] }, { "data": { "image/png": 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NjTfeWPj5//yf/zNJcv311+e0006r/xcAAACOCK08bHD4fTNmJPuN2ihv3ZrK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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 375, "width": 719 } }, "output_type": "display_data" } ], "source": [ "from scipy.stats.kde import gaussian_kde\n", "burnin=50\n", "r = trace1['r'][burnin:]\n", "\n", "fig = plt.figure(figsize=(12, 6)) \n", "\n", "gs = gridspec.GridSpec(1, 2, width_ratios=[1, 1]) \n", "ax0 = plt.subplot(gs[0])\n", "ax0.scatter(y[:, 0], y[:, 1], s=50)\n", "plt.axis([0, 215, 0, .5])\n", "plt.xlabel('Number of Subjects')\n", "plt.ylabel('Effect Size')\n", "\n", "my_pdf = gaussian_kde(r)\n", "x=np.linspace(-1, 1, 200)\n", "ax1 = plt.subplot(gs[1])\n", "ax1.plot(x, my_pdf(x), 'r', lw=2.5, alpha=0.6,) # distribution function\n", "ax1.plot(x, np.ones(x.size)*.5, 'k--', lw=2.5, alpha=0.6, label='Prior')\n", "posterior = my_pdf(0) # this gives the pdf at point delta = 0\n", "prior = .5 # height of order-restricted prior at delta = 0\n", "BF01 = posterior/prior\n", "print ('the Bayes Factor is %.5f'%(1/BF01))\n", "ax1.plot([0, 0], [posterior, prior], 'k-', \n", " [0, 0], [posterior, prior], 'ko',\n", " lw=1.5, alpha=1)\n", "# ax1.hist(r, bins=100, normed=1,alpha=.3)\n", "plt.xlabel('Correlation r')\n", "plt.ylabel('Density')\n", "\n", "# Compare to approximation Jeffreys (1961), pp. 289-292:\n", "import scipy as scipy \n", "freqr=scipy.corrcoef(y[:, 0], y[:, 1])\n", "BF_Jeffrey=1/(((2*(n-1)-1)/np.pi)**.5 * (1-freqr[0,1]**2)**(.5*((n-1)-3)))\n", "print ('the approximation Jeffreys Bayes Factor is %.5f'%(BF_Jeffrey))\n", "\n", "# Compare to exact solution Jeffreys (numerical integration):\n", "BF_Jeffex = scipy.integrate.quad(lambda rho: ((1-rho**2)**((n-1)/2)) / ((1-rho*freqr[0,1])**((n-1)-.5)), -1, 1)\n", "print('the exact Jeffreys Bayes Factor is %.5f'%(BF_Jeffex[0]/2))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 13.2 Evidence for differences in ability\n", " \n", "$$ \\mu_{1},\\mu_{2} \\sim \\text{Gaussian}(0, .001) $$\n", "$$ \\sigma_{1},\\sigma_{2} \\sim \\text{InvSqrtGamma} (.001, .001) $$\n", "$$ r \\sim \\text{Uniform} (0, 1) $$ \n", "$$ \\hat\\theta_{i} \\sim \\text{MvGaussian} ((\\mu_{1},\\mu_{2}), \\begin{bmatrix}\\sigma_{1}^2 & r\\sigma_{1}\\sigma_{2}\\\\r\\sigma_{1}\\sigma_{2} & \\sigma_{2}^2\\end{bmatrix}^{-1}) $$ \n", "$$ \\theta_{ij} = \\Phi(\\hat\\theta_{ij})$$\n", "$$ k_{ij} \\sim \\text{Binomial}(\\theta_{ij},n)$$" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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UVPXv31/bt2/X3r17lZeXp9LSUtlsNkVGRqpdu3bq1q2bbrjhhlp3NQIAAEDg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\nw6lTp7BixQqMGzeu3bnR0dE4dOiQxvfDwMAAFRUVqKiowOX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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 324, "width": 335 } }, "output_type": "display_data" } ], "source": [ "# Data\n", "# Proportion correct on erotic pictures, block 1 and block 2:\n", "prc1er=np.array([0.6000000, 0.5333333, 0.6000000, 0.6000000, 0.4666667, \n", " 0.6666667, 0.6666667, 0.4000000, 0.6000000, 0.6000000,\n", " 0.4666667, 0.6666667, 0.4666667, 0.6000000, 0.3333333,\n", " 0.4000000, 0.4000000, 0.2666667, 0.3333333, 0.5333333,\n", " 0.6666667, 0.5333333, 0.6000000, 0.4000000, 0.4666667, \n", " 0.7333333, 0.6666667, 0.6000000, 0.6666667, 0.5333333,\n", " 0.5333333, 0.6666667, 0.4666667, 0.3333333, 0.4000000,\n", " 0.5333333, 0.4000000, 0.4000000, 0.3333333, 0.4666667,\n", " 0.4000000, 0.4666667, 0.4666667, 0.5333333, 0.3333333,\n", " 0.7333333, 0.2666667, 0.6000000, 0.5333333, 0.4666667,\n", " 0.4000000, 0.5333333, 0.6666667, 0.4666667, 0.5333333,\n", " 0.5333333, 0.4666667, 0.4000000, 0.4666667, 0.6666667,\n", " 0.4666667, 0.3333333, 0.3333333, 0.3333333, 0.4000000,\n", " 0.4000000, 0.6000000, 0.4666667, 0.3333333, 0.3333333,\n", " 0.6666667, 0.5333333, 0.3333333, 0.6000000, 0.4666667,\n", " 0.4666667, 0.4000000, 0.3333333, 0.4666667, 0.5333333,\n", " 0.8000000, 0.4000000, 0.5333333, 0.5333333, 0.6666667,\n", " 0.6666667, 0.6666667, 0.6000000, 0.6000000, 0.5333333,\n", " 0.3333333, 0.4666667, 0.6666667, 0.5333333, 0.3333333,\n", " 0.3333333, 0.2666667, 0.2666667, 0.4666667, 0.6666667])\n", "\n", "prc2er=np.array([0.3333333, 0.6000000, 0.5333333, 0.2666667, 0.6666667,\n", " 0.5333333, 0.6666667, 0.4666667, 0.4666667, 0.6666667,\n", " 0.4000000, 0.6666667, 0.2666667, 0.4000000, 0.4666667,\n", " 0.3333333, 0.5333333, 0.6000000, 0.3333333, 0.4000000,\n", " 0.4666667, 0.4666667, 0.6000000, 0.5333333, 0.5333333,\n", " 0.6000000, 0.5333333, 0.6666667, 0.6000000, 0.2666667,\n", " 0.4666667, 0.4000000, 0.6000000, 0.5333333, 0.4000000,\n", " 0.4666667, 0.5333333, 0.3333333, 0.4000000, 0.4666667,\n", " 0.8000000, 0.6000000, 0.2000000, 0.6000000, 0.4000000,\n", " 0.4000000, 0.2666667, 0.2666667, 0.6000000, 0.4000000,\n", " 0.4000000, 0.4000000, 0.4000000, 0.4000000, 0.6666667,\n", " 0.7333333, 0.5333333, 0.5333333, 0.3333333, 0.6000000,\n", " 0.5333333, 0.5333333, 0.4666667, 0.5333333, 0.4666667,\n", " 0.5333333, 0.4000000, 0.4000000, 0.4666667, 0.6000000,\n", " 0.6000000, 0.6000000, 0.4666667, 0.6000000, 0.6666667,\n", " 0.5333333, 0.4666667, 0.6000000, 0.2000000, 0.5333333,\n", " 0.4666667, 0.4000000, 0.5333333, 0.5333333, 0.5333333,\n", " 0.5333333, 0.6000000, 0.6666667, 0.4000000, 0.4000000,\n", " 0.5333333, 0.8000000, 0.6000000, 0.4000000, 0.2000000,\n", " 0.6000000, 0.6666667, 0.4666667, 0.4666667, 0.4666667]) \n", "Nt = 60\n", "xobs = np.vstack([prc1er, prc2er]).T*Nt\n", "n,n2 = np.shape(xobs) # number of participants\n", "\n", "plt.figure(figsize=[5, 5])\n", "plt.hist2d(xobs[:, 0], xobs[:, 1], cmap = 'binary')\n", "plt.xlabel('Performance Session 1', fontsize=15)\n", "plt.ylabel('Performance Session 2', fontsize=15)\n", "plt.axis([0, 60, 0, 60])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "100%|██████████| 3500/3500.0 [01:05<00:00, 53.25it/s]\n" ] }, { "data": { "image/png": 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Wj+xD72H2vAP7doK/+9w7Kp0US1YtXQ3zl2ClpZ3/AzoZm2XhcVl4XA7yB54jfEhsYwhE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\no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ksu4dRTTx3Tdjo7O/nmN79JSUkJt912G1//+tfHtD4hhBDieKMqqtGv+0+MbRuxPPFH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\nLlzI/fffn7TNRMZt9+7dvPjii9TU1KCUoqysjI0bN7J8+fKJesqXtJHiu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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 136, "width": 855 } }, "output_type": "display_data" } ], "source": [ "def phi(x):\n", " # probit transform\n", " return 0.5 + 0.5 * pm.math.erf(x/pm.math.sqrt(2))\n", "\n", "with pm.Model() as model2:\n", " # r∼Uniform(−1,1)\n", " r = pm.Uniform('r', lower=0, upper=1)\n", " \n", " # μ1,μ2∼Gaussian(0,.001)\n", " mu = pm.Normal('mu', mu=0, tau=.001, shape=n2)\n", " \n", " # σ1,σ2∼InvSqrtGamma(.001,.001)\n", " lambda1 = pm.Gamma('lambda1', alpha=.001, beta=.001, testval=100)\n", " lambda2 = pm.Gamma('lambda2', alpha=.001, beta=.001, testval=100)\n", " sigma1 = pm.Deterministic('sigma1', 1/np.sqrt(lambda1))\n", " sigma2 = pm.Deterministic('sigma2', 1/np.sqrt(lambda2))\n", " \n", " cov = pm.Deterministic('cov', tt.stacklists([[lambda1**-1, r*sigma1*sigma2],\n", " [r*sigma1*sigma2, lambda2**-1]]))\n", " \n", " tau1 = pm.Deterministic('tau1', tt.nlinalg.matrix_inverse(cov))\n", "\n", " thetai = pm.MvNormal('thetai', mu=mu, tau=tau1, shape=(n, n2))\n", " theta = phi(thetai)\n", " kij = pm.Binomial('kij', p=theta, n=Nt, observed=xobs)\n", " \n", " trace2=pm.sample(3e3, njobs=2)\n", "\n", "pm.traceplot(trace2, varnames=['r']);" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the Bayes Factor is 1.13844\n", "the exact Jeffreys Bayes Factor is 0.45612\n" ] }, { "data": { "image/png": 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KMUgNAEDWI0DguFhMof377WUCBD4iPn68rRZsbvagEwAA4BUCBCRJwQMHpGg0\noWYVFckcO9ajjpCOzNJS50FqbqQGACBrECAgSQrt2WOrxaqrJcPwoBukrVBI8dJSWznY1ORBMwAA\nwAuh0z8lPXV2dmr16tXauHGjjh49qoKCAk2fPl3XX3+9amtrT/v1y5YtO+XjK1euVGFhoVvtpr3Q\n3r22WmwIf4/IPvHKSltgCDY1KTZtmkcdAQCAVPJlgDh69Ki++93vqqurS1deeaWqq6vV3Nys5557\nTm+99ZZWrFihSZMmnfZ1qqqqBg0SeXl5bredvkzTcYCaAAEnjke5sgIBAEDW8GWAePzxx9XR0aFb\nb71Vc+fOPVmfPHmyfvazn2nNmjW65ZZbTvs6xcXFuvTSS5PZqi8Em5pk9PUl1Kz8fJkOPygC8cpK\nW41BagAAsocvZyBKSko0b948zZkzJ6E+a9YsGYahhoYGjzrzp6DT/MOkSVLAlx8PJJnpECACBw9K\nkYgH3QAAgFTz5QrEYNuOent7ZVmWwuHwGb2eZVmKRCLKz893oz3fcRqgjg9hCxiykxUOyywpUeDw\n4Y8ULQVbWxWfONG7xgAAQEr4MkAM5sUXX5QkLViwYEjP7+rq0v33368NGzYoEokoHA7rkksu0fLl\nyzV69Ohh91Pp8JvatGNZUnu7NGBgvPCyyyQ/9O9DvvhcnM6550pbtyaUCvv7+cwMQ0Z8LuA6Phdw\nwucCXsuYAPHmm29q9erVqq2t1ZVXXjmkr2lsbNSkSZP0rW99S6ZpavPmzXr11Ve1Y8cO/fSnP1Vx\ncXGSu04DTU1Sd3diLS9P4jfJOJUJE2wBQg4XEQIAgMyTEQFi7dq1euihh1RaWqrbb79dodDpv607\n7rhDxcXFCUe+XnrppRo7dqx+//vf6+mnn9by5cuH1VeTD06myV23TuEBASJWWanu1laPOspcJ35j\n5IfPxemE8vJUOOBzE3/7bR3LgO8t1TLpcwH38LmAEz4XcOLFipTvp2RXr16tBx54QDU1Nbr77rtV\nUlIypK+bNWuW430RJ1Yvtm/f7mqf6crxAjmOb8VpOB3lGmhulkzTg24AAEAq+XoF4re//a2effZZ\nXXzxxfq7v/s7V+5uKC4ulmEY6unpcaHDNGdZzhfIMUCN07BKSmSFwzJ6e0/WjP5+BTo6ZI4b52Fn\nAAAg2Xy7ArF69Wo9++yzWrx4sb7zne+cUXhoaGjQiy++qPb2dttjLS0tsixLY8eOdbPdtBQ4eFDG\nsWOJxVCGlabZAAAgAElEQVRI8QkTvGkI/mEYXCgHAECW8mWAqKur0+9+9zvNmTNHN954owKnua/g\nwIEDamtrO/nnhoYGPfzww1q9erXtuWvWrJGkhAvqMpXj6sPEiVJOjgfdwG8cL5QjQAAAkPF8uYXp\nsccekyTNmDFDGzdudHzOhRdeeHJV4uabb1ZlZaXuvfdeSdJll12ml19+WS+99JI6Ozs1e/Zsmaap\nDRs2aPv27ZoxY4auuOKK1HwzHgq9/76txvwDhooVCAAAspMvA8TeD35z/pvf/GbQ59x///0qLS11\nfCwYDOr222/X888/r5dfflkrV66UYRiqqKjQDTfcoKVLlyoYDCal97RhWY4BIk6AwBA5rkA0N3vQ\nCQAASCVfBohVq1YN+/m5ubm69tprde2117rVlq8EDh6U0dWVWAyFFKuu9qYh+I5ZViYFg1I8frJm\ndHbK6OqSNWKEh50BAIBk8uUMBIbPcfsS8w84E6GQ4g6rfKxCAACQ2QgQWYr5B7iBQWoAALIPASIb\nWZbzBXLnnONBM/AzAgQAANmHAJGFAq2t9vsfcnIUnzjRm4bgWwxSAwCQfQgQWchx+1J1tRTy5Uw9\nPGQ6BIhAW5vU3+9BNwAAIBUIEFnIMUBMnuxBJ/A7KxyWWVIyoGgp2NrqTUMAACDpCBDZZpD7HwgQ\nOFtcKAcAQHYhQGSZQFOTjN7ehJqVl6f4hAkedQS/Y5AaAIDsQoDIMo63T9fUHL8QDDgLBAgAALIL\nASLLOB7fyvYlDIPjIHVLi2RZHnQDAACSjQCRTUyTAAHXmSUlsvLzE2pGJKJAR4dHHQEAgGQiQGSR\n4IEDMvr6EmpWfr7i48d71BEygmGwjQkAgCxCgMgijqcvTZokBfgYYHg4iQkAgOzBT45ZxHGAmu1L\ncAErEAAAZA8CRLaIxxXct89WZv4BbnAKEIHmZg86AQAAyUaAyBLBxkYZkUhCzQqHHbeeAGfKLCuz\nbYULHD0q49gxjzoCAADJQoDIEsw/IKlCIcXLymzlIKsQAABkHH56zBKOAYLtS3CR4xzEgQMedAIA\nAJKJAJENYjGFnOYfzjkn9b0gYzmexMQKBAAAGYcAkQWCDQ1SNJpQswoLZZaXe9QRMpHjjdQECAAA\nMg4BIgs4bl+qrZUMw4NukKkctzC1tdnCKwAA8DcCRBZg/gGpYBUUyBw1KrFomgq2tnrTEAAASAoC\nRKaLRhVqaLCVCRBIBsdVCLYxAQCQUQgQGS5UXy/FYgk1a8QImaWlHnWETGY6DFIHuJEaAICMQoDI\ncINuX2L+AUnguAJBgAAAIKMQIDIc8w9IpUG3MFmWB90AAIBkIEBkskhEwf37bWUCBJLFHD1aVl5e\nQs3o61Pg8GGPOgIAAG4jQGSwUH29FI8n1MyRI2WOGeNRR8h4hsEcBAAAGY4AkcGYf4AXmIMAACCz\nESAymFOAiLN9CUkWd1iBIEAAAJA5CBCZqq9PwcZGW5n5ByQbd0EAAJDZCBAZKrRvn2SaCTWzpETm\n6NHeNISsES8vt22TCxw+LKOnx6OOAACAmwgQGYrjW+GZnBzHiwoDrEIAAJARCBAZigABLzEHAQBA\n5iJAZCCjt1fBAwdsdQIEUoWTmAAAyFwEiAwU3LPHdvOvOXasrFGjPOoI2YYAAQBA5iJAZCC2L8Fr\njgGitVWKxTzoBgAAuIkAkYFCe/bYagQIpJJVVCRz5MjEomkq2NLiTUMAAMA1BIgMY/T2Op65H6ut\n9aAbZLP4+PG2mtNsDgAA8BcCRIYJ7t3rPP9QXOxRR8hWjtuYCBAAAPgeASLDhPbutdVikyZ50Amy\nneMKBIPUAAD4HgEiwzjOP7B9CR5wXIFobrbdkA4AAPyFAJFJ+vqc738gQMAD1qhRsgoKEovRqAJt\nbd40BAAAXEGAyCCh+nrbb3fNkhJZJSUedYSsZhgMUgMAkIEIEBnEcf6B1Qd4iAABAEDmIUBkEKf5\nhzgBAh5ikBoAgMxDgMgU/f0K7t9vK7MCAS85DlI3NdmOGgYAAP5BgMgQoYYGKR5PqJkjR8ocPdqj\njoAP7iDJy0uoGX19CnR0eNQRAAAYLgJEhggOtn3JMDzoBvjAYIPUbGMCAMC3CBAZwvH+By6QQxqI\nV1TYagxSAwDgXwSITBCLHd/CNLDM/APSACcxAQCQWQgQGSDY2CjFYgk1q6hI5rhxHnUEfGjQLUwM\nUgMA4EsEiAwQqq+31WI1Ncw/IC2YpaVSKJRQM44dk3H0qEcdAQCA4SBAZIDgvn22WrymJuV9AI6C\nQec5iMZGD5oBAADDRYDwO8tyXoGorvagGcBZvKrKVgsRIAAA8CUChM8FDh2ScexYYjEUctx3Dngl\n5hAgWIEAAMCfCBA+57h9qarKtucc8JLTCkSwsZFBagAAfIgA4XODDlADacQsK5OVm5tQM3p6FDh8\n2KOOAADA2SJA+JzTCgTzD0g7gYDMykpbObh/vwfNAACA4SBA+JjR26tga6utHidAIA0xBwEAQGYg\nQPhYsKHBtofcHDtWVlGRRx0Bg3Ocg2AFAgAA3yFA+FiQ+Qf4SHzCBFsteOAAg9QAAPgMAcLHQk4n\nMLF9CWnKHDtWVn5+Qs2IRBRoa/OoIwAAcDYIEH5lmo7bP1iBQNoyDMf7SZiDAADAXwgQPhVsbpYR\niSTUrHBYZmmpRx0Bp+e4jYkAAQCArxAgfMpp/iFeXS0ZhgfdAEPjNEgdIkAAAOArBAifcvqtLfc/\nIN05HuXa1CSZpgfdAACAs0GA8CmnAOH0210gnVglJbIKChKL0agCLS3eNAQAAM4YAcKPIhHnC+QI\nEEh3huE4B8E2JgAA/IMA4UNOZ+ebo0fLKiz0qCNg6LhQDgAAfyNA+BDbl+BnMaeTmBoaPOgEAACc\nDQKEDzlt93DaFgKko/jEibZasKVFGnAsMQAASE8ECB9yPIHJ4YIuIB1ZRUUyR48eULS4DwIAAJ8g\nQPiM0durQHu7rc4WJviJ0ypEiDkIAAB8IeR1A2ers7NTq1ev1saNG3X06FEVFBRo+vTpuv7661Vb\nWzuk13j33Xf1xBNPaNeuXerv71dFRYWuuOIKXX311TLS9EK24IEDtpo5bpyUn+9BN8DZiU2YoJyt\nWxNqzEEAAOAPvgwQR48e1Xe/+111dXXpyiuvVHV1tZqbm/Xcc8/prbfe0ooVKzRp0qRTvkZdXZ1+\n/OMfa8yYMfrsZz+roqIibdq0SStXrlRra6u++MUvpuabOUNOp9U4DaUC6cxxBaKh4fjpYmka3gEA\nwHG+DBCPP/64Ojo6dOutt2ru3Lkn65MnT9bPfvYzrVmzRrfccsspX+ORRx5RTk6O7r77bpWUlEiS\nFi5cqH/6p3/Sc889p8WLF6umpiaZ38ZZcTyBifkH+Ey8slIKBqV4/GTN6OyUcfSorFGjPOwMAACc\nji9nIEpKSjRv3jzNmTMnoT5r1iwZhqGG02yF2LVrl5qamnTZZZedDA8nXH311bIsS3/6059c79sN\njgGCFQj4TU7O8RAxQIhtTAAApD1frkAsW7bMsd7b2yvLshQOh0/59bt375YkTZ061fbYlClTEp6T\nToxjxxQ4fDixGAg4/iAGpLvYxIm2LXnBhgZFL7jAo44AAMBQ+DJADObFF1+UJC1YsOCUzzt48KAk\nacyYMbbHwuGwCgsL1draOux+Kt3+wb6uThp423RVlQrTcKsVBuf658KvZs+WBgxSFx49KmXp3w+f\nCzjhcwEnfC7gNV9uYXLy5ptvavXq1aqtrdWVV155yuf29vZKkvLy8hwfz8vLO/mctLJvn71WXZ3y\nNgBXOB10UF+fMBcBAADST0asQKxdu1YPPfSQSktLdfvttysUSo9vq6mpydXXK9i2TTnd3Qm13qIi\n9bv8PkiOE78xcvtz4VuWpWLLktHTk1A+tmVLVh0MwOcCTvhcwAmfCzjxYkXK9ysQq1ev1gMPPKCa\nmpqEE5VO5cSMRF9fn+PjfX19KigocLVPNwQd/oWRTT9oIcMYhuNxrsH6eg+aAQAAQ+XrAPHb3/5W\nq1at0sUXX6w777xTI0eOHNLXlZWVSZIOHTpke6ynp0c9PT0qLy93tdfhMnp7FThyZEDRUDzN+gTO\nhNMdJk53nQAAgPTh2wCxevVqPfvss1q8eLG+853vDDrP4GTatGmSpJ07d9oee+eddyRJ06dPd6dR\nlwSam201c9w4KSfHg24Ad8QdZng4yhUAgPTmywBRV1en3/3ud5ozZ45uvPFGBQKn/jYOHDigtra2\nk3+uqanRpEmTtH79enV0dJysW5alZ555RsFgUIsWLUpa/2cj2NJiq8UrKjzoBHCP0x0mgYMHbXMR\nAAAgfaTHtPEZeuyxxyRJM2bM0MaNGx2fc+GFF55clbj55ptVWVmpe++99+TjX/3qV3XXXXfpRz/6\nkZYuXarCwkKtW7dOdXV1+tznPpd2W5iCDisQbF+C31nhsMyyMgUGHJscrK9X7GMf86grAABwKr4M\nEHv37pUk/eY3vxn0Offff79KS0sHfXzKlCm66667tGrVKq1atUrRaFRVVVW66aabtGTJEtd7Hi5W\nIJCpYhMnKndAgAg1NBAgAABIU74MEKtWrXLl+ZMnT9b3vvc9N1pKLstSwClAsAKBDBCvrpY2bUqo\ncRITAADpy5czENkmcOiQjEgkoWbl58sawpG1QLqLOR3lun+/ZJoedAMAAE6HAOEDjicwlZdLhuFB\nN4C7zLIyWfn5CTUjEnH83AMAAO8RIHzAcYCa+QdkCsPgOFcAAHyEAOEDDFAj0zluYyJAAACQlggQ\nPsARrsh0jisQDFIDAJCWCBDpLhJR4COX3Z0QLyvzoBkgOWITJthmegLt7TKOHfOoIwAAMBgCRJoL\ntrVJlpVQM0tKpHDYo46AJAiHHUMx25gAAEg/BIg0x/wDsgXbmAAA8AcCRJoLNDXZaiYBAhnIcZCa\nAAEAQNohQKQ5BqiRLZxWIIKNjVwoBwBAmiFApDPLYgsTsoY5bpysAbM9Rn+/Y4gGAADeIUCkMaOz\nU0ZPT2IxJ0fm2LHeNAQk0yAXyrGNCQCA9EKASGPBgwdttfi4cVKA/9qQmWJOAYKTmAAASCv8JJrG\nAm1ttppZWupBJ0BqOJ7EtG9f6hsBAACDcjVA/PrXv9auXbvcfMmsFhhsBQLIULGqKvuFcocOyejq\n8qgjAAAwUMjNF/vjH/+oP/7xj6qsrNTixYu1cOFClZSUuPkWWcVpCxMrEMho+fmKl5fbBqeD9fWK\nnX++R00BAICPcnUFYsmSJSoqKlJTU5P+8z//U3/7t3+rn/zkJ1q/fr1isZibb5UVHFcgGKBGhnPc\nxsQcBAAAacPVFYgbb7xRX/va1/TWW29p3bp12rx5s7Zu3aqtW7eqsLBQ8+fP16JFizR58mQ33zYz\n9fcrcOSIrWyyhQkZLlZdrdz16xNqDFIDAJA+XA0QkhQMBjV79mzNnj1bsVhMW7Zs0bp167Rlyxa9\n8MILeuGFF1RVVaUlS5ZowYIFGjlypNstZIRAe7tkWQk1s6REys31qCMgNRxXIPbvl2IxKeT6v7IA\nAMAZSur/G4dCIc2ZM0dz5sxRJBLRpk2b9Nprr+mtt97SY489pv/4j//Q3LlztXTpUk2dOjWZrfiO\n4/wD25eQBcwxY2QVFsro7v6wGI0q2Nys+IQJ3jUGAAAkpfAY12AwqNzcXOXm5ir0wW8RTdPU66+/\nrh/+8Ie655571N7enqp20p7j/AMD1MgGhuF8HwQXygEAkBaSvh9g586deuWVV7R+/Xr19vZKknJy\ncjR//nxdfvnlikQiWrNmjbZt26Y77rhDK1asUFlZWbLbSnsBhzDF/AOyRXziROW8/XZCLdTQoH6P\n+gEAAB9KSoA4dOiQ1q5dq1deeUUtLS0n65MmTdLll1+u+fPnq6Cg4GR99uzZWrVqlZ544gk9+uij\nuu2225LRlq8EnS6RI0AgS7ACAQBA+nI1QKxbt06vvPKKtm/fLtM0JUkFBQVasGCBLr/8ctXU1Az6\ntcuWLdPWrVu1Y8cON1vyJ8viEjlktXhVlRQISB/8e0SSAocPyzh6VBYHLwAA4ClXA8QvfvGLk//5\n/PPP15IlSzR37lzl5OQM6evPOecc7dmzx82WfMno7JQRiSTUrNxcfnBC9sjLO36hXFNTQjnU0KDo\njBkeNQUAACSXA8To0aO1ZMkSLV68WKVnMfA7f/58TZs2zc2WfMlp9cEcO1YyDA+6AbwRr6mxBYhg\nfT0BAgAAj7l+E/W0adOGFB4eeeQRPfLIIwm1qVOnat68eW625EuOR7hyAhOyTGziRFuNG6kBAPCe\nqwHiiSee0NatW4f03IMHD+rPf/6zm2+fMRznH7gDAlkm7jAzFWxsPH6hHAAA8MywtzC9PeCoxY6O\nDlttoIMHD2rnzp0nB62RiBUI4PjN61ZRkYxjxz4sxmIKNjUp7rA6AQAAUmPYAeKuu+5K+POGDRu0\nYcOGIX3tDPYyO+IEJkDHL5RzuA8iuG8fAQIAAA8NO0B873vf0549e7R792698cYbys/PV1FR0Sm/\nJhwOq7a2Vp///OeH+/aZJxpV4PBhW9lkCxOyULymhgvlAABIM8MOELNmzdKsWbMkSZ/73Od0+eWX\n6wtf+MKwG8tWgfZ2ybISauaoUVJenkcdAd5xGqQOMkgNAICnXD3G9aabblJVVZWbL5l1gu3ttho3\nUCNbOV4od+SIjCNHZI0a5WFnAABkL1cDxOLFi918uawUaGuz1QgQyFq5uYpXVh4/fekjQg0NihIg\nAADwxLACxIMPPqiZM2eevLvhwQcfPKOvNwxDN91003BayDiBQ4dsNY5wRTaLVVfbAkSwvl7RCy7w\nqCMAALLbsALE2rVrVVhYeDJArF279oxfgwCRKNDRYauZo0d70AmQHuLV1dKAO2NC9fUedQMAAIYV\nID7zmc9oypQpCX/G8DiewDRmjAedAOnBcZD6wAEpGpVycjzoCACA7DasAPHZz372lH/GGYrFFDhy\nxFY2S0o8aAZID1ZJiawRI2R0dX1YjMcVPHDA8bZqAACQXAGvG8CHAkeO2I5wtUaMkHJzPeoISAOG\noVh1ta0c4jhXAAA84eopTJLU0dGhZ555Rp/+9KdVXFx8sv7ss8/qhRde0KFDh1RTU6O/+Zu/Sdj+\nBOcBarYvAcfnIHLq6hJqQeYgAADwhKsrEIcPH9YPf/hDPfPMM2ptbT1Zf/755/Xoo4+qpaVF/f39\neu+99/QP//APamlpcfPtfc/xBCYGqAHHFYhgQ4NtxQ4AACSfqwHimWeeUUdHh66++mpNmDBBkhSP\nx/XEE09Ikr7+9a/r0Ucf1Te+8Q319fXp6aefdvPtfY8TmABn8fHjpWAwoRY4elSGw6EDAAAguVwN\nEFu2bFFlZaW+9KUvKT8/X5K0Y8cOdXZ26txzz9UVV1yh/Px8XX755Zo2bZrqBmxJyHaOW5gYoAak\nnBzFKyttZeYgAABIPVcDxKFDhzRt2rSE2tatWyVJl112WUJ9/Pjxam9vd/PtfY8ZCGBwjtuYmIMA\nACDlXA0Q0WhUwQHbDLZv3y5JmjlzZkLdMAwZhuHm2/ueY4BgCxMg6YML5QZgBQIAgNRzNUCMHDlS\nTU1NJ//c0tKihoYGlZWVqaysLOG5Bw8eVFFRkZtv72tGb6+M3t7EYigka+RIbxoC0ozjCsSJC+UA\nAEDKuBogpk2bpnfeeUd//OMftX//fv3bv/2bJGnevHkJz2tqatKOHTs0adIkN9/e1wadf2CVBpAk\nWaNGyRwYqE1Twf37vWkIAIAs5eo9EJ/61Ke0ceNG/frXvz5ZGz16tD75yU+e/PPWrVv1wAMPKB6P\na8mSJW6+va+xfQk4vfjEiQp8sC3yhFBDg+K1tR51BABA9nF1BaKmpkY/+MEPdMEFF6iiokIXXXSR\n7rzzzoStSn19fers7NR1112nSy65xM239zXHI1wZoAYSMEgNAID3XL+J+mMf+5i+//3vD/r4jBkz\n9K//+q+qdDiSMZuxAgGc3qCD1JbFdj8AAFLE1RWIoSgsLCQ8OOAWauD04uPHS6HE33sYXV0KcKEc\nAAAp4/oKhGVZeuedd1RfX6+enh5ZlnXK53/mM59xuwVf4hI5YAhCIcXHj7dtWwrW17NiBwBAirga\nII4cOaJ77rlHDWdwNjsBQpJpsoUJGKLYxIm2ABGqr1f0wgs96ggAgOziaoD493//dzU0NCgnJ0fT\npk1TSUmJAoGU75LyHePIEck0E2pWQYEUDnvUEZC+4jU10p/+lFBjkBoAgNRxNUBs27ZNBQUF+slP\nfqLy8nI3XzqjOe3fZvUBcBabONFWCzY3S5GIlJfnQUcAAGQXV5cHuru7NXPmTMLDGQo6bV/iCFfA\nkTVypH0+yDQVbGz0piEAALKMqwGiuLhYhYWFbr5kVmD+ATgzcYdViNAZzF4BAICz52qAuPDCC/X2\n22+7+ZJZwfESOQIEMCjHbUzMQQAAkBKuBojPf/7zMk1TDz/8sKLRqJsvndGYgQDOTLymxlYL1dcf\nv1AOAAAklatD1K+++qo+/vGP69lnn9X69etVW1urMWPGKBQa/G2++tWvutmCL7GFCTgz8YoKKSdH\n+sgvKozubgU6OmSOHethZwAAZD5XA8Rjjz2W8Odt27ad9muyPkDEYjK6uhJrhiFz5Ehv+gH8IBRS\nrKpKob17E8rB+noCBAAASeZqgFi4cKEMw3DzJTNe4OhRW80aMUI6xaoNgOOD1AMDRKihQdGLLvKo\nIwAAsoOrP6V+85vfdPPlsoLhNP8wapQHnQD+Equu1sBbHxikBgAg+bgm2mNOKxBsXwJOL15dbasF\nm5ulvj4PugEAIHskbZ9MU1OTduzYoebmZvX29uob3/jGyce6uro0YsSIZL21rwSOHLHVWIEATs8a\nMULm6NGJhxBYlkKNjYqdc453jQEAkOFcDxDt7e361a9+pbq6uoT6iQDR2Nio73//+/rKV76ihQsX\nuv32vkOAAM5evLradopZsL6eAAEAQBK5uoWpu7tbf//3f6+6ujqFw2FddNFFqh6wzaC9vV3RaFS/\n+tWvtGfPHjff3pccA0RJiQedAP7jeKEcN1IDAJBUrgaIJ598Uh0dHVq0aJEeeugh3XbbbTr33HMT\nnjNr1izddtttMk1Tzz77rJtv70uG0ylMzEAAQ+I0B8GFcgAAJJerAWLz5s0qLS3V17/+deXn5w/6\nvFmzZmnq1Kl6++233Xx7X2ILE3D2Tl4o9xFGT48C7e0edQQAQOZzNUC0t7dr6tSpp7x5+oQJEybo\nqMNv37NKb6+MgSfGhEKyioq86Qfwm2BQsQkT7OV9+1LfCwAAWcL1Y1yHepFcLBYbUtDIZI6rDyNH\nSlzGBwyZ4zYm5iAAAEgaVwNERUWF3n77bcVisVM+r7+/X9u2bVN5ebmbb+873AEBDB+D1AAApJar\nAWLOnDnq6OjQL3/5S/X29jo+p6OjQ/fee68OHz6sOXPmuPn2vsMJTMDwOV4o19LChXIAACSJq3uI\nli5dqldffVXr16/X1q1bNXXqVLV/MMx43333qaOjQ7t27VI8HldlZaU++clPuvn2vuMUICwGqIEz\nYhUVyRwzRoGOjo8ULYX271dsyhTvGgMAIEO5GiAKCgp0991364EHHtC2bdu0bdu2k4/9+c9/Pvmf\nZ86cqRtvvPGUJzUNVSwW0+OPP67/+Z//0cc+9jHdeeedQ/q6ZcuWnfLxlStXqrCwcNj9nYrBCUyA\nK2I1Ncr9aIDQ8UFqAgQAAO5zfYp51KhR+v73v6+GhgbV1dWpra1NfX19ys/PV3l5uc4//3xVVVW5\n8l5NTU36xS9+oebmZllnce57VVXVoEEiLy9vuO2d1qBD1ADOSHziROmNNxJqoYYGRTzqBwCATJa0\nY5AmTpyoiQ7DjW45duyYbr/9dpWXl+sf//Ef9e1vf/uMX6O4uFiXXnppErobGu6AANwx6CC1ZXGq\nGQAALktKgOjp6VFnZ6f6+vpUVFSkUaNGuX5kaywW08KFC/WFL3xBubm5rr52SliW8ylMBAjgjJkV\nFbLy8mREPlxzMHp7FWhrk1lW5mFnAABkHtd+qu/r69PTTz+tDRs2qGHAEYo5OTmaNm2aFi1apPnz\n5ysQGP7hT6NGjdLXvva1Yb+OJFmWpUgk4spMxlAZXV1SPJ7YR36+lMIegIwRCCheVaXQ++8nlEMN\nDeonQAAA4CpXAsTOnTv1L//yL+rs7HR8PBqNqq6uTnV1dXrqqad06623qrKy0o23Hpauri7df//9\n2rBhgyKRiMLhsC655BItX75co0ePHvbrn/J77O+XBg5pV1aqKA3+XpBc6fDZz0izZ0stLQmlwqNH\nJZ/8ffO5gBM+F3DC5wJeG3aA2LNnj+655x719/ersrJSV111lc477zyNGTNGeXl56u7uVmNjo7Zu\n3aqXXnpJjY2N+sEPfqB77rlHFRUVbnwPZ62xsVGTJk3St771LZmmqc2bN+vVV1/Vjh079NOf/lTF\nxcXJe/NDh+w1F0ILkLVqa+21PXtS3wcAABluWAHCsiz98pe/VH9/v5YuXaq//uu/tm1PKi4u1rnn\nnqtzzz1X1113nR566CGtX79eP//5z/Wzn/1sWM0Pxx133KHi4mLVfuSHjksvvVRjx47V73//ez39\n9NNavnz5sN6jqalp0Mdy33tP4e7uhFq/Yaj3FF8DfzvxG6NTfS5w9oxwWMUD/jel3bvV+f77ssJh\nb5oaAj4XcMLnAk74XMCJFytSwxpG2LJli5qamnTppZfqC1/4wmlnG8LhsL797W9r1qxZamho0Ouv\nvz6ctx+WWbNmJYSHE6688kpJ0vbt25P6/pzABLjLKiiQOW6crR4cMJMFAACGZ1gBYuPGjTIMQ3/1\nV3815K8xDENf/vKXZRiG1q9fP5y3T4ri4mIZhqGenp6kvg93QADuczzOtb7eg04AAMhcwwoQu3fv\n1iWXPp0AACAASURBVIQJE1ReXn5GX1dWVqYpU6Zo9+7dw3n7s9bQ0KAXX3xR7e3ttsdaWlpkWZbG\njh2b1B44whVwX7ymxlYLESAAAHDVsALE4cOHVV1dfVZfO378eB11+CE6GQ4cOKC2traTf25oaNDD\nDz+s1atX2567Zs0aSdLcuXOT2pPTCoRVUpLU9wQyneMKxP79xy+UAwAArhjWEHVPT48KBx5FOkT5\n+fmKRqNn/d6NjY1qbGxMqHV2diZsi7rwwguVl5enm2++WZWVlbr33nslSZdddplefvllvfTSS+rs\n7NTs2bNlmqY2bNig7du3a8aMGbriiivOurfTisWO3wPxUYYhM5mnPgFZwCwrk5WfL6Ov72TN6OtT\noLVV5hmulAIAAGfDPoXJjUvhzsa6detsKwiNjY36+c9/fvLP999/v0pLS21fGwwGdfvtt+v555/X\nyy+/rJUrV8owDFVUVOiGG27Q0qVLFQwGk9a70/Ylq6hIcvm2biDrBAKKT5ig0K5dCeVQfb36CRAA\nALjCtz+xLlu2TMuWLRvSc1etWmWr5ebm6tprr9W1117rdmunZXACE5A0sepqW4AI1tdLSd6WCABA\nthh2gDhy5MhZDUMfcfghOls4DlBzAhPgirjDXBaD1AAAuGfYAWLdunVat26dG71kjcDA+QcRIAC3\nxB0GqQMHD8ro6ZFVUOBBRwAAZBZvBhiynOE0A8EANeAKKxyWWVZmq3OhHAAA7hjWCsR///d/u9VH\nVgl0dtpqnMAEuCc2caJyW1sTaqH6esWmT/eoIwAAMgcrEB5wChAWW5gA1zhdKMeN1AAAuIMA4QGn\nLUysQADuGfRCOdP0oBsAADILASLVLIstTECSmaWlssLhhJoRiSjQ0uJRRwAAZA4CRIoZ3d1SPJ5Q\ns/LypPx8jzoCMpBhOJ7GFGKQGgCAYSNApJjhNP/A6gPgOsdtTMxBAAAwbASIFGP7EpAaToPUXCgH\nAMDwESBSjFuogdSITZggGUZCLdDeLuPYMY86AgAgMxAgUowtTECK5OcrzoVyAAC4jgCRYmxhAlIn\nXl1tq4X27Ut9IwAAZBACRIo5rkCwhQlIihgBAgAA1xEgUsxxBoIVCCAp4rW1tlpw/34pGvWgGwAA\nMgMBIsXYwgSkjllSYj+kIB5nDgIAgGEgQKRSLOZ4Aow1YoQHzQBZwDCcj3NlGxMAAGeNAJFCjvMP\nRUVSKORBN0B2iBEgAABwFQEihQJdXbYa25eA5IpNmmSrBevrJdP0oBsAAPyPAJFCjvMPnMAEJJVZ\nXi4rPz+hZvT1Kdjc7FFHAAD4GwEihYwjR2w1LpEDkiwQcJyDCO7Zk/peAADIAASIFGILE+AN5iAA\nAHAPASKFuEQO8IbTHERo3z7p/7d35/FR1ff+x99nlkw2EkLCagRC2NeERRAREFwoSK1FofXhrV6r\n91a9tbW96q/1YcHW4n6v9lofba8tfbQ+LEJprYpFcMFEEC47hC0ge4AAAQkhy2zn90dMZJgJDMxy\nZpLX8/HIA/meOWc+B76Geee7HNOMfzEAACQ5AkQc8RA5wBq+K68M2u3MOHNGtqoqiyoCACB5ESDi\niIfIARZxOOTt3j24ee9eC4oBACC5ESDiiClMgHVCLqQmQAAAcMkIEPFSXy+joSGwzeGQmZ5uTT1A\nGxNyITU7MQEAcMkIEHEScv1Du3aSYVhQDdD2eHv2DPr/zXbypIxTp6wpCACAJEWAiJNQW7gyfQmI\no9RU+fLzg5odn39uQTEAACQvAkScGOzABFjOW1gY1EaAAADg0hAg4oQdmADrhQwQe/bwPAgAAC4B\nASJO2IEJsJ63Z0/JFvhtz3bqlGysgwAAIGwEiDhpcRE1gPhxuRofKncepjEBABA+AkSchFxEzRQm\nIO5CTWOyEyAAAAgbASJOQk1hYgQCiL8WF1KzDgIAgLAQIOLBNBmBABKEt0cPyW4PaLOdPi3biRMW\nVQQAQHIhQMSBUV8veb2BjU6nzNRUawoC2rKUFHm7dw9q5qnUAACEhwARBy1OX+Ip1IAleB4EAACX\njwARB0xfAhKLt1evoDbWQQAAEB4CRBywgBpILL4ePSSHI6DNOHNGtspKiyoCACB5ECDiINQIBE+h\nBizkdIZeB7FrlwXFAACQXAgQcRDyKdSMQACW8vbtG9TmJEAAAHBRBIg4CDkCQYAALBUqQDg+/zx4\nxzQAABCAABEHIUcgmMIEWMp3xRUy09MDGz0eOfbts6QeAACSBQEiDhiBABKQYYQehSgvt6AYAACS\nBwEiDgy2cQUSkqdPn6A2AgQAABdGgIg1t7vxSdTnstlkZmRYUw+AZt4QAcJ++LCMmhoLqgEAIDkQ\nIGKsxelLPIUasJzZvr38nTsHtbOdKwAALSNAxBhbuAKJjWlMAABcGgJEjPEQOSCxtfg8CNO0oBoA\nABIfASLGGIEAEpu3oEByOALajOpq2SorLaoIAIDERoCIMbZwBRKcyyVvz55BzU6mMQEAEBIBIsZ4\niByQ+EI+D2L7dgsqAQAg8REgYowRCCDxefr1C2pz7N0r1dVZUA0AAImNABFjPEQOSHz+Ll3kz8k5\nr9HfuJgaAAAEIEDEmC3EFCZGIIAEYxjy9u8f1Mw0JgAAghEgYsnrlXH2bFCzmZlpQTEALsQzYEBQ\nm3PHDsnvt6AaAAASFwEihoyamqA2MyMjaMtIANbzFhZKTmdAm3H2rOwHD1pUEQAAiYkAEUM8RA5I\nIk5nyKdSO5nGBABAAAJEDPEQOSC5eENMY2IdBAAAgQgQMcQWrkBy8YRYSG0/ckTGqVMWVAMAQGIi\nQMQQD5EDkouZnS1ft25B7c4dOyyoBgCAxESAiCFGIIDk4xk4MKiNdRAAAHyFABFDPEQOSD4hnwex\ne7dUX29BNQAAJB4CRAzxEDkg+fiuvDJ4swOvV86dO60pCACABEOAiCFGIIAkZBjyDBoU1OwsK7Og\nGAAAEg8BIoZYAwEkJ8/gwUFtjh07JI/HgmoAAEgsBIhY8vsDfmumpkopKRYVAyBc3l69ZKalBbQZ\nDQ1y7NplUUUAACQOAkQc8RA5IEk4HKF3Y2IaEwAABIh4YvoSkDxCroPYti1oZBEAgLaGABFHLKAG\nkoe3b1+Z5005NGpr5dizx6KKAABIDASIOPJnZlpdAoBwpaTI269fUDPTmAAAbR0BIo4YgQCSS8jd\nmLZulUzTgmoAAEgMBIgYenXHDpWf8zA51kAAycXTv79ktwe02U6fln3/fosqAgDAeg6rC4iU1+vV\n/Pnz9c4772jAgAGaM2dO2Ofu3LlTixYt0q5du+R2u9W1a1dNnjxZU6ZMkWEYEdf26Lp10rp1mtC5\nsx4dPFgjGYEAkktamrx9+jQ+A+Iczk2b5OvZ05qaAACwWFIHiMOHD+vll1/WkSNHZF7ilIKysjLN\nnTtXubm5uv3225WZmak1a9Zo3rx5qqys1N133x21Oj+prNSnx47pxXHjdHufPlG7LoDYcw8ZEhQg\nUrZsUf306ZKNQVwAQNuTtP/61dTU6LHHHpPf79czzzxzyee/9tprcjqd+vnPf66pU6dq/Pjx+vGP\nf6yRI0fqn//8p/bt2xfVen2mqR8/9ZRWrFgR1esCiC3v4MFB05iM6mrZ9+61qCIAAKyVtAHC6/Vq\n/Pjx+uUvf6lu3bpd0rm7du3S4cOHdfXVVysnJyfg2JQpU2SapkpLS6NZriTJ5/PpV7/6VdSvCyB2\nzLQ0eULsxpSyaZMF1QAAYL2kncLUvn173XfffZd17u7duyVJffv2DTrW58spRk2vibZPP/1U3/ve\n95R1CeshnnvuuQsef/TRRyMtS5J0/fXX68Ybb2zx+NKlS/XBBx9E5b3a4j39+7//uyTp7NmzEb1P\nIt1Ta/x7CnVPtqoqOc7/nrBundyrVrV4nXDvKSMjQ1Jk/YK/p8uXqPcUSb9I1HuKBPfU6HL7RSLf\n0+Xinr7y+uuvR+X9L0XSBohIHD9+XJKUm5sbdCwtLU0ZGRmqrKyM2ftXVVWpa9euYb/+YiMsTd9Q\nIpWbm3vB98rNzY3ae7XFe2oS6fsl0j21xr+nkO+TmiodOBD0FGqn2y2dN4rZ5FLvKZL74+/p8iX6\nPV3Oeyf6PV0O7imyGpLhni4V92StpJ3CFIm6ujpJksvlCnnc5XI1vyYW3G53zK4NIAbsdinEDxz0\n5Q8jAABoS9rkCEQiuJThx8OHD0ftWhdSVVV1wfeqqqqK2nu1xXtqEun7JdI9tca/p5bex5aZKceR\nI4GNR4/K3a2bFGLb53DvKRpTmPh7unyJek+R9ItEvadIcE+NLrdfJPI9XS7uyVptcgQiLS1NklRf\nXx/yeH19vdLT02P2/pcyfQlAYvC3bx+0G5O8XtlOn7amIAAALGKYl/oAhQQ1c+ZMDRw4MKwHyb3/\n/vv6/e9/r+9973uaNGlSwLHa2lrdfffdGjRokGbPnh1RTaEeRjdu3Di9+eabEV0XyalpbmO4IxVI\nPOlvvCHnxo0BbZ6iItXeccdlX5N+gVDoFwiFfoFQLnU30mhokyMQ/b7cknHHeQ+HkqTt27dLkvr3\n7x/197Xb7XrooYeifl0A8eEeNiyozbl1q9TCaCYAAK1RmwgQFRUVOnbsWPPve/bsqYKCAq1atUpV\nVVXN7aZpavHixbLb7ZowYUJUa7Db7Xr++ed1zTXXRPW6AOLH26+fzC+nQDbzeBpDBAAAbUTSLqI+\ndOiQDh06FNBWXV2tVefsy15cXCyXy6WHH35Y3bp100svvdR87N5779WTTz6p2bNna+rUqcrIyNDK\nlStVVlamWbNmqUuXLlGp05A0oUsXPTh3rsbedFNUrgnAIg6HPMOGKeW85z+kbNwoz4gRFhUFAEB8\nJW2AWLlypf76178GtB06dEj/9V//1fz7V155RZ06dQp5fp8+ffTkk09qwYIFWrBggTwej/Lz83X/\n/ffruuuui1qd66ZPV9+sLJ2ePDlq1wRgHXdRUVCAcJSXyzhzRma7dhZVBQBA/CRtgJg5c6ZmzpwZ\n1msXLFgQsr2wsFA/+clPollWkL5ZWTLT0yVH0v5RAziHr6BA/pwc2U6d+qrRNOXcuFHua6+1rjAA\nAOKkTayBsJo/K8vqEgBEi2HIU1wc1JyyYYMFxQAAEH8EiDhgWgPQurhDBAj7oUOy8WRqAEAbQICI\nA0YggNbF37mzfCH23XYyCgEAaAMIEHFgZmZaXQKAKPMMHx7UlrJ+vdQ6ns0JAECLCBBx4GcKE9Dq\nuIcNk8572rzt5EnZDxywqCIAAOKDABEHJlOYgFbHzM6Wt7AwqJ3F1ACA1o4AEWPl1dWMQACtVKjF\n1M6NGyWfz4JqAACIDwJEjA1/5x3d9p//qRUrVlhdCoAo8wwZIjmdAW1Gba0cO3daVBEAALFHgIiD\nT//v//Ttb39bb775ptWlAIim1FR5Bg4Mak7ZuNGCYgAAiA8CRJz4fD498sgjjEQArYy7qCiozbl1\nq1Rfb0E1AADEHgEijnw+n371q19ZXQaAKPL26yczPT2w0eNpDBEAALRCBIg4W7FihXbv3m11GQCi\nxeGQZ+jQoOaU9estKAYAgNgjQMSZaZoqKSmxugwAUeQO8VA5x+7dMqqrLagGAIDYIkBY4MyZM1aX\nACCKfD16yJ+TE9homo1bugIA0MoQICzQjudCAK2LYcgTYhSC3ZgAAK0RASLODMPQhAkTrC4DQJSF\n2o3JfuiQbMeOWVANAACxQ4CIs2uuuUaFhYVWlwEgyvydO8t3xRVB7SkbNlhQDQAAsUOAiCO73a6H\nHnrI6jIAxIi7uDiozblhg2SaFlQDAEBsECDixG636/nnn9c111xjdSkAYsRTVCQZRkCb7eRJ2ffv\nt6giAACijwARY4ZhaNy4cfrLX/6iWbNmWV0OgBgys7Lk7d07qJ1pTACA1sRhdQGt2S9+8QuNHz9e\nvUN8oADQOrmLi+XYtSugzblpk+qmT5ccfMsFACQ/RiBi6J577iE8AG2MZ/BgyekMaDNqa+UoL7eo\nIgAAoosAAQDRlJoqz8CBQc1MYwIAtBYECACIspC7MW3bJtXXW1ANAADRRYAAgCjz9usnMz09sNHj\nkXPLFmsKAgAgiggQABBtdnvjlq7nSdm40YJiAACILgIEAMSAO0SAcOzeLeP0aQuqAQAgeggQABAD\nvh495O/QIbDRNOXctMmaggAAiBICBADEgmHIPXx4UHPK+vUWFAMAQPQQIAAgRjwhdmOyHz4sW2Wl\nBdUAABAdBAgAiBF/x47y5ecHtfNMCABAMiNAAEAMhXwmxIYNkmlaUA0AAJEjQABADHmKiiTDCGiz\nnTol+4EDFlUEAEBkCBAAEENmu3by9u4d1O7cvNmCagAAiBwBAgBiLNRD5ZxbtjCNCQCQlAgQABBj\nnkGDJFvgt1vbF18wjQkAkJQIEAAQY2Z6urx9+gS1M40JAJCMCBAAEAeeoUOD2pjGBABIRgQIAIiD\nlqYxac8eiyoCAODyECAAIA5amsakdeviXwwAABEgQABAnLhDTGPSunVMYwIAJBUCBADEiXfwYMlu\nD2xkGhMAIMkQIAAgTsy0tNDTmNavj38xAABcJgIEAMSRe8iQ4MYNG5jGBABIGgQIAIgjb4jdmFRV\nJdvhw9YUBADAJSJAAEAcmenp8hYUBLU7t261oBoAAC4dAQIA4swzeHBQGwECAJAsCBAAEGeeQYOC\n2uxHjsh24oQF1QAAcGkIEAAQZ2b79vLl5we1MwoBAEgGBAgAsEDIaUxlZRZUAgDApSFAAIAFQk5j\n2r9fRnW1BdUAABA+AgQAWMDfubP8HTsGtTu3bbOgGgAAwkeAAACLMI0JAJCMCBAAYJFQAcKxe7eM\nujoLqgEAIDwECACwiC8/X8rJCWz0++XYvt2aggAACAMBAgCsYhhSUVFQM9OYAACJjAABAFYKESAc\n5eWSx2NBMQAAXBwBAgCs1LevlJER0GS43Y0hAgCABESAAAAr2WzS0KFBzUxjAgAkKgIEAFituDio\nybl9u+T3W1AMAAAXRoAAAKsNHCgzJSWgyaitlWPPHosKAgCgZQQIALCa0ylv375BzY6tWy0oBgCA\nCyNAAEACaPGp1KZpQTUAALSMAAEACcA7YEDjgupz2E6flv3QIYsqAgAgNAIEACQAMy1N3t69g9qd\nTGMCACQYAgQAJAjPoEFBbWznCgBINAQIAEgQnoEDg9psx47JduyYBdUAABAaAQIAEoSZnS1fjx5B\n7UxjAgAkEgIEACQQpjEBABIdAQIAEkioAGE/eFDG6dMWVAMAQDACBAAkEH/HjvJ37hzUzjQmAECi\nIEAAQIIJOY2JAAEASBAECABIMKGeSu34/HMZdXUWVAMAQCACBAAkGN8VV8jfvn1go98vx/bt1hQE\nAMA5HFYXEImamhotXLhQa9as0alTp5SVlaXi4mLNmjVLOTk5Fzx35syZFzw+b948ZWRkRLNcAAiP\nYcgzaJBcK1YENDvLyuQZPtyiogAAaJS0AcLtdmvOnDmqqKjQlClTVFhYqCNHjuidd95RWVmZnnnm\nGWVmZl7wGvn5+S0GCZfLFYuyASAs3hABwlFeLnk8ktNpUVUAACRxgFi8eLEOHDig7373u7rpppua\n23v06KEXXnhBixYt0l133XXBa2RlZWnMmDGxLhUALpm3Vy+ZaWkB6x4Mt1uO8nJ5QyyyBgAgXpJ2\nDURJSYlcLpcmTZoU0D5q1Cjl5uaqtLRUpmlaVB0ARMhmk2fgwKBmdmMCAFgtKQNEbW2tKioq1KtX\nLznPG8o3DEOFhYWqrq7WsWPHwrqeaZqqr6+PRakAcNlCbue6bZvk91tQDQAAjZJyCtOJEyckSR06\ndAh5PC8vT5JUWVmpziEeyNTkzJkzeuWVV7R69Wo1NDQoLS1No0aN0h133NHitS9Ft27dIr4GWh/6\nBUIJ2S/y8qS3325c93COzNpaqW/fOFUGK/H9AqHQL2C1pByBqPtyTnBLC51TU1Ml6aKjCocOHZIk\nff/739ePfvQjjRo1SiUlJXr88cdVXV0dxYoB4DKkpEih1jts2BD/WgAA+FJSjkBEw09/+lNlZWWp\nV69ezW1jxoxRXl6e/va3v+ndd9/VHXfcEdF7HD58ONIy0Yo0/cSIfoFzXaxfOPPzlX7ebkz+Tz/V\nmXHjJMOIeX2wBt8vEAr9AqFYMSKVlCMQaWlpkloeYWhqb3pdKEVFRQHhocmNN94oSdqyZUukZQJA\nxLwDBki2wG/VtlOnZOcDBADAIkkZIDp16iTDMHTy5MmQx48fPy5J6tq16yVfOysrS4ZhqLa2NqIa\nASAazPR0eUP8sMNZVmZBNQAAJGmASE1NVffu3bV371653e6AY36/X+Xl5crNzW1eTH2+AwcOaNmy\nZc2Lsc919OhRmabZ4rkAEG8hd2MiQAAALJKUAUKSJk2apIaGBn3wwQcB7SUlJTp9+rQmT57c3FZR\nURGwpeuBAwf0v//7v/rrX/8adN2///3vkqTRo0fHqHIAuDShAoStslK2o0ctqAYA0NYl7SLqG264\nQZ9++qn+/Oc/6/jx4yosLNTBgwf17rvvqnv37po+fXrzax9++GF169ZNL730kiTp6quv1scff6yP\nPvpI1dXVGj58uPx+v1avXq0tW7ZoyJAhAQEEAKxktm8vX48esu/fH9Du3LxZDV26WFQVAKCtStoA\n4XA49Pjjj2vhwoVavXq1lixZouzsbE2ePFkzZ85scYtXSbLb7Xrssce0ZMkSffzxx5o3b54Mw1DX\nrl115513aurUqbLb7XG8GwC4MPeQIUo7L0CkbNqkhhtuYDcmAEBcGaZpmlYX0VqxzRrOxfZ7CCXc\nfmF88YWy5s4Naj/zwx/Kz0OlWh2+XyAU+gVCYRtXAEBIZvv28hYUBLWnbN5sQTUAgLaMAAEAScIz\ndGhQm3PTJomBZABAHBEgACBJeIYODVrvYKuqkr2iwqKKAABtEQECAJKE2a5dyGlMzk2bLKgGANBW\nESAAIIl4ioqC2pybNzONCQAQNwQIAEginsGDJVvgt27bqVOyHzhgUUUAgLaGAAEAScTMzJS3sDCo\nPWXdOguqAQC0RQQIAEgy7uLioDbnxo2Sx2NBNQCAtoYAAQBJxjNkiEyXK6DNqK+Xc9s2iyoCALQl\nBAgASDYuV+NaiPOkrF1rQTEAgLaGAAEAScg9YkRQm6O8XMbp0xZUAwBoSwgQAJCEfIWF8ufkBDaa\nplI2bLCmIABAm0GAAIBkZBghRyFS1q3jmRAAgJgiQABAkvIMHx7UZquslP3QIQuqAQC0FQQIAEhS\n/rw8eQsKgtpT1qyxoBoAQFtBgACAJOYJMY3JuX69jLo6C6oBALQFBAgASGLuoUNlpqYGtBlut5yM\nQgAAYoQAAQDJLDU15GJq12efsZgaABATBAgASHLusWOD2mxVVXLs3GlBNQCA1o4AAQBJzt+xo7x9\n+wa1u1assKAaAEBrR4AAgFagIcQohGPnTtmOH7egGgBAa0aAAIBWwNu/v/wdOgS1p3z2mQXVAABa\nMwIEALQGNlvIUYiUNWtk1NZaUBAAoLUiQABAK+EZNUpmSkpAm9HQIFdJiUUVAQBaIwIEALQSZlqa\n3KNGBbWnrFjBKAQAIGoIEADQijRMnCg5HAFtRkODXKWl1hQEAGh1CBAA0IqY2dlqGD06qJ1RCABA\ntBAgAKCVCTkKUV/PKAQAICoIEADQypjZ2XJfdVVQe8qKFTLOnrWgIgBAa0KAAIBWqL6FUYjU99+3\npiAAQKtBgACAVshs3z70KMTq1bIfOmRBRQCA1oIAAQCtVP3kyTJTUwMbTVNpb70lmaY1RQEAkh4B\nAgBaKbNdO9Vff31Qu/3AAaWsXWtBRQCA1oAAAQCtmPuaa+Tr0iWoPfW992TU1VlQEQAg2REgAKA1\ns9tVd8stQc3G2bNKffttCwoCACQ7AgQAtHK+wkJ5ioqC2lPWrZNz40YLKgIAJDMCBAC0AXXTpsl0\nuYLa0/72NxknT1pQEQAgWREgAKANMLOzVff1rwe1G/X1ypg/X/L7LagKAJCMCBAA0EZ4Ro6UZ9iw\noHb7vn1KXbbMgooAAMmIAAEAbYVhqO6b35Q/JyfokOvDD1kPAQAICwECANoQMy1Ntd/6lmQYQcfS\nFyyQfd+++BcFAEgqBAgAaGN8BQUhHzAnr1cZf/yjbCdOxL8oAEDSIEAAQBvUcP318gwZEtRu1NYq\n4w9/kHHmjAVVAQCSAQECANoiw1Dtt74lX/fuQYdsJ04o83e/I0QAAEIiQABAW+V06uxdd4VcVG2r\nrCREAABCIkAAQBtmtmuns/fcIzM1NehYc4iorragMgBAoiJAAEAb5+/cWWfvu6/lEPHrX8tWWWlB\nZQCARESAAADId+WVLYeIU6eU+eqrbPEKAJBEgAAAfOlCIcKoq1Pm734n5+bNFlQGAEgkBAgAQDPf\nlVfq7L/9m8zMzOCDXq/SX39dqUuWSH5//IsDACQEAgQAIIAvP181Dzwgf25uyOOujz5Sxh//KKOu\nLs6VAQASAQECABDEn5enmgcflO/KK0Med+zYocyXX5b94ME4VwYAsBoBAgAQkpmZqZp/+zd5Bg8O\nedx28qQyf/1ruZYvl0wzvsUBACxDgAAAtMzlUu2//Ivqb7pJMozg436/Ut97TxmvvSbjiy/iXx8A\nIO4IEACACzMMNUyerLN33RVyhyZJcuzapXYvvqiUlSsZjQCAVo4AAQAIi3fgQNU89JB8+fkhjxsN\nDUp76y1l/OY3sh09GufqAADxQoAAAITNn5enmgceUMOECS2+xrF3r9r9938r7W9/k3HmTByrAwDE\nAwECAHBpHA7VT5ums/feK392dujXmKZSVq1Su+efl+uDD9jyFQBaEQIEAOCyePv2Vc2PfiT36NEt\nvsaor1fq0qVq9/TTSl2yREZNTRwrBADEgsPqAgAAyctMS1PdjBlyDxum9EWLZKuqCvk6o75epMFk\ncwAAIABJREFUro8+kqukRO5hw+QeM0a+7t1D7+wEAEhoBAgAQMR8vXvrzI9+JNeKFXJ99JGM+vrQ\nL/R6lbJunVLWrZOva1e5R4yQZ9gwmS1NhQIAJBwCBAAgOpxONUycKPfIkUpdtkwpq1dLfn+LL7cf\nOaK0d99V2uLF8hYWyl1cLM+QIVILW8UCABIDAQIAEFVmZqbqbr1VDRMmyPXJJ0pZs0byei9wginH\n7t1y7N4tvfWWPAMGyF1cLG+/fpKDf6YAINHwnRkAEBP+Dh1Ud+utqp88Wa7SUqWsWSOjtvbCJ3k8\ncm7eLOfmzTLT0+UZOlTuoiL5CgpYLwEACYIAAQCIKTMrS/XTpqn+xhvl3LJFrlWrZN+376LnGbW1\nSlm1SimrVsmfkyNPcbHcRUXyd+kS+6IBAC0iQAAA4sPplGf4cHmGD5ft+HE5N2xQyvr1sp08edFT\nbadONe7i9NFH8uXnq2HsWHmGDZOczjgUDgA4FwECABB3/o4d1XDjjWq44QbZDxxQyoYNcm7aJOPs\n2Yueaz90SOkLFshcvFju0aPVMGaMzPbt41A1AEAiQAAArGQY8vXooboePVQ3fbocu3YpZf16Obdu\nlTyeC5969mzjqMTy5fIMGqSGsWPl69WLtRIAEGMECABAYrDb5e3fX97+/aWGBjm3blXKhg1ylJdL\nptnyeX6/nFu2yLllS+OzJcaOlbuoSHK54lc7ALQhBAgAQOJxuZrXSxhnzsi5aZNS1q+X/dChC55m\nP3JEaYsWKfW99+QeOVLusWPlz82NU9EA0DYQIAAACc1s107ucePkHjeucb3EypVK2bRJ8vlaPMeo\nq5OrtFSuTz+Vp39/ua++Wt6+fSWbLY6VA0DrRIAAACQNX/fuquveXfXTpill9WqlrF4t2+nTLZ9g\nmnJu3y7n9u3yZ2fLU1Qkd3Gx/N26xa9oAGhlCBAAgKRjtmunhuuvV8N118lZVqaUlSvl2Lv3gufY\nTp+W65NP5PrkE/nz8uQZMECeAQMaH1Jnt8epcgBIfgQIAEDystvlGTZMnmHDZKuokGvlSqVs3HjR\nHZxsJ040TnEqLZWZkiJffr58BQXydu8uX+fOMnNy2M0JAFqQ1AGipqZGCxcu1Jo1a3Tq1CllZWWp\nuLhYs2bNUk5OzkXP37lzpxYtWqRdu3bJ7Xara9eumjx5sqZMmSKDfzg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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 375, "width": 392 } }, "output_type": "display_data" } ], "source": [ "from scipy.stats.kde import gaussian_kde\n", "r = trace2['r'][1000:]\n", "\n", "fig = plt.figure(figsize=(6, 6)) \n", "\n", "my_pdf = gaussian_kde(r)\n", "x1=np.linspace(0, 1, 200)\n", "\n", "plt.plot(x1, my_pdf(x1), 'r', lw=2.5, alpha=0.6,) # distribution function\n", "plt.plot(x1, np.ones(x1.size), 'k--', lw=2.5, alpha=0.6, label='Prior')\n", "posterior = my_pdf(0) # this gives the pdf at point delta = 0\n", "prior = 1 # height of order-restricted prior at delta = 0\n", "BF01 = posterior/prior\n", "print ('the Bayes Factor is %.5f'%(1/BF01))\n", "plt.plot([0, 0], [posterior, prior], 'k-', \n", " [0, 0], [posterior, prior], 'ko',\n", " lw=1.5, alpha=1)\n", "# ax1.hist(r, bins=100, normed=1,alpha=.3)\n", "plt.xlim([0, 1])\n", "plt.xlabel('Correlation r')\n", "plt.ylabel('Density')\n", "\n", "# Compare to exact solution Jeffreys (numerical integration):\n", "freqr=scipy.corrcoef(xobs[:, 0]/Nt, xobs[:, 1]/Nt)\n", "BF_Jeffex = scipy.integrate.quad(lambda rho: ((1-rho**2)**((n-1)/2)) / ((1-rho*freqr[0, 1])**((n-1)-.5)), 0, 1)\n", "print('the exact Jeffreys Bayes Factor is %.5f'%(BF_Jeffex[0]))\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 13.3 Evidence for the impact of extraversion\n", " \n", "$$ \\mu_{1},\\mu_{2} \\sim \\text{Gaussian}(0, .001) $$\n", "$$ \\sigma_{1},\\sigma_{2} \\sim \\text{InvSqrtGamma} (.001, .001) $$\n", "$$ r \\sim \\text{Uniform} (-1, 1) $$ \n", "$$ \\hat\\theta_{i} \\sim \\text{MvGaussian} ((\\mu_{1},\\mu_{2}), \\begin{bmatrix}\\sigma_{1}^2 & r\\sigma_{1}\\sigma_{2}\\\\r\\sigma_{1}\\sigma_{2} & \\sigma_{2}^2\\end{bmatrix}^{-1}) $$ \n", "$$ \\theta_{i1} = \\Phi(\\hat\\theta_{i1})$$\n", "$$ \\theta_{i2} = 100\\Phi(\\hat\\theta_{i2})$$\n", "$$ k_{i} \\sim \\text{Binomial}(\\theta_{i1},n)$$\n", "$$ x_{i} \\sim \\text{Gaussian}(\\theta_{i2},\\lambda^x)$$" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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Wqbq6WpMnT25ZxxdffKGnn35aw4cP1/Tp08PKI0mHDx8Oex1ArGRkZEhiHMP9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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 324, "width": 505 } }, "output_type": "display_data" } ], "source": [ "k2 = np.array([36, 32, 36, 36, 28, 40, 40, 24, 36, 36, 28, 40, 28, \n", " 36, 20, 24, 24, 16, 20, 32, 40, 32, 36, 24, 28, 44,\n", " 40, 36, 40, 32, 32, 40, 28, 20, 24, 32, 24, 24, 20, \n", " 28, 24, 28, 28, 32, 20, 44, 16, 36, 32, 28, 24, 32,\n", " 40, 28, 32, 32, 28, 24, 28, 40, 28, 20, 20, 20, 24,\n", " 24, 36, 28, 20, 20, 40, 32, 20, 36, 28, 28, 24, 20,\n", " 28, 32, 48, 24, 32, 32, 40, 40, 40, 36, 36, 32, 20,\n", " 28, 40, 32, 20, 20, 16, 16, 28, 40])\n", " \n", "x2 = np.array([50, 80, 79, 56, 50, 80, 53, 84, 74, 67, 50, 45, 62, \n", " 65, 71, 71, 68, 63, 67, 58, 72, 73, 63, 54, 63, 70, \n", " 81, 71, 66, 74, 70, 84, 66, 73, 78, 64, 54, 74, 62, \n", " 71, 70, 79, 66, 64, 62, 63, 60, 56, 72, 72, 79, 67, \n", " 46, 67, 77, 55, 63, 44, 84, 65, 41, 62, 64, 51, 46,\n", " 53, 26, 67, 73, 39, 62, 59, 75, 65, 60, 69, 63, 69, \n", " 55, 63, 86, 70, 67, 54, 80, 71, 71, 55, 57, 41, 56, \n", " 78, 58, 76, 54, 50, 61, 60, 32, 67])\n", " \n", "nsubjs = len(k2)\n", "ntrials = 60\n", "sigmax = 3\n", "\n", "plt.figure(figsize=[8, 5])\n", "plt.scatter(x2, k2)\n", "plt.xlabel('Extraversion', fontsize=15)\n", "plt.ylabel('Performance Session 2', fontsize=15)\n", "plt.axis([0,100,0,60])\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "Auto-assigning NUTS sampler...\n", "Initializing NUTS using jitter+adapt_diag...\n", "100%|██████████| 3500/3500.0 [01:10<00:00, 44.22it/s]/home/laoj/Documents/Github/pymc3/pymc3/step_methods/hmc/nuts.py:467: UserWarning: Chain 0 contains 7 diverging samples after tuning. If increasing `target_accept` does not help try to reparameterize.\n", " % (self._chain_id, n_diverging))\n", "\n" ] }, { "data": { "image/png": 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zwL4WHy/vbqUrYDMxNxlXgkb6iYiIHJaRkRHrEHpxOp0cPHiQ999/n8985jOx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\nK/PmzWPjxo3MmTMnvt1MqZ+KqqrqhL/rDBYMBvne975HdXU169evp7y8n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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 136, "width": 855 } }, "output_type": "display_data" } ], "source": [ "with pm.Model() as model3:\n", " # r∼Uniform(−1,1)\n", " r = pm.Uniform('r', lower=0, upper=1)\n", " \n", " # μ1,μ2∼Gaussian(0,.001)\n", " mu = pm.Normal('mu', mu=0, tau=.001, shape=n2)\n", " \n", " # σ1,σ2∼InvSqrtGamma(.001,.001)\n", " lambda1 = pm.Gamma('lambda1', alpha=.001, beta=.001, testval=100)\n", " lambda2 = pm.Gamma('lambda2', alpha=.001, beta=.001, testval=100)\n", " sigma1 = pm.Deterministic('sigma1', 1/np.sqrt(lambda1))\n", " sigma2 = pm.Deterministic('sigma2', 1/np.sqrt(lambda2))\n", " \n", " cov = pm.Deterministic('cov', tt.stacklists([[lambda1**-1, r*sigma1*sigma2],\n", " [r*sigma1*sigma2, lambda2**-1]]))\n", " \n", " tau1 = pm.Deterministic('tau1', tt.nlinalg.matrix_inverse(cov))\n", " \n", " thetai = pm.MvNormal('thetai', mu=mu, tau=tau1, shape=(n, n2))\n", " theta1 = phi(thetai[:,0])\n", " theta2 = 100 * phi(thetai[:,1])\n", " \n", " ki = pm.Binomial('ki', p=theta1, n=Nt, observed=k2)\n", " xi = pm.Normal('xi', mu=theta2, sd=sigmax, observed=x2)\n", " \n", " trace3=pm.sample(3e3, njobs=2)\n", "\n", "pm.traceplot(trace3, varnames=['r']);" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "the Bayes Factor is 0.48178\n" ] }, { "data": { "image/png": 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BAID8GSqiLH8C4BGECgAA5M9QQU8FAK8gVAAAIJ+GisZGKZFwoRoASEaoAACgu/vYORX9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"text/plain": [ "" ] }, "metadata": { "image/png": { "height": 372, "width": 394 } }, "output_type": "display_data" } ], "source": [ "r = trace3['r'][1000:]\n", "\n", "fig = plt.figure(figsize=(6, 6)) \n", "\n", "my_pdf = gaussian_kde(r)\n", "x1=np.linspace(-1, 1, 200)\n", "\n", "plt.plot(x1, my_pdf(x1), 'r', lw=2.5, alpha=0.6,) # distribution function\n", "plt.plot(x1, np.ones(x1.size)*.5, 'k--', lw=2.5, alpha=0.6, label='Prior')\n", "posterior = my_pdf(0) # this gives the pdf at point delta = 0\n", "prior = .5 # height of order-restricted prior at delta = 0\n", "BF01 = posterior/prior\n", "print ('the Bayes Factor is %.5f'%(1/BF01))\n", "plt.plot([0, 0], [posterior, prior], 'k-', \n", " [0, 0], [posterior, prior], 'ko',\n", " lw=1.5, alpha=1)\n", "# ax1.hist(r, bins=100, normed=1,alpha=.3)\n", "plt.xlim([-1, 1])\n", "plt.xlabel('Correlation r')\n", "plt.ylabel('Density')\n", "\n", "plt.show()" ] } ], "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 1 }