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@fehiepsi
Created October 5, 2019 01:27
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Chapter 5. The Many Variables & The Spurious Waffles"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"import arviz as az; az.style.use(\"arviz-darkgrid\")\n",
"import matplotlib.pyplot as plt\n",
"import numpy as onp\n",
"import pandas as pd\n",
"from scipy.interpolate import BSpline\n",
"from scipy.stats import gaussian_kde\n",
"\n",
"from jax import lax, vmap\n",
"import jax.numpy as np\n",
"from jax.random import PRNGKey\n",
"\n",
"import numpyro as npyro\n",
"from numpyro.contrib.autoguide import AutoMultivariateNormal\n",
"import numpyro.distributions as dist\n",
"from numpyro.infer_util import init_to_values, predictive\n",
"import numpyro.optim as optim\n",
"from numpyro.svi import SVI, elbo"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.1"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# load data and copy\n",
"WaffleDivorce = pd.read_csv(\"../data/WaffleDivorce.csv\", sep=\";\")\n",
"d = WaffleDivorce\n",
"\n",
"# standardize variables\n",
"d[\"A\"] = ((d.MedianAgeMarriage - d.MedianAgeMarriage.mean())\n",
" / d.MedianAgeMarriage.std())\n",
"d[\"D\"] = (d.Divorce - d.Divorce.mean()) / d.Divorce.std()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.2"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"1.2436303013880823"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d.MedianAgeMarriage.std()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.3"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"def model(A, D=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bA = npyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bA * A\n",
" npyro.sample(\"mu\", dist.Delta(mu), obs=mu)\n",
" npyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
"\n",
"m5_1 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_1, elbo, optim.Adam(0.1))\n",
"data = (d.A.values, d.D.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(1000))\n",
"p5_1 = svi.get_params(last_state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.4"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"prior_pred = predictive(PRNGKey(10), m5_1.model, {}, num_samples=1000,\n",
" return_sites=[\"mu\"], A=np.array([-2, 2]))\n",
"mu = prior_pred[\"mu\"]\n",
"plt.subplot(xlim=(-2, 2), ylim=(-2, 2))\n",
"for i in range(20):\n",
" plt.plot([-2, 2], mu[i], \"k\", alpha=0.4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.5"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# compute percentile interval of mean\n",
"A_seq = np.linspace(start=-3, stop=3.2, num=30)\n",
"post = m5_1.sample_posterior(PRNGKey(1), p5_1, (1000,))\n",
"post_pred = predictive(PRNGKey(2), m5_1.model, post, A=A_seq)\n",
"mu = post_pred[\"mu\"]\n",
"mu_mean = np.mean(mu, 0)\n",
"mu_PI = np.percentile(mu, q=(5.5, 94.5), axis=0)\n",
"\n",
"# plot it all\n",
"az.plot_pair(d[[\"D\", \"A\"]].to_dict(orient=\"list\"))\n",
"plt.plot(A_seq, mu_mean, \"k\")\n",
"plt.fill_between(A_seq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.6"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"d[\"M\"] = (d.Marriage - d.Marriage.mean()) / d.Marriage.std()\n",
"\n",
"def model(M, D=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bM = npyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bM * M\n",
" npyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
"\n",
"m5_2 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_2, elbo, optim.Adam(0.1))\n",
"data = (d.M.values, d.D.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(1000))\n",
"p5_2 = svi.get_params(last_state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.7"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(xticks=[], yticks=[])\n",
"ax.annotate(\"A\", (0.03, 0.97), ha=\"center\", va=\"center\", c=\"k\", fontsize=16)\n",
"ax.annotate(\"D\", (0.5, 0.03), ha=\"center\", va=\"center\", c=\"k\", fontsize=16)\n",
"ax.annotate(\"M\", (0.97, 0.97), ha=\"center\", va=\"center\", c=\"k\", fontsize=16)\n",
"ax.arrow(0.05, 0.94, 0.43, -0.88, head_width=0.02,\n",
" length_includes_head=True, fc=\"k\", ec=\"k\")\n",
"ax.arrow(0.055, 0.97, 0.89, 0, head_width=0.02,\n",
" length_includes_head=True, fc=\"k\", ec=\"k\")\n",
"ax.arrow(0.95, 0.94, -0.43, -0.88, head_width=0.02,\n",
" length_includes_head=True, fc=\"k\", ec=\"k\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.8"
]
},
{
"cell_type": "code",
"execution_count": 85,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" a -0.03 0.10 -0.03 -0.20 0.12 937.10 1.00\n",
" bA -0.63 0.16 -0.62 -0.90 -0.39 915.93 1.00\n",
" bM -0.08 0.16 -0.08 -0.37 0.17 909.89 1.00\n",
" sigma 0.82 0.09 0.82 0.67 0.97 965.80 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"def model(M, A, D=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bM = npyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
" bA = npyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bM * M + bA * A\n",
" npyro.sample(\"D\", dist.Normal(mu, sigma), obs=D)\n",
"\n",
"m5_3 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_3, elbo, optim.Adam(0.03))\n",
"data = (d.M.values, d.A.values, d.D.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(2000))\n",
"p5_3 = svi.get_params(last_state)\n",
"post = m5_3.sample_posterior(PRNGKey(1), p5_3, (1000,))\n",
"npyro.diagnostics.summary(post)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.9"
]
},
{
"cell_type": "code",
"execution_count": 93,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x940 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"coeftab = {\"m5.1\": m5_1.sample_posterior(PRNGKey(1), p5_1, (1000,)),\n",
" \"m5.2\": m5_2.sample_posterior(PRNGKey(2), p5_2, (1000,)),\n",
" \"m5.3\": m5_3.sample_posterior(PRNGKey(3), p5_3, (1000,))}\n",
"az.plot_forest(list(coeftab.values()), model_names=list(coeftab.keys()),\n",
" var_names=[\"bA\", \"bM\"], credible_interval=0.89);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.10"
]
},
{
"cell_type": "code",
"execution_count": 94,
"metadata": {},
"outputs": [],
"source": [
"N = 50 # number of simulated States\n",
"age = dist.Normal().sample(PRNGKey(0), sample_shape=(N,)) # sim A\n",
"mar = dist.Normal(age).sample(PRNGKey(1)) # sim A -> M\n",
"div = dist.Normal(age).sample(PRNGKey(2)) # sim A -> D"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.11"
]
},
{
"cell_type": "code",
"execution_count": 95,
"metadata": {},
"outputs": [],
"source": [
"def model(A, M=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bAM = npyro.sample(\"bA\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bAM * A\n",
" npyro.sample(\"mu\", dist.Delta(mu), obs=mu)\n",
" npyro.sample(\"M\", dist.Normal(mu, sigma), obs=M)\n",
"\n",
"m5_4 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_4, elbo, optim.Adam(0.1))\n",
"data = (d.A.values, d.M.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(1000))\n",
"p5_4 = svi.get_params(last_state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.12"
]
},
{
"cell_type": "code",
"execution_count": 98,
"metadata": {},
"outputs": [],
"source": [
"post = m5_4.sample_posterior(PRNGKey(1), p5_4, (1000,))\n",
"post_pred = predictive(PRNGKey(2), m5_4.model, post, A=d.A.values)\n",
"mu = post_pred[\"mu\"]\n",
"mu_mean = np.mean(mu, 0)\n",
"mu_resid = d.M.values - mu_mean"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.13"
]
},
{
"cell_type": "code",
"execution_count": 100,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# prepare new counterfactual data\n",
"M_seq = np.linspace(start=-2, stop=3, num=30)\n",
"pred_data = {\"M\": M_seq, \"A\": 0}\n",
"\n",
"# compute counterfactual mean divorce (mu)\n",
"post = m5_3.sample_posterior(PRNGKey(1), p5_3, (int(1e4),))\n",
"post_pred = predictive(PRNGKey(2), m5_3.model, post, **pred_data)\n",
"mu = post_pred[\"mu\"]\n",
"mu_mean = np.mean(mu, 0)\n",
"mu_PI = np.percentile(mu, q=(5.5, 94.5), axis=0)\n",
"\n",
"# simulate counterfactual divorce outcomes\n",
"D_sim = post_pred[\"D\"]\n",
"D_PI = np.percentile(D_sim, q=(5.5, 94.5), axis=0)\n",
"\n",
"# display predictions, hiding raw data with alpha=0\n",
"az.plot_pair(d[[\"M\", \"D\"]].to_dict(orient=\"list\"), plot_kwargs={\"alpha\": 0})\n",
"plt.title(\"Median age marriage (std) = 0\")\n",
"plt.plot(M_seq, mu_mean, \"k\")\n",
"plt.fill_between(M_seq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2)\n",
"plt.fill_between(M_seq, D_PI[0], D_PI[1], color=\"k\", alpha=0.15);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.14"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [],
"source": [
"# call predictive with the original data\n",
"post = m5_3.sample_posterior(PRNGKey(1), p5_3, (int(1e4),))\n",
"post_pred = predictive(PRNGKey(2), m5_3.model, post, M=d.M.values, A=d.A.values)\n",
"mu = post_pred[\"mu\"]\n",
"\n",
"# summarize samples across cases\n",
"mu_mean = np.mean(mu, 0)\n",
"mu_PI = np.percentile(mu, q=(5.5, 94.5), axis=0)\n",
"\n",
"# simulate observations\n",
"D_sim = post_pred[\"D\"]\n",
"D_PI = np.percentile(D_sim, q=(5.5, 94.5), axis=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.15"
]
},
{
"cell_type": "code",
"execution_count": 135,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"ax = plt.subplot(ylim=(float(mu_PI.min()), float(mu_PI.max())),\n",
" xlabel=\"Observed divorce\", ylabel=\"Predicted divorce\")\n",
"plt.plot(d.D, mu_mean, \"o\")\n",
"x = np.linspace(mu_PI.min(), mu_PI.max(), 101)\n",
"plt.plot(x, x, \"--\")\n",
"for i in range(d.shape[0]):\n",
" plt.plot([d.D[i]] * 2, mu_PI[:, i], \"b\")\n",
"fig = plt.gcf()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.16"
]
},
{
"cell_type": "code",
"execution_count": 136,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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NN98wgSQiIm2xmRG6YwZCD34Bc7vhMN8/wnGciSMpJGjHrSdNmoStW7diz549GDRokKxrrF69Gjt37kTPnj2xfPlyjBs3DvPmzcOkSZNw6dIlzJgxQ+GoiYiI5BOyLiPim6cQevALxwGbWd2AKCgFbfJ4//33o3bt2l5dY8WKFQCAsWPHQii0krZ///6oX78+UlJSSu22QERE5G/63/+HyC/6QX/5EMSwSsjr8xHMfxujdlgUhII2efRWfn4+Dh06hHr16pWahHbo0AFmsxmHDh1SIToiIqK/2G2wbf4A4atfgGC6AVv1u5H7xErY6j+odmQUpJg8unD+/HnY7XbUdRYfK8Z5/OzZs36LiYiIqDjh5nnYd30CASLMLR9H3sBlEKPvUDssCmJBu2HGW1lZWQCAihUrlvp8hb/29Lubto6OjoZOxxxdLqOxfNch04rQ0NsfG41GSSUt+N4FJjXeN1dfX3K+7soloxH2PtMBnQEVWvQFP03SaOnrq6zvOy3F6cTk0cdu3rypdggBy2g0IjMzU+0wCPir04fjh1tmZibMbtbg870LTGq9b66+vjz9uis3RDtC9v8fbLXvK+gQY7znMcd7x+87ybTy9eXu+87fcUr5A5LJowtRUVEAXI8s5vzVN8vVyCQREZHiTDcRvuF1GM5sgz2qJnKf+gEI4+8h8i8mjy7UqVMHOp3O5ZpG53FXayKJiIiUpPvjKMLXjobuVjpEfQjMCS8AoRqYw6Ryh4vxXAgLC0OLFi3w+++/l1pgfNeuXQgNDUXLli1ViI6IiMoNUYTh0FeIWD4YulvpsEffgbxBX8HaYiDYkJnUwOQRQEZGBk6fPl2wScZpwIABAICZM2dCFMWC4ytXrsTp06fRo0cPTlsTEZHvWPMRlvIqwrckQ7BZYK3fCblDVsJe/W61I6NyLGinrVesWIHU1FQAwMmTJwuO7du3DwDQuXNndO7cGQAwa9YsrF69ukTv60ceeQQpKSlYt24dLl68iLZt2+LChQvYuHEjatasiXHjxvn5X0VEROWKPhSCNQ+ioIf5b2NhuXcoRxtJdUGbPKampmL16tVFjh04cAAHDhwAANSuXbsgeXRFr9fjk08+waJFi/DDDz9gyZIliI6ORt++fTF69Gj2tSYiIt+wWwGdARAEmLq+D931M7DXaqV2VEQAAEEsPB9LimO5EvlY7kU7cnKAuDhH+YYLFzLd1hnjexeY1CzVU9rXl6dfd0HBmo+w/04GzLnI7zFd8igjv+c8p5WvLymlevwZJ0v1EBERBQjhxnmErx0NfcZxiBBguXco7DWaqR0WUQlMHomIiFSm/20Twje+CSE/C2KEEaYe05k4kmYxeSQiIlKLzYLQnbMQmrrE8bBWa5h6zoIYVV3duIjKwOSRiIhIJeHrxsJwahMAwHzvMJgT/wnoQ1SOKjA5d3BwM7rvMXkkIiJSieWeIdBf3AdTl/dga9hF7XACligC3btHQRCAlJQsJpA+xuSRiIjIX+w26K6dhj2mEQDAVicBOc9tYZtBL+XmAvv2GQo+Lhc781XEDjNERER+IOReQ/iqfyDi68chXP/99hNMHCnAMHkkIiLyMV36AUR80Q+G87sBUYQu83f3LyLSKE5bExER+YooIiR1CUL/NxOCaIO9yp0w9ZoDe7WGakdGJBtHHonIrchIICHBioQEKyIj1Y6GKECYbiH8h5EI2zENgmiDpXFP5A7+homjRthstxvspR0SizzWEi3GyeSRiNxy7mDkLkYi6UIOLYPh9BaI+hCYOr3laDfI9Y2asH2HiCeG3k7CXn1dxKODRGzfoX5iVphW42TySESSCALrpxF5wnLfs7A07om8gctgbfk4v4E0YvsOEW++JeLq1aLHr1wB3nxL/cTMSctxMnkkIiJN0uJ0XZksuQjZ8wlgszge60OQ33MG2wxqiM0mYs78sr+O5n6o/tea1uNk8khERJqj9HSdKN7uQOINV9cRrp1GxLIBCPtpHkJ3zvH+RuQThw47Ru7KkpHhOE9NWo+TySMREWmK0tN1zu4jPXpEeZVAurqO4fhaRC4bAP2107BXqAZr/b/Lvwn51LXryp7nK1qPk6V6iIhIM6RO1yV2APR6aWsIleo+UuI6YWaEbZ+CkENfAwCsce2Q32M6xArV5N2AfK5qFWXP8xWtx+lV8mi1WrFt2zYcOXIEmZmZaNGiBR599FEAwJ9//onMzEw0aNAABgNzVCIicu/IUenTda1b+Sem0gi3LiFi6yvQ//kLRAiwJLwIc/vhgE6vXlDkVssWQExM2V9jsbGO89Sk9ThlT1vv27cPnTt3xsiRI7Fw4UKsWLECqampBc/v3r0bffv2xZYtWxQJlIiIgt/1TGnnqT2tCJsFuuu/QwyvDFPfhTB3eIWJo594s35VrxcwemTZI9ajRgiSR7V9Retxykoef/31Vzz//PO4du0annrqKcydOxdisXeya9euCA8Px8aNGxUJlIiIgl8Vo7TzVJmuK/R7TjTGw9R7HnKfXAVbvb+pEEz5pMT61aSOAiYnC6hWbHVBbCwwOVlAUkdtlFTScpyy5pM/+ugjmM1m/Oc//0H79u1LPSciIgL169fHsWPHvAqQiIKL8wc+S95RaZo30+Z0nZCdgfDVEwCsKDhmq9vBrzHwe0e59atJHQW0ugeoW9fxePpUAe0SpK+j9Retxilr5PHnn39Gy5YtXSaOTrVq1UJGRoaswIgo+Ci165WClxan6/TndyPiy34wpKe6P9lH+L2jvMJfQ/e0VH+q2hUtxilr5DE7OxvVq1d3e57ZbIbdbpdzCyIKQkqNGlBwc0zXATPnFM2SYmMdiaPfputEO0L2LkToT/MhQIStakv/3LcU/N4hLZGVPMbExOD06dNuzzt58iRq1aol5xZERFSOqT5dl5eJ8PXjYTj7PwCApVl/5LWdCIz3z+2JtEzWtHViYiJOnTqFTZs2uTxn1apVuHTpEpKSkmQHR0REgUepbi5qTdcJOVcR+UU/GM7+D6IhHKau7yP/oUlASJhf7k+eC7hWlgFOVvL4wgsvIDIyEmPGjMGcOXNw5MgRAIDJZMLJkyfx8ccf491330XlypUxbNgwRQMmIiLtCoa1eWJkVdhq3wu7sS7yHl8O69191Q6JyqB0K0tyT9a0de3atbFw4UKMHj0aCxYswMKFCyEIAjZs2IANGzZAFEVUqVIFH374IWJiYpSOmYiINErO2rzISCAhwVrwsSrysxz/D4sCBAH5Xd51ZMJhFVUKiKRwtrIsvr3C2cpycjI0U3onmMhu/XLfffdhw4YN+Pbbb7F7926kp6fDZrOhRo0aaN++PQYNGoRKlSopGSsREQUhQQBSUrIKPvY3XcZxhK8dDXvVhjA9PN8RRCh3pGidL1pZkjRe9Q2sWLEihg4diqFDhyoUDhERlUeq1C4URRiOrkTY1vcg2MyAzQIhOwNilPtqIqQ+T1pZtrrH8bg818hUUlA3nT58+DDmz5+PtLQ0WCwWNGjQAE8//TR69+4t6fWrVq3CG2+84fL5nTt3clqeiCgQWfIQtiUZIce+AwBY63WEqdtUIEJiixtSndRWllevOdbhOke4mUB6T1byuH37dvznP//B8OHDkZCQUOo5e/bswccff4x//OMf+Nvf/N+6ae/evXj22WcREhKCnj17IioqChs3bsS4ceOQnp6OF198UfK1OnXqhKZNm5Y4Hqna4hwiIpJLuP47wteMgv7abxAFHcz3vwJL238Agqw9pKQSqa0sK0SyRqbSZCWP33zzDY4fP46WLV0XTG3ZsiWOHTuGFStW+D15tFqtmDBhAgRBwNKlS3HXXXcBAIYPH45BgwZh/vz56NatG+o6C4i50blzZ/Tr18+HERNRoGCLuAAn2hG+5hXor52CPbIa8nvMgK1O6YMgpG1SW1k2b+a/mMoLWX9mHTt2DE2aNEF4eLjLcyIiItC0aVMcPXpUdnBy7dmzB+fPn0evXr0KEkfAsUbz5ZdfhtVqxapVq/weFxEFtmAoQ1PuCTrkd3kP1vj7kffESiaOAUyLrSzLC1nJ49WrVxEbG+v2vNjYWFy9elXOLbyyb98+AI5i5sV16NChyDlSHD9+HIsXL8a///1v/Pjjj8jOzlYmUCIKKM4yNHv3GpCbq3Y0JJX9RnrBx2mHRFiqt4Sp/38gVnT/e6wwFqLWHkcrSwHVqhU9HhsLTE72YyvLckbWtHVUVBT+/PNPt+f9+eefiIiIkHMLr5w9exYAEB8fX+K56OhoGI1GnDt3TvL1Pv/88yKPo6KiMHHiRPTp08fta6Ojo6HTcR2NXEYjF68HqtLeu9DQos8H2tqjQI9fCm+/5+R+jkpbDqDE5zt1eQpi9/0LQBoARwHpmjV1eOO1SHTpLL1jzKbN+Zg05fZfDHKvI5eUz0V5+HlZ2ufhkT7Agw+IiI52HF/wUSUkdjAUjDi6+txp6fu5rPdOS3E6yUoemzdvjl27duG3335Dw4YNSz3n1KlTOHjwINq3b+9VgHI4RwajoqJKfb5ixYr4448/3F4nLi4Ob7/9NhITExEbG4tr165h27ZtmDt3LsaPH4/KlSu7bb948+ZNz/8BBMDxTZKZKXE7HWmKq/cuJwcAHD8kMzMzYTb7Ny5vBXr87ijxPSfnc+RcDlB8N6xXn2+7FX98PQ8t/vg3cgxFNzf++acdo8dmY3JyjqSRKVeFqD29jjfcfS7Ky89LV5+Hwsfr35mNW7c8e42a38/u3jt/xynljxBZQ2KDBw+G1WrFCy+8gM2bN5d4fvPmzXj++edht9vx+OOPy7mFJrRp0waDBw9GnTp1EB4ejtq1a2PIkCGYNWsWRFHEvHnz1A6RiCjgKb0cQMi5gvAVz6DBH/8GAHxzdmCp58390P3Us9RC1JzCpvJE1shjUlIShg4diiVLlmDkyJGoXLky6tSpA0EQcO7cOdy4cQOiKOKJJ55Ap06dlI7ZrYoVHe2ksrKySn0+Ozvb5aikFImJiahZsyZ++eUXmM1mhBYeUyYi0ojyuDNcf2EfwlLGQpdzFTnWSLyblowNF7uXeq6zgHTrVq6vd+iw9ELUZV3HW8XXW7ZLYNcUUo/sIuGvv/46mjZtioULF+LMmTNFhlzr16+Pf/zjH3jkkUcUCdJTzhI8586dQ7NmRffo37x5E5mZmWjVyrvvcqPRiMuXL8NkMjF5JCLNcTUVHOz0F/ZCl3MVN8Mb4ql1s3Eup16Z51+7Xvb13D3v6XlybN8hYuac28njq6+LqF4dGD2SfZtJHV51mOnTpw/69OmDjIyMgjWENWrUkLQT25fatGmDhQsXYufOnejZs2eR53bt2gUAaNu2rezrZ2dn48yZM6hUqZJXI5hERL7inAp2fqyFRfb+YG73MsTQCjiCQTj3jetyck5Vq3j3vKfnecrVessrV4A33xIxOZkJJPmfrDWPU6ZMwUcffVTwODY2Fi1atECLFi1UTxwBoH379oiLi8PatWtx/PjxguPZ2dn4+OOPYTAY0Ldv34LjGRkZOH36dIlp7tTU1BLXNplMmDBhAkwmE3r06AGhvPw5T0Qkgb/L2eguH0b49yMAa/5fB/Sw3PcMmreKgLvusbGxQMsWZZ/TsgUUuY4cXG9JWiUreVy6dCl+/fVXpWNRjMFgwKRJkyCKIgYPHoyJEyfigw8+QJ8+ffDbb79hxIgRqFfv9lTGrFmz0KNHD2zatKnIdQYPHoyePXvitddew4wZM/DGG2+gW7duWL9+PZo0aYIxY8b4+59GRKRZ23eIeGJo0enVRweJ2L7DB8mNKCLk4JeIWP4EDKe3IHTvgiJPK1VAWs1C1J6styTyJ1nT1tWrV4eo8fYK7dq1w7JlyzBv3jysX78eFosFDRo0wKhRo/Dwww9LusawYcOQlpaGnTt34tatWwgJCUH9+vUxZMgQPPnkk2V22CEicieYNrT4dXo1PxthmyYi5OQGAIC14UMw3/dMidMcBaRRZL0g4BgpHDVCegFppa7jKS2stwwGrjYbRUYCCQlWAEBkpKtXU2lkJY9dunTB6tWrkZ2dXbCzWYtatGiBTz/91O15U6dOxdSpU0scf/31130RFhFRUG1okTq9mtjB+x3CuisnEb7mFUc9aI4AACAASURBVOhunIOoM8DccRwsrZ5ymYEndRTQ6h7gr32UmD5VkLVTWanreELt9ZbBwN1mo5QUx3K1QP7+U4OsaesRI0agVq1aeP7553Hs2DGlYyIiCnrB1OrQX9Or+jP/RcRXA6G7cQ72ijWQN+BzWFo/7fY3f+EE756W8qeYdbrbr2vZwvc9k9VcbxkMnKPhxbskO0fDt+8QIQhMHOWQNfL48ssvIzQ0FAcOHED//v0RExODWrVqlVqyRhAEfPbZZ14HSkSkNtbaK52/plft1RoB+jBYa98HU49pQIR/2/Hl5RX92NcTb471lo5Ex5Wy1lsG07IIT/lzNLw8kpU87tu3r+BjURSRkZGBjIyMUs/lbmQiCgasteeav6ZXxUq1kfv4VxCN8YAga+Is4MhdbxlMyyLk0Epx92AlK3ncsmWL0nEQEWkWa+2VzTm9WtYvaznTq/pTWwA8WuSYWKXsot/BSM56y/Ja59OJm418S1byWLt2baXjICLSJE5/ueacFvV2erUEmxmhO2ZA2LsSxZNHrfL1FHHJdZu+uY/WSV064qvR8PK8FKCw8jHuT0QkE2vtlc45LdqjRxRE0Tm9KqBataLnxcYCk5PLLmdTOCE4vu8ywpc/hdCDX/gqdMUV/1yQb3hSR9QXm43Uep+dJYUSEqyaKSnkVXvC69evY+XKlUhNTS1Y8xgbG4v77rsPffv2RdWqVRUJkohILZz+Kl1p06JypleLryVtsGMIDFGXYdFXQl6vacA0X/4rlFHep4j9wd3SkYn/Knpc8dFwqPc+O9etOj/WAtnJ448//og333wTOTk5RQqGHzt2DNu3b8eCBQvw/vvv46GHHlIkUCIiNbDWnmc8mV4tLSEwht3ELzfuxqv7Z+HZpnE+jNQ/OM3pPSlLRz5eWPJ5tYq7+4LWvn5kJY9HjhzB2LFjYbfb0aVLFzz88MO44447AADp6en4/vvvsXnzZowZMwZfffUVmjdvrmjQRET+4qvNIL6m9bJCrhKClef648Nf/wmzPazUhCCQlPcdz0qRsnTk6lXg7mYWVKwgFJnaVaO4e3kga83jokWLYLPZMGfOHMybNw+dO3dGkyZN0KRJE3Tq1Anz5s3DvHnzYLVa8e9//1vpmIkoQBVPaAo/1io1exvL5dce0zIdOgzUtqXCGFp0vn/GL6/DbA8D4D5h8CVRhNfr2oKpELyapCwJEQRg4ltZpSbpShWJp9tkJY+pqalo1apVmVPSnTt3RuvWrbF//37ZwRFR8AiEhMYVbzaD+JuUrhqqE+2ocuI/+PT+YXi/9XgIou32U1oIjxtgNEXqkpBqVbU3vRusZCWPWVlZqFmzptvzatasiaysLDm3IKIgEhAJjRtJHQV8ueT2b6bpUwWs+EpbiaPUskKqjviabiL8+xFodnkmDDobruVXhR7aSh5djRgW/rwdPqKdkXMlRkm1jG0atUdW8hgTE4MTJ064Pe/EiROIcfeOE5HPaOGXSkAkNBIpOf3liyl8rZcV0v1xFJFf9ofhzH8h6kMx+/TbmHBwCsxiyda2gPuEwZ+27xDx7Au336M339LGyLlzlPRvf1P/e91XAnHpSLCTlTwmJibizJkzmDNnTpGd1k6iKGL27Nk4c+YMEhMTvQ6SiDynlak3rSc0avDVFL5mywqJIgxpyxCxfDB0t9Jhj45D3qBlaDRwIADXv/BffkEbyYBz5PzataLHnSPnO3ep9w3mHCXdtQtBva4ykJaOlAeydlu//PLL2LhxIxYuXIiUlBR0794dtWvXhiAIuHjxIlJSUnDx4kVUrlwZL7/8stIxE5EEWqk9p9mERiW+bHWohbJChf9QKfjYakLogc8g2Cyw1u8EU9f3gfBKSKoOTE4Gps0svZTKffeqnxDILRNDyuPOae2QlTzWqFEDn332GcaNG4fffvsNCxcuhPDXKlXnSGSjRo0wY8YM1KhRQ7loiSjgaCGh0QpftzrUQlmhvLyiH1esCCAkAqbec6E/vweW1k8X2dWQ1FFA40bAXXc5Hk9OFvD3JMe/PydHmZicHTqcH3viyNHbn8/CmzEKf/xXjwwAwME0Ee3bMaHxFbZp1AbZRcIbN26MNWvWYO/evdi/f3+JDjMJCQmKBUlEgUsLCY1WeDKF37qV59f3RVcNV6TUkTQc+x5I6gMAsMc0gT2micu4nVo0l5YQeFJ825sOHdczi16ntI8Lj7aOGy+iZk1g9EhoYuSUyBe8ak8IAAkJCUwUicglfyY0WuePKXx/dNUo3lLw1ddFVK/uSJjuamgpOB76v9nQ3d0U9mqNvL5nYXKKb8st4VLF6PlrXLXM84Y3o6dESpO1YWbFihUswUNEknGxu4O/pvB9WVaorLJLn0w9B9vSFwqOWVo/BXuV+l7fszh/Ft9u3kz+ru+PFii3o96ZKLNTDWmBrORx4sSJ6NChA1555RVs2rQJZrNZ6biIKMgEQp1EX/NnvTpfdNUoa83mAzU246ukAaiU+1vBMUubZwBdYC9Kk1ImxpXCCbYSO+oFgUWwSRtkJY+DBg1ChQoVsHHjRrzyyivo0KEDJkyYgD179igdHxEFkfLeJizQ69W5WrP5UuP5mN12FKJCsnAqu0HB8YgIadfVWvHt4us5Ezug1JFzTwVSUXyisshKHt955x3s3LkTCxcuRM+ePWGz2fDtt99i2LBh6NixI6ZNm4bjx48rHSsRUcAL5Cl8V2sxb5krAwA+OzUUI/YsKjguZZRMa8W3XdXgBFBk5PzF5+Xfwx9F8QOxj7yvONeLJiRYuV5UIbI3zOj1eiQlJSEpKQkmkwlbtmzBmjVrsGvXLvzf//0fFi9ejDvvvBO9e/fGiy++qGTMREQBzR/16kqtt+ilwmsxDcLtjTHLfh+C41l3I+16a9hLeZ0rzvWTVmvR477YcOJJPK5qcE781+3355GHBaz+XnS7e7403uyol6KsDU1a/uPEV7zZbU+lkzXyWFx4eDh69uyJBQsWYNeuXUhOTsZ9992H06dPY+7cuUrcgoioCC20XvSGr6fwi9dbVELLFkD1GBteaPQxFic+WXBchIC0660BSN9corXi257G481aSMB3RfGDoY+8L3C9qLIUSR4Lu3XrFq5fv47r18tJuwgi8ju1Wi/6a/pLq4mxPj8TX3Z9ES81+QgNok4Xeub2b2WpLQWl1LyUM6onl5x4nEsQqlb1/H6+KIofTH3kSdu8rvMIANevX8f69euxZs0aHDp0CICj00yrVq3Qu3dvJW5BRFRArdaL/pj+klPD0B906QcQvm4MKmb/CasuArNOv1vkeU9bCmqtHaXceJI6CmhQX0Tz5o7Hw54GNvwIXLnq+jW+KopfuBuOK76eMqfyQXbymJeXh02bNmHNmjXYvXs3bDYbRFFE/fr10bt3b/Tq1Qt33HGHkrESEanO18mcVnqSFxBFhKQuQej/ZkIQbbBXuRPmXnPwbGgDvLfScUrhNZu3brnvPAN4N/ImpbuNp+TGs32HiGkzbz9e/BlQxc21fLWjvnA3nLJoLXGnwCMreRw7diy2bt0Kk8kEURRRvXp19OjRAw8//DCaNm2qdIyyHT58GPPnz0daWhosFgsaNGiAp59+2qPRULPZjEWLFmHNmjW4dOkSoqOjkZSUhNGjRyNGbuVYIvI7T9rZ0W0hez5G2O4PAQCWxj2R3+VdILQC9IX6Tjt7DHuyUaNw20pXbf+qVwcqRVogCELBMgFfbQaR0kYzJgY4Ueixqw0/t245/h8VVfS4kl1+nAon0pmZ0qajy0MfefItWWse161bB4PBgH79+mHJkiXYtm0bxo8fr6nEce/evRg8eDD279+Prl274vHHH0dmZibGjRuHBQsWSLqG3W7HSy+9hPnz5yM6OhpPP/00WrdujVWrVmHAgAG44s8FOUQkm1prJIOBtfljsEfVhOnBicjvMR0ILX0o1NONGoU3nLhKHkePFLB+fXbB9L0vN4NI2QBTeD2nlPWFYWG3P/ZFUfziZYUWLAJ0bn6rl5c+8uRbskYe582bh7///e8IDQ1VOh5FWK1WTJgwAYIgYOnSpbjrrrsAAMOHD8egQYMwf/58dOvWDXWddTJcWL16NXbu3ImePXti5syZEP76qbZy5Ur861//wowZM/DBBx/4+p9DRF7S3FSwlokidJfTYK/lWBQnVoxF7rD1gCHM5UukbtRI7FB0etmTPtxy7+EJd/EUXs8pZX1h4STXOTqrFFdlhYo/Lk7LRegpcMgaeXzooYc0mzgCwJ49e3D+/Hn06tWrIHEEgIoVK+Lll1+G1WrFqlWr3F5nxYoVABzT9EKhP4f79++P+vXrIyUlBdnZ2cr/A4iIVCCacxC2YTwivx4M/ckNt58oI3EEPNuoUZzUtpVSdkO7uocnpMYjdX2hL0hJpHXF8sNAKEJPgUPxUj1asG/fPgBAYmJiiec6dOhQ5BxX8vPzcejQIdSrVw+1a9cu9Tpms7lgdzkRkZYUbg0opU2gcO00rAu6I+T4GoiCHrps6ctyvN2oIaXmpdRNHkpsBnEVT+FSTbVqen8fuaQk0vZCuWV57CNPviVp2rpTp04QBAGLFy9GXFwcOnXqJPkGgiBg8+bNsgOU4+zZswCA+Pj4Es9FR0fDaDTi3LlzZV7j/PnzsNvtLqe2ncfPnj1bkJCWJjo6Gjp3i1DIJaPRqHYIAavw5IDRaPT7VG1p711ZMXmyocXTf5u/PhdK/BuUirXwdapUKfs69sOrYft+LGDOBaKqwzBgAULrtpd8/fg6UQBuuY2pbnwUjMaQMq/l6t9cN97i1T08UVY8u3c7/m+3G1G9+g1kZJQ+TywIQPVYXcEGGyW/7kz5+QCkz3o98PcqQbNUQ82fa768d6D9rpOUPKanpwNwrCUs/FirnFPJUcW3uv2lYsWK+OOPP8q8RlZWVsG5panw11eNu2nrmzdvlvk8uWY0GpGZqeLcUIBzlExxbKv877brire/K4ur9y4nBwAcPyQzMzNhNjuOe1rb0NV1lDpfDqX+DUrFKuk6VjPCtk9ByKGvAQDCnYnI7jIFYoVqgJvvvcLXrxuf5XancmwscGe9LGRmlvzESIn1znqiV/fwhNT34JXhIt58q/TnRBF48XkR27fC7XU8FR7m2cYgX33Nq8Ef38v+vrfWftdJSWQlJY8nTpwo8zERaUug9bYNhg0tOTm3/w05OYCLvzsLOKdAnR+rQX/xZ4Qc+hoiBFgSXkRkjwkQb7of3StxHb2A0SMdO55d8Xajhj/u4SnnBpsZs0Wc/OuYIHheMN1TcsoKkfd8UV80UAXlfKpztNA5elhcdna2y1FJJ+fzrkYWcxx/grgcmSRSS3nobVu43I5WSu942kvaOULpqy4yxX/RldaSzla3A/Lbj4Cp70KYO7wCQSd9O3DxVo3OVn3VqhU9T8mNGv64h5yYln52+74zPvD9+kJPywqVN8nJyWjXrl2p1VCmTZuGdu3aITk5uci5xf8bPXp0kdcVL4v06usiHh0UHD9P5VCkPaHWONcjnjt3Ds2aNSvy3M2bN5GZmYlWrcruzVSnTh3odLqC9ZPFOY+7K/dD5E/+KGeiBdnZt/+Ne/eJ+HtSYP57fFWw3NXI8z9HWNEpdBGszR6FGFUdAGBpP1zWPUpr1ZjUUUCrewDnj8XCnWeU4o97eKrkBhvf39OTskLlUfXq1bFp0yaMGjUK4eHhABwbYTdt2oQaNWoUObddu3aYOHFikWMhIbfXzboqi+T8g3xysjZndHxJUvJ46dIlr25Sq1Ytr17vqTZt2mDhwoUFNRoL27VrFwCgbdu2ZV4jLCwMLVq0QFpaGtLT00vsuN61axdCQ0PRsmVLZYMn8oIn5UwCtbetox3c7V+Yb74lomZN7U7J+5urX3S4lYHqG8chrGoqDOd+Qt7ALwDBu8mn0pJffyRSaiRrcvh6aUJZiXROTpkvDXqNGzdGeno6tm3bhm7dugEAtm3bhtjY2BK/z0NDQ1G1atVSr1Ne/iD3lKTk8cEHHyxS59ATgiDg2LFjsl4rV/v27REXF4e1a9fiqaeeKuh8k52djY8//hgGgwF9+/YtOD8jIwNZWVmIjY0tMp09YMAApKWlYebMmSWKhJ8+fRqPPPIIp61JU/xZzkQNrtrBlecRgMJc/aJrXfVnzGw7FlXDriHHWgG450mvE8dgplTSV9rorNICJZFWQ69evbB27dqC5HHNmjXo3bs3Dhw4IPka5eEPcjkkJY9t2rQpccxisSAtLQ2AoxyNc3Tx0qVLBTuM77nnniJDv/5iMBgwadIkPPfccxg8eDB69eqFihUrYuPGjbh48SJGjx6NevXqFZw/a9YsrF69GlOmTEG/fv0Kjj/yyCNISUnBunXrcPHiRbRt2xYXLlzAxo0bUbNmTYwbN87v/zaiskjtWRuIvW3LywiAN4vyXf2im9d2OCqF5eDXm43w6v7ZGNelHlorFbACtLB5qDAlkz72UldP9+7d8cknn+DSpUsQBAFHjhzBpEmTSiSPu3btwgMPPFDk2JNPPolnnnkm6P8gl0tS8vjFF18UeZydnY2nnnoKjRs3xmuvvVaizuGuXbswY8YMmM1mfPrpp8pF64F27dph2bJlmDdvHtavXw+LxYIGDRpg1KhRePjhhyVdQ6/X45NPPsGiRYvwww8/YMmSJYiOjkbfvn0xevRoxMTE+PhfQeQZKbswA7W3rTcjAIGyS9LbXfKFf4FVNNwC4JiK0wsiVp/rh6lH3kS+PVxzv+j8MULnKa3EQfJVrlwZ999/P1JSUiCKIu6//35Urly5xHmtW7fGa6+9VuRYpUqVAAT3H+TekLVhZs6cOUhPT8fGjRsRHR1d4vkOHTrg7rvvRteuXTFr1iy89ZaLQlg+1qJFC0nJ69SpUzF16tRSnwsNDcWIESMwYsQIpcMjUpwWy5koRe4IQKCULVJiUX7hX2AW++2Kxu8degsbLvcu9TytYLJGvtC7d2/MmDEDAPDqq6+Wek5ERATi4uJKfS6Y/yD3hqxFLxs3bkS7du1KTRydKleujHbt2vm9uwxReafFcibuSCkrI2cEIFDKFkmdki/t81JYy+YiYmMc2We+PbzgeEr67cSxPP6io+BRvESUO+3atYPVaoXVakVCQoLH95NSFilQ/yD3hqyRxxs3bsBkMrk9Lz8/Hzdu3JBzCyLyghbLmbgidWTQ0xGAQFojqcii/PwsVNg4EfMebYpBn/zD5XXK4y86X9Pams1g5ukSB71ej6+//rrg49KYzWZcu3atxOucU9zuyiJp8Q9yX5OVPMbHx2PPnj04ffo06tevX+o5p0+fxk8//VRqf2ki8r1A2IXpyVStp1PygbRL0ttF+borJxC+ZhR0N86jsX4bZkzsi/c/Kjr0rIVfdJ70/i6L1pI1La7ZDGaefo4ruGlZtWfPnhJl/eLj47F8+fKCx4H0B7k/yEoen3jiCbz99tsYMmQInnnmGXTv3r2g6OYff/yB9evXY8mSJbBYLHjiiScUDZiIgoOckUHnCEDhOo9A6YlRIO2SlL0oXxRhOLoSYVsnQbDlwx5VE6Zes9GuZiy+bCNq6hedp72/y6LFZE0rcRDc7rOYNm1akXOl7ssIhD/I/UVW8jhw4ECcPXsWixcvxuzZszF79uyCGojiX39aiqKIoUOHYuDAgcpFS0RB48hReSODSR0FNG4E3HWX4/HkZKHUDjP+3iVZeD3i4SOedb2RtSjfkoewLckIOfYdAMBaryNM3aYCEUYA2vtFp3T/ciZrROqR3Z5w/PjxeOihh/DVV1/hwIEDyMjIAADExMTg3nvvxcCBA3HvvfcqFigRBZfrmdLOK21ksHBi1KJ56YmRP3dJetv1xuNd8nYbIr55Evo/f4Eo6GDuMAqWNs9JLvyt1PRxabQ2pUxEyvOqt3WrVq3c9ogmInISC+VGxpLl1kold2TQX2WLlOp649GifJ0elmb9IWT9ifweM2CrI30XqZLTx6XR4pQyESnLq+SRiMgTeXm3P25Q3/cjg77eJan0ju4yF+XbzBCyMyBG3wEAsLYYBGuj7kCExCz8L0pPH5eGSaP6OAJMvsTkkYhU4a+RQV/ukvTFju7S1ioKt9IRvnYMhLzryB2yEgiv5MjQPEwcKfg4k0SDwVAkSeQIMPmSrCLhRFT+iGLRaWcl+KugecmETJnr+mNHt/7MdkR+0R/6Pw5DMGVBl/m7/ItR0HEmif/7X8kkURCYOJJvcOSRiNxSap1cRETJjwO5fpqvd3SH7v4QEYc/AgDYqjeHqddsiNG15V2MghaTRPI3Jo9E5JZS6+QK/4Ir/LHWyspI5esd3aH7FwOhgPmeITB3fA0whLp/ERGRj3HamohIJl/3vRVDImDqORPmBycwcSQizWDySER+U3jNpNLrJ9XiXLdZtWrR40qs28wduBTWxj28jJCISFlMHonIbwqX6in8caBL6ijgPwtvJ4mTkwWs+MqDxDHvBkIOLi1xWDTGKxWi6gp34Ek7JBZ5TESBRdKax++++86rmzzyyCNevZ6IqLDSNt6oTUrXm9LoLh9G+NrR0GVdhhgaCdTt66MI1bN9h1ik1uarr4uoXl16Bx4i0hZJyePrr79e0LvaE6IoQhAEJo9EpChXG28CiigiJG0pQrdPg2C3wF65DuyxTRW7vFaKRDs78NjtRY972oGHiLRDUvI4fPjwEsnjuXPnsGbNGkRGRiIxMRE1a9YEAFy+fBk7d+5Ebm4uHn74YdSpU0f5qImINKbwNOzhIyL+nlRGuaH8bIRtmoiQkxsAANaGD8H00CQgLArIUSYeLRSJVroDDxFpg6TkceTIkUUenzlzBgMGDEDfvn3xxhtvoFKlSkWez8rKwpQpU7Bp0yZ8/fXXykVLREFJK6Nkcm3fIWLazNtJ0ptviahZs/RpWd2VkwhfOwq6zLMQdQaYO74KS6snfZLhlXbJ4msPfVlT0xcdeIhIfbI2zMyaNQtVqlTB5MmTSySOABAVFYVJkybBaDRi1qxZXgdJRJ5zJmQJCVbNJGTFR+ecj52jZN4UIC+LLz8XzmnZa9eKHndOy27fUXTkTcjJgJB5DvaKNZA34HNYWj/lt6HB7TtEPDG06NrDRweVjFEp/ujAQ0T+J6tI+M8//4zExETodK5zT51Oh+bNm2Pnzp2ygyMi+bQwbVmYu9E5X8boq8+FnGlZW91E5Hf/ANa6iUCEscT5vhqFlbL28JE+yt0P8H0HHiJSh6yRR7PZjMuXL7s97/LlyzCbzXJuQUQK0ErbMk9H53xBqc9F4R7fUqZlw3POQfzsaQg3LhQcszbtXWri6IxT6VFYqUmu0uVznB14yuJNBx4iUoes5LFZs2Y4ePAgUlJSXJ6zfv16HDhwAM2aNZMdHBEFPrUSF19w9vju0SMKouh+urVTzY1Y1vExVL7xM8K2vif5Pkon/VLXHqYesCp3U/i+Aw8RqUPWtPXIkSMxbNgwjB07FqtWrUK3bt1Qq1YtCIKA9PR0bNiwAbt27YJer8eIESOUjpmIAkgwbZoo3uPb1XSrAVaMu3sGnqj/BQDgZnRrGLpITx6VJnVN4ZWrdjRsoOy9HR14UKTOI+AYcRw1wrsOPESkDlnJY9u2bTF37lxMmDABO3fuxK5du4o8L4oioqOj8d577yEhIUGRQIkoMAXzpgnntGzx5Hh22xF44I7/AQC+uTQMXUeMhhiqXm9qqWsKY6r5pulYUkcBre4B6tZ1PJ4+VfDpLm8i8i1ZySMAdO7cGe3bt8eGDRuQmpqKjIwMiKKI2NhY3HvvvejWrRsqVqyoZKxEpBJvyrsE86YJx7SsY91m4WnmNjGpuGWuhIkHJ+Oh4Z2gD1U3SXKV5BYWGwvc29qAW7d8E0Phr5d7WkrvwENE2iM7eQSAChUqoH///ujfv79S8RCRxnjbWk5q4hKomyYKT8v++texE7eaYt7F9zFweJwmpmULJ7mucO0hEUnlmzkKDbhy5QrefPNNJCYmonnz5ujatSs+/PBDj3Z/X7x4EY0bN3b537p163z4LyBSn3OX9NWrRY97sktarxfQpVPZ53R+MICnMHOvIynRhi+X3I7/eo//YP4SbSSOTo4kV0C1akWPx8YCk5O59pCIpPNq5HH79u1Yvnw5jhw5gszMTPTu3RtTpkwpeO6nn37CM888g+rVqysSrFRXrlzBgAEDcPnyZXTu3Bl169ZFamoq5s+fj7S0NCxatKjMGpXFNWnSBJ07dy5xvGHDhkqGTaQpSrWWs9lEbNpS9r02bwVe+IcYcAmk7uLPCF83Fta7+0HfanTB8ZatwzQ5Lcu1h0TyBXonLCXJTh7feecdLF++HKIookKFCrBai5Z4qFSpEj777DPUqFEDw4YN8zpQT8yYMQOXLl3C22+/jcGDBwNwbOJ54403sHr1aqxevdqjqfamTZuWaNFI/uOsqaeFeoVOWoxJaUrtkg6m3daFhRz4DBH7p0MQbdCf3go0e0ntkCTh2kMiebTWeEFNsqatv/32W3z99ddo0aIFvvvuO6SmppY4p1WrVqhevTq2bt3qdZCeyM7ORkpKCuLi4vD4448XHBcEAWPGjIFOp8OKFSv8GhPJV7yunhZoMSZfUGqXdLDutg7bNQ+CaIOlaW/kDf4aCAlTOyQi8jGtNF5Qm6yRx+XLlyM6OhoLFiyA0Vh6lwQAqFOnDi5evCg7ODnS0tJgNptx//33Qyj2DsfGxqJRo0Y4dOgQ8vPzERYm7Yd9RkYGli1bhqysLMTGxqJ9+/aoUaOGL8KnYorX1atQQeWAoM2YfEGpXdLBtNta9+cxAB0AAKI+BKbO78La/DHHbxM20yKickJW8njq1CkkJCSUmTgCQExMDA4dOiQrMLnOnTsHAKjrXNRTTHx8PE6cOIELFy6gQQNp1XB37dpVpJalwWDAk08+iddee82jtZNEgUSpXdJBs9vanIOIRUSxFQAAIABJREFU74cDSAMA5D26GBH1mqobExGRCmQlj4IgwG63uz0vIyMDERERcm4hW1aWYz1CVFRUqc87a086zytLREQERowYgS5duuCOO+6A2WxGWloaZsyYgcWLFyMkJARjx44t8xrR0dFMML1Q+A8Uo9GoiVG+wrWetRKTr7z5ej7+OS4bxWdpnIP6/xpfEdWqlT6CX/i98+Y6pdHrb68XOH2mIhI7GPyw6cOIrO5vAX81iolufH+R9z5Qvi7cxeluUMBX9yXv+eq9I98LtPdOVvJ455134ujRo8jLy3OZHGZmZuL48eO4++67ZQWWkJCAGzduSD7/888/V7ybTdWqVUtslHnwwQfRvHlz9OrVC4sXL8Zzzz2H6Ohol9e4efOmojGVJ0ajEZmZmQAc31SZmZnwoNKSz+TkAFqLyVfuuxeY9K5QorVcTIyjLuB99+YiMzO3xOtuv3dFrzNtpmfXKc3tupNVAQAvDr/1V91J5cvN6K7+BljyYK/pGBbNiXug4Lni732gfF2UFWfx981f9yXv+fK9I9/S2nsnJZGVlTw6S/IkJyfjvffeg8FQ9DKiKGLSpEnIzc1Fnz595NwCvXr1Qo7jp40k1f4qXuYccXQ1spidnV3kPDliYmKQlJSE77//HkeOHEFiYqLsaxFpnVLlXZI6CmjcCLjrLsfjyckC/p7k2XWcdSeLT3w4605OTpZWuFwKw7EfELb5HYjhlZD7xCogMgAWZWoYy5wQBQ9ZyePgwYOxceNGrF69GqmpqQXJ06+//ooPPvgA//3vf3H27Fm0a9cOffv2lRXYxIkTZb0uPj4eAHD27NlSnz937hx0Oh3i4uJkXd/JmZmbTCavrkMUCJQq71L4Oi2ae3YdpepOumXNR9h/30fIkW8c960aQPWDNIxlToiCh6zFeCEhIfj0008xaNAgXLp0CcuWLQMAHDt2DIsXL8aFCxfw6KOPYsGCBX5f73fPPfcgNDQUP/30E8RidVQyMjJw8uRJtGzZUvJOa1cOHz4MAKhdu7ZX1yEiaTypFymXcOM8Ir5+HCFHvoEIAfntR8DUdxFHHRXCMidEwUF2kfCIiAi88847eOWVV7Bv3z6kp6fDZrOhRo0aSEhI8HtXGaeKFSuiR48e+O677/DVV18VKRI+a9Ys2O12PPbYY0Vek5WVhYyMDERFRSE2Nrbg+OHDh9G0aVOEhIQUOX/x4sU4cOAAGjRogCZNmvj+H0VEPq8Xqf9tE8I3vgkhPwtihBGm7tNhq9tB3sWIiIKYV+0JAaBKlSro1q2bErEoZuzYsdi7dy+Sk5Oxe/du1K1bF/v378eBAweQmJhYYip906ZNeOONN9C3b19MnTq14Pj06dNx5swZtGnTBjVr1oTJZEJaWhqOHTuG6OhoTJs2rUQtSSLyDV/Xiww5sRZCfhZstVrB1HMWxKiStVxtttuzGWmHRLb2I6JySdaccqdOnTB9+nS3582cObPUntC+Fhsbi2+++Qb9+vXDgQMHsHjxYly7dg0jR47EJ598Inkq/eGHH0bTpk1x8OBBLF26FCtXrkReXh6eeuop/PDDD7J3khOVV4WLM3haxctZL7Is3tSLND00CfkdRiHvsc9KTRy37xDxxNDbyeOrr4t4dJCI7TsCq82Qc+NKQoKVG1eISBZZI4/p6em4ft393FBmZibS09Pl3MJrsbGxeP/99yWd269fP/Tr16/E8ccee6zEFDcRyVd4oN7TQXu9XsDokY5d1a6MGiFIHgnUn9sFw6nNyH/wLUcwYVGwJLxY6rlSdnnfd29gjEBy4woRecunu1ny8vJKlPEhIpIrqaOAyckC/qrMVSA21lH6R1KZHrsNoT99iPCV/0DIoa9hOL6mzNOl7vIuPKWtddy4QkTe8ElmZ7fb8fvvv2Pv3r2oVauWL25BROWUV3Unc68jPGUcDOd3AwAszQfA2qhrmS+Rusv7yFEJwRMRBQHJyWPTpkV7uH733Xf47rvvynyNKIoYMGCAvMiIiFyQU3dSl34A4Wv/CV1OBkRDBPI7vwPrXQ+7fZ3U3dvXtdMggojIpyQnjzVr1iz4+PLlywgPD3fZwiYkJASxsbHo1KkTnnzySe+jJCLyguHwNwjbkgxBtMFurAdT77mwV2so6bVSd29XCazWtEREsklOHrdu3VrwcZMmTdCtWzdMmTLFJ0ERUXBSq0WdvUo9AIClcU/kd3kXCK0g+bXOXd5lTV3HxgLNm3kbpXzOfghcx0hE/iBrzePnn39e0EuaiEgqv+70NecUJIn2O9ogb8gK2GOaeHxjpXd5K00Uge7dowo+t0wgicjXZO22btu2Le68806lYyGicsDnO31FEYbD36DCp50hXDtdcNge21T2jRXZ5e0jubnAvn0G7N1rQG6uamEQUTkiK3n8/PPP0bRpU2zfvt3lOdu3b0fTpk2xdOlS2cERaVHxLiOBVKIl6FlyEbZhPMI3vw3BdAMhR75R7NJJHQV8ueR2kjh9qoAVX6mbOBIRqUFW8rhx40bExsYiKSnJ5TkdO3ZETEwMfvzxR9nBEWktUQuWLiOeCoSuJMK104hYNhAhx9dAFPTITxwDc9J4Re9Rcpc3E0ciKn9kJY+///47GjYse6eiIAho1KgRzpw5Iyswok2b8zWVqDm7jFy9WvS4s8tIMCeQzvV0Wl1TZzixDpHLBkB/7RTsFWKQ99hiWNr+AxB82geBiKhckvWT9datW4iOjnZ7XnR0NG7evCnnFlTObd8h4p/jsjWTqAVjlxFPabUrif7MfxGeMg6CJRfWuHbIe2IV7He0UTssIqKgJWu3dUxMDE6ePOn2vJMnT7qsBUnkijNRE8vIw+Z+KCKxg8SuIl5wxiC1y8ihw0DrVj4NiYqx1f0bbHe0ga32vTC3HwHoJFQM9wG1yhAREfmbrJHHhIQEnDp1qsz1jBs3bsRvv/2GhIQE2cFR+eRJouZLzhIoPXpE4eo1aa+R2o2EvKO/+PPtBzoD8h79P5g7jFItcQS0P7VPRKQUWSOPzz33HNatW4dx48Zh//79GDhwIOLi4iAIAs6fP4/ly5fj66+/RkhICJ577jmlY6YgJzUB83Wi5iyBAgAVJI4kSe1GQjLZrQjdOQfCT18BKLSeWifrR5nimDQSUXkg6ydu/fr18cEHH+D111/Hl19+iS+//BKAY5OMKIoQRRFhYWF4//330bhxY0UDpuAnNQHzZ6LWvJm0LiMtW/gvJq3wV3cTITsD4evGQJ+eCgs4L0xEpBbZWxG7d++OH374AQMHDkSdOnUQGhqKkJAQ1KlTB48//ji+//579OzZU8lYqZxwtoMrKxnxd6Lm6DJSdnakZpcRtRSe2i9rjaq39Od3I+LLftCnp0IMrYC87lN9dzMiIiqTV3M98fHxeOeddxQKhcjB2Q5uwtvaagfn6DICzJxTNK7YWEc85bFYdOGp/dxcoIL0ltHSiHaE7F2I0N0fQhDtsFVrDFPv2bCF1lP4RkREJJU2FgoRFZPUUcDsGRWQPDm7yHG1E7WkjgJa3QPUret4PH2qgHYJvt/1XV4JWX8gdP//QRDtsDTrj/wHJgAh4UCO2pEREZVfTB5Js7p0DkOjhjmaS9RKdhlRMZggJ1aqBVPX9yHkZ8HarJ/a4RARESQmj506dYIgCFi8eDHi4uLQqVMnyTcQBAGbN2+WHSCVb0zUyhlRRMjBL2Cv2gC2+PsBALaGXVQOioiICpOUPKanpwMArFZrkcdERIrJz0L4xokw/PYj7BFVkDt0LRDBJgNERFojKXk8ceJEmY+JiLyhu3IC4WtGQXfjPERdCCztXgbCK6sdFhERlYJrHolIVYajKxG25T0Itv9v777Do6ryP46/Z5KZJCQhhF6UEiEJSOgkgIViKEJAqrA/iu6C2AVEEVZQF9SliOKKuy6uINilV6UIUkUJRTooLZAgNUB6Jpn7+yNmJKYwCYFJ+byex8fk3DP3fmduAh/OuffcFOy+1UiOeAd7tcauLitHegShiIjCo4i4ij0Nj7WvYDmwGIC02veR/OCUIj1VnfkIwsyvRURKI6fCY0xMzE0dpHr16jf1ehEpgUxuYE/HMJlJbfMcttDHwFTg5xbcNgqNIlLaORUeO3TogKmAf2KaTCYOHjxYoNeKSAmUbgM3C5hMpIS/iq3Rw9hrNHd1VSIi4iSnwmPLli2ztdlsNvbs2QOAn5+fY3QxJiaGq1evAtCkSRMsFkth1SoixVlaKtZNUzFfiyb5ofczRhktZRQcRUSKGafC4yeffJLl+/j4eIYMGUJQUBBjxozhnnvuybJ969atvPXWW6SmpvK///2v8Kp10o4dO1i/fj379+/n4MGDxMfH06tXLyZPLtjzcJcvX87cuXP59ddfsVgsNGnShOeee46QkJBCrlykZDJdi8Zz+Sjczu0DwHwmEvudoS6uSkRECqJAFxjNmDGD6Oho5s2bly04Atxzzz3MmTOH6Oho3n777ZsuMr8WLlzI7Nmz2bdvH5UrV76pfX3wwQe88MILXLp0iQEDBvDggw+ya9cu/vKXv/Djjz8WUsUiJZfb8e8p80kf3M7tw/DwI6nnfxQcRUSKsQKFxzVr1tCqVSv8/Pxy7VOuXDlatWrlkqfLDBw4kBUrVrBz507++c9/Fng/J0+e5L333qN27dosW7aMsWPHMnHiRL788kvc3d0ZP368Y+F0EfkTexrWLe/gteRJTClXSa8SQuKghaQHtHN1ZSVKerrh+HrPz0aW70VEboUChccrV66QnJx8w34pKSlcuXKlIIe4KSEhIdSrVw+3m3yW3aJFi0hLS+PJJ5/E19fX0V6vXj0eeughoqKi2L59+82WK1LiGIaBx5rxWH+aBUBq4/8jqf+nGH41XFyZ60ycOJFWrVrRqlUr7rnnHh566CGmTJnCtWvXHH169uzJl19+6fQ+N24yGPToH2HxxbEGfQcYbNykACkit06BwmOtWrXYvn07x44dy7XPsWPH2LZtG7Vq1Spwca72008/AeQ4NX/fffcBGddXish1jIzgYmsyCMOzHMndppP6wARwt7q4MNdr1aoVK1euZPHixfz9739ny5YtTJs2rUD72rjJ4OVXDC5ezNp+4QK8/IoCpIjcOgUKj4MGDSIlJYWBAwcya9YsTp8+jc1mw2azcfr0aWbNmsXgwYOx2WwMGjSosGu+bU6ePEmZMmWoVKlStm2ZofjkyZO3uSqRIsqwYz6fsSyXyWTCXrUhCcPWkRbU1cWFFR1Wq5UKFSpQuXJlwsLCCA8PL9C10+npBjPeyzscvjtTU9gicmsU6Akz/fv35+TJk8yZM4d33nmHd955x7EOpPH7qINhGDz66KP079+/8Kq9zeLj4ylfvnyO23x8fBx98uLn54fZXPQXPi6q/P39s3zt7X37jm29bqDs+mPn1l4aXf9Z+K5+kTLR3+H+2Aqg/O/n7tY8LaY4ngMPDw9SUlIcP9OnT59mx44dWK1WR5ubmxteXl5Zfu5z8tMOGxcuXMuzz/nzcPyEL6Et87dc2o2OLUWXzl3xVdzOXYEfT/jSSy/RqVMnvvjiC3bt2sX58+cBqFSpEs2bN6d///40b17w9dvCwsLydb3kvHnzCAsLK/DxbpXMNS8l//z9/YmNjSUzgMTGxpKaevuOn5BAjsfOrb00uv6zMH75HsML4qP24Vs95Pdzd+uPW1zOQUpKCt9//z1NmjTBbreTkpICwIgRIxyfVXp6OklJSTf87E6ecm5E8eSpOOrVdf4BD3/8zklxo3NXfBW1c+dMkL2pZ1s3bdqUpk2b3swuchUREUFCxt8QTqlYsWKh1+Dj40NcXFyO2zJHHDNHIKX0KFMGwsLSHF+XWoaB5eevgScAsPvdQVLfKdgrBbu2riKsWbNmjBkzhuTkZJYtW8bp06fp169fvvdTIecJkQL3ExHJj5sKj7fShAkTXF0CtWvXZvfu3Vy4cCHbdY+nTp1y9JFbpygGNZMJVq2Kc3xdKqUm4LFmPKb9m8gMj4kDPsPbX/+YyouXlxd33nknAKNHj+app57io48+4vHHH8/Xfho3gkqVMm6OyU3lyhn9REQK201djHf58mU+/vhjRo8ezdChQ/nwww8d244ePcp3331HUlLSTRfpKpmPZdy6dWu2bZs3b87SR26NzKC2alVckQpqJlMpDo6A5cBiLEe/xTBftxyWVcExv4YOHcrnn3/OhbxSYA7c3EyMfDbvH8ARz5hwcyvFP6QicssUODyuXLmS8PBwpkyZwsqVK9m2bRvHjx93bD916hTPPPMMq1evLpRCb6W4uDiOHTvmuG4zU+/evXF3d+c///lPlunrX375haVLl1KzZk1atWp1u8stdUp7UCuKbE3+D9vdvUnq/eGNO0uumjdvTp06dZg7d26+X9v2fhNvTDTx5yt2KleGNyaaaHu/fmlE5NYo0LR1ZGQkL774ImXLlmXkyJE0a9aMvn37ZunTrl07fH19Wbt2LT179iyUYvNT34IFC4CM0VGAnTt3MnbsWAACAgIYPny4o//atWsZN25ctudf16lTh2eeeYYZM2bQo0cPOnfuTGJiIitXriQtLY1Jkybh7l5kZ/5FCo8tGUvkR9haDAWLJ5jMpHR+A7vzlyVLLv7yl7/w+uuvM3jw4Hy/tu39Jpo2gcyrZ6ZNNtEqDI04isgtVaDk89///hd3d3c+/vhjgoNzvjjeYrEQEBDAr7/+elMFFkRUVBSLFy/O1hYVFQVAaGholvCYlyeffJIaNWowd+5cvvjiCywWC02bNuW5556jUSNdUCQlnyn2JJ4rRuF24TDmuN9I6TTJ1SUVyWthb+SVV17Jsb1z58507twZgCVLluR7v9cHxSaNTdzkg7VERG6oQOHx559/pnHjxrkGx0xVq1blyJEjBSrsZvTu3ZvevXsXWv8ePXrQo0ePwihNipE/PzO4NI7ouB1dg+eav2NKTcDuVZ60oAddXRKgm5ZERFypQNc8JicnO7UOUHx8vGPxcJHipNQ/Mzg9FeuGN/FaMQJTagLpNZqTNGgR6bXauLoyB10LKyLiGgUKj9WrV7/hiGJaWhpHjhwp1s+2ltKptD8z2BT3G15fD8G6+xMAUlv8jaS+czB8q7i4MhERKQoKFB7bt29PVFQUn332Wa595syZw8WLFwkPDy9wcSK3m54ZDGBgjj2F4VGWpIfeJ/X+F8Et50fc/Xlqv2R/LiIiAgW85vGxxx5j5cqVvP766+zZs4cHHngAyLizecOGDaxbt47FixdTrVo1hgwZUqgFizjj90es53ta8+e9eS+8DBnPDP55LzS7NQ9Xcg3DcHxYhm81knq8h+FbFcPvjlxfsnGTwfQZWaf2q1SBkc9Cz4duecUiIuIiBQqP5cuXZ86cOYwcOZLly5ezYsUKADZt2sSmTZswDIOAgABmzpyJr69voRYsciOGAQ8+6Ou4qSI/AfLS5cLtVxyYEi7i8c0YbE0HkX5XBwDsd7TI8zWZU/t2e9b2zKl9b+8UWhT80fYiIlKEFXiRwrvuuoulS5eyfv16tm3bRnR0NOnp6VStWpU2bdrQuXNn3LRmhLhAYiL89JO742tvb+dfW9qeGWw+E4nnyucxJ1zAfPkEibXuBXdrnq9xZmp/8tREvvrcKHV3p4uIlAYFCo/x8fEA+Pj4EB4erusapcQoNc8MNuxYImdj3TIDk5FOeoW7SI5494bBEZyb2v/tnJ2f95pK1tS+iIgABbxhpkWLFgwdOrSwaxFxuVLxzODkq3gufQaPzdMxGenYgruT9H9fY1S4y6mXl8apfRER+UOBwqOvry933JH7hfQixVmJfmZw8jXKfNoH9+MbMNwsJIe/RsqDU8Di/GNaStvUvoiIZFWgaev69etz+vTpwq5FpMgosc8M9ixLWp37cT+5meSIGdir3J3vXTgztV+1ipnGjbRsj4hISVSgkcfHHnuMffv28e233xZ2PSJFRvZnBhfT4JiaAIl/zCGnth1L4sCFBQqO4NzU/tgxZYrv5yUiInkq0Mijp6cn/fr1Y9SoUSxdupQOHTpQrVo1PDw8cuzfsmXLmypSRArGdOlXvJaPxO5dkeQ+H4HZLeOmGCdujMlLxtQ+WdZ5hIyp/RHPmOgY7kFsbOJNHUNERIqmAoXHwYMHYzKZMAyDDRs28P333+fZ/9ChQwU5jIjcBPeDy/BY9xqmtCRIicN0LQaj3J2Ftv8SO7UvIiJ5KlB47NmzJ6b8PrpDRG6PtBQ8NryJZd/XGd/WbEVK17cwylQo9ENln9ov9EOIiEgRU6DwOHny5MKuQ0QKgelKFJ4rRuJ2/hAGJmytniS11VMZ09UiIiKFoMBPmBGRIsYw8PxmTEZw9PIn+cFppNe+x9VViYhICZOv8Lhx40bWrVvH2bNnsVqtBAUF0bt3b+68s/CuoxKRAjKZSOk4EevGKaR0egPDt6qrKxIRkRLI6fA4evRoVq1aBYBhZNxhuWHDBmbPns3bb7/NAw88cGsqFJFcmeJ+w3x2D+mBXQCwVwzMuKtaRETkFnEqPM6fP5+VK1fi7u5Ojx49aNCgAQkJCWzYsIE9e/bw0ksvsWHDBnx9fW91vSLyO7dTW/Fc9SKkxJHkUwV7dT1IWkREbj2nwuOSJUswm818+OGHtG7d2tH++OOPM27cOJYsWcKaNWvo06fPLStURH5nT8e6/T9Ytv8bEwbplerfkjupRUREcuLUE2aOHj1K48aNswTHTI8//jiGYXD06NFCL05E/iTxMp6Lh2Pd/j4mDGwhD5P0ly8wytV0dWUiIlJKODXyGB8fT82aOf/llNkeHx9feFWJSDbm6F14rnwec/w5DHcvUsJfJa3BQ64uS0REShmnwqNhGJjNOQ9SZrbb7fbCq0pEsnH7bS/m+HPYyweQHDEDe8V6ri5JioAyZSAsLM3xtYjIraZ1HkWKCVuzR8Dkhq1hb7B6u7ocKSJMJli1Ks7xtYjIreZ0eFyyZAlLlizJcZvJZMp1u8lk4uDBgwWvUKSUMp8/iHXruyR3ezsjLJpM2JoNdnVZUgQpNIrI7eTUDTOQMXVdkP80nS2ST4aB+96v8friL7if2IR167uurkhERMTBqZHHw4cP3+o6RATAlojHun9gObQMgLSAdhnPphYRESkiSuQ1jzt27GD9+vXs37+fgwcPEh8fT69evZg8eXK+9nPmzJk8n5zz9ttv061bt5stVwQA06VjeK4YidulXzFMbqTeMwJby6FgcnqCQERE5JYrkeFx4cKFLF68GC8vL6pVq3bTywgFBwcTHh6erb1ePd3tKoXD7dQ2PJc9i8mWiN27EsndpmO/o6WryxIREcmmRIbHgQMHMnToUAICAti3bx/9+/e/qf3Vr1+fZ599tpCqE8nOXrEehrUM6VUbkdJ1GoZ3RVeXJCIikqMSGR5DQkJcXYLIjSXFgpc/AIZ3JZL6f4ZRtgaY3VxcmIiISO5KZHgsbOfPn+fzzz8nLi6OypUr07p1a6pWrerqsqQYczu2Hs9vx5HSYQJp9SMA9IhBEREpFhQenbB161a2bt3q+N7d3Z3BgwczZsyYXJ+8I5IjexrWLTOwRn4EgPuBhaQFd9NCfSIiUmwoPObBy8uLZ555ho4dO3LHHXeQmprKnj17eOutt5gzZw4Wi4XRo0fnuQ8/Pz8FzJvg7++f79dYrVlf713Ah7EU1n4yGdd+I33hExintgNgbv0Ynp0m4OVuvcEri668PqOCnDtxPZ234kvnrvgqbueuyIbHsLAwrly54nT/efPmERYWVqg1VKhQIduNMh06dCAkJISIiAjmzJnDsGHD8PPzy3UfV69eLdSaShN/f39iY2Pz/bqEBICMX8TY2FhSUwt2/MLaD4Bb1A94rHoRc+IlDKs3yZ3eID2wM8QlAAkF37GL5fYZFfTciWvpvBVfOnfFV1E7d84E2SIbHiMiIkhIcP4v1YoVb9/dqZUqVaJt27YsXbqUffv2ce+99962Y0vxY4o9hefCxzAZ6aRXDCK5+wwM/9quLktERKRAimx4nDBhgqtLyFNmMk9OTnZxJVLUGf61sDV/FFNSLCkdJoDF09UliYiIFFiRDY9F3d69ewGoUaOGiyuRosgcswfDpzJG2eoApN73vJ4UIyIiJYL+NgPi4uI4duwY58+fz9K+d+9ebDZbtv5z5sxh165d1K1bl+Dg4NtVptxmZcpAWFgaYWFplCnj5IsMA8uueXh9PRjPlc9D+u8XASo4iohICVEiRx4jIyNZsGABAJcvXwZg586djB07FoCAgACGDx/u6L927VrGjRuX7fnX06ZN4/jx47Rs2ZJq1aqRnJzMnj17OHjwIH5+fkydOhWTllgpsUwmWLUqzvH1DaXE47lmPO6/rAbA7lsN0m3gVnzvphYREfmzEhkeo6KiWLx4cba2qKgoAEJDQ7OEx9z06NGD1atXs3v3btavXw9A9erVGTJkCEOHDtVC4aWAs/82MF84jOfyEZivRGGYLaS2HYOtycASv35j5uhs5tciIlLymQzDMFxdRElWlG6/L25uZqmeO+/MuKHp9OnYm16f8Ubc9y/E47tJmNJTsPtWIzniHezVGt/agxYhmX+CXJ+Ti9rSE+IcnbfiS+eu+Cpq565YL9UjUiykp2LZ/Smm9BTS6txPcpfJjudVlxYlfHBVRET+ROFR5Ga4WUmOeAf3X9dha/E33RgjIiIlnv6mE8kn9yPfYImc7fje8K+NreUwBUcRESkVNPIo4qy0VKybpmLd8xkGJtJrNC9V1zaKiIiAwqOIU0zXovFcPgq3c/sAsIUOx17lbhdXJSIicvspPIrcgNvx7/H8ZiymlKsYHn4kPziZ9IB2ri5LRETEJRQeRfJg+eF9PH6YCUB6lRCSI97B8NMjKUVEpPRSeBTJg+FdCYDUJgNJvX8MuOtpMSIiUropPIr8mS0ZLJ4ApIX0I7FiPezVm7rBYlddAAAgAElEQVS4KBERkaJBa4uIZDLsWH6aRZl5D0HSlYw2k0nBUURE5DoKjyIASVfwXPIkHlvewXw1CsvhFa6uSEREpEjStLWUeuaze/FcOQrztRgMNw9SOownrWEfV5clIiJSJCk8SullGFj2fI514xRMdht2v5okd5+BvXJ9V1cmIiJSZCk8Sqll2TUXj41TAEir25Hkzm+Ah6+LqxIRESnadM2jlDjp6Ybj6z0/G1m+v56tQU/s5WqS0m4syd3fVXAUERFxgsKjlCgbNxkMevSPsPjiWIO+Aww2bspoM5/ZAcbv273KkThkObZmj4DJ5IpyRUREih2FRykxNm4yePkVg4sXs7ZfuAATX0sidt7LlPl6CO77F/yxUYt+i4iI5IuueZQSIT3dYMZ7OU9P1/Q+xbQWo7jz4hEMkxlT8tXbXJ2IiEjJofAoJcLPezNGGP+sXZXveLPFOHwsCVxKqUB06FQCWra5/QWKiIiUEJq2lhLh0uWc2//ZfCw+lgR2XmrOgO8XcIzWt7cwERGREkYjj1IiVCif+7Y5v/yNmYdHkG6459lPREREbkzhUUqExo2gUqXsU9djIt9i68W2AFSunNFPRERECk7T1lIiuJnszOzzATW9T2Vp33y+rePrEc+YcHPTkjwiIiI3Q+FRij1TwkU8Fw0jKOY9PokYRZVKaVm2V64Mb0w00fZ+BUcREZGbpWlrKdbMZyLxXPk85oQLGJYyeLQbxtyBFmrXztg+bbKJVmFoxFFERKSQKDxK8WQYWCI/wrplBiYjnfQKd5Ec8S5GhbtwS/ijW5PGJtzcXFemiIhISaPwKMVPSjye376E+7H1ANiCu5PS8TWwlHFtXSIiIqWAwqMUP+5WTAkXMdwspLR/mbSQh/VsahERkdukxIXHxMRE1q5dy/r16zl8+DBnz57FarUSHBzMgAEDiIiIyPc+N2/ezKxZszhw4ACGYdCwYUOGDx/OfffddwvegeTIMMCwg9kN3KwkR7yDKSkWe5W7XV2ZiIhIqVLi7raOjIxkzJgxbN++nfr16/PII4/QqVMnjhw5wujRo5k0aVK+9rds2TKGDRvGL7/8Qq9evejTpw/Hjx9n2LBhLFu27Ba9C8kiNQGPVS9i3fKOo8koW13BUURExAVMhmEYri6iMB0+fJhffvmFLl26YLFYHO0XL17k4YcfJjo6mvnz59Oo0Y1Xi7569Srh4eG4ubmxePFiqlWrBsD58+fp3bs3KSkprFu3Dj8/v1z3ERsbe/NvqpTy9/fn6i8/4bliJObLxzHMFhL/+g2GX408X5eQAHfe6Q/A6dOxeHvfjmrlev7+/vrZL4Z03oovnbviq6idO39//xv2KXEjj8HBwXTv3j1LcASoWLEi/fv3B2DHjh1O7evbb7/l2rVrDBo0yBEcASpXrsyQIUO4du0a3377beEVL1nY98zH6/P+mC8fx+5dmaR+H98wOIqIiMitVeLCY17c3TMu8XRzcu2Wn376CYB7770327bM6x0z+0ghSkvBY+2rpC98FlNaEmm12pA4eDH2Gs1cXZmIiEipV+JumMlNeno6S5YswWQy0aZNG6dec/LkSQBq1aqVbVtm26lTp7Jtu56fnx9mc6nK6DfFMAzSZ/fCOLkdTCbM7Z7Hs93zeJmdX6zRav3ja39/f01bu4gzUx9S9Oi8FV86d8VXcTt3pSY8vvvuuxw9epQ+ffoQGBjo1Gvi4+MB8PX1zbatTJkyuLm5ERcXl+c+rl69mv9iSzn3+n3wOHcE94f/w9UKjeHqtXy9PiEBIOMXMTY2ltTUwq9R8lbUruER5+i8FV86d8VXUTt3zgTZIhsew8LCuHLlitP9582bR1hYWI7bvvrqK/773//SoEEDXn755cIqUQpLug3TtWgM/9oApNWPIK3O/fhXqwVF6BdKREREinB4jIiIICEh4cYdf1exYsUc2xcuXMirr75KYGAgs2fPxjsfc5g+Pj4AxMXFZUviiYmJpKen5zgqKc4zxZ3Dc+XzmK6eJmnQIgzv38+jZ1nXFiYiIiI5KrLhccKECTe9jwULFjBhwgTq1q3L3Llz831NQe3atdm/fz+nTp3K9trMax1zuh5SnON2aiseq8ZgTrqMYfXBdPn4H+FRREREiqQSeyfHggULGD9+PAEBAcydO5fy5cvnex8tW7YEYMuWLdm2bd68GYDQ0NCbK7Q0sqdj+eF9PBc+hjnpMumV65M4aCH2O/VZioiIFHUlMjzOnz8/S3CsUKFCnv2TkpI4duwYMTExWdoffPBBfH19+fTTTzl79qyj/fz588ybN4+yZcvSpUuXW/IeSqzEy3guHo7HDzMxYWAL6UdS/88xytV0dWUiIiLihCI7bV1QP/zwAxMmTMAwDFq0aMEXX3yRrU/9+vUJDw93fL93716GDBlCaGgon3zyiaPdz8+PCRMmMGbMGHr16kW3bt0wmUx88803XLx4kalTp+b5dBnJzvrD+7if2obh7kVK+KukNXjI1SWJiIhIPpS48Hj27Fkyn7j41Vdf5dinV69eWcJjXh566CH8/f2ZNWsWixYtAuDuu+9m8uTJjoXCxXmp9z2POf43Uu8Zib1iPVeXIyIiIvlU4p5tXdQUpbWbXCL5Gpb9C7E1fxRMpny9tKBrX+nZ1q5X1NYtE+fovBVfOnfFV1E7d8V6nUcp/sznD+K5fCTmq6fBbMbW7BFXlyQiIiI3SeFRCp9h4L5vPh4b3sCUnoq9bA3Sqzd3dVUiIiJSCBQepXDZEvFY9w8sh5YBkBbQnuQu/wRP3VgkIiJSEig8SqExXT6O5/IRuF36FcPkRuo9I7C1HAqmErkilIiISKmk8CiFxpR0BXPsSezeFUnu9jb2O1q6uiQREREpZAqPcnMMw3EXtb1GM5K7TsdeoymGdyUXFyYiIiK3guYTpcBMV8/g9fUQzBePOtrSAzspOIqIiJRgCo9SIG7HNlDm0z64RUfise4fGSOQIiIiUuJp2lryx56GdcsMrJEfAZBetRHJXaflewFwERERKZ4UHsVppvjzeK58HrfonQCkNh1M6v0vgJvVxZWJiIjI7aLwKE4xxZ7E66tBmBMvYVi9Se70OumBXVxdloiIiNxmCo/iFMPvDuzl78IoU5Hk7u9g+NdxdUkiIiLiAgqPkrukWLB4g7sVzO4kd58B7p5g8XJ1ZSIiIuIiuttacmSO2UOZT/tg3Tj5j0YvfwVHERGRUk4jj5KVYWDZ/QnWTdMw2dNwj/qB1JR48PBxdWUiIiJSBCg8yh9S4vBcMx73X9YAYAvsQkrHSQqOIiIi4qDwKACYLxzGc/kIzFeiMMwWUtu+hK3J/2n9RhEREclC4VEgLQXPRcMxJ1zA7luN5Ih3sFdr7OqqREREpAjSDTMC7h6kPPAqaXXakjhooYKjiIiI5Eojj6WUKfYEpvgL2O8MBSC97gOk39VB09QiIiKSJ408lkLuR76hzKd98Vo+AlPc2T82KDiKiIjIDWjksTRJS8W6aSrWPZ8BkF65AZjcXFyUiIiIFCcKj6WE6Vo0niuex+23vQCktnyM1HueA7N+BERERMR5Sg6lgNvxjXh+8xKmlKsYHn4kP/hP0gPau7osERERKYYUHksB91/XYkq5SnqVEJIj3sHwq+HqkkRERKSYUngsBVLaj8deria2Zo+Cu9XV5YiIiEgxprutSyC30z/h8e04MOwZDRZPbKHDFRxFRETkpmnksSQx7Fh2/A/r1ncxGXbSq4aQ1uT/XF2ViIiIlCAKjyVF0hU8v30J9xObALA16Ena3b1cXJSIiIiUNAqPJYD57F48V47CfC0Gw82DlA7jSWvYR4t+i4iISKFTeCzm3A8uw2PNeEx2G3a/miR3n4G9cn1XlyUiIiIllMJjMWevcBeYTKTV7Uhy5zfAw9fVJYmIiEgJZjIMw3B1ESIiIiJSPGipHhERERFxmsKjiIiIiDhN4VFEREREnKbwKCIiIiJOU3gUEREREadpqR4p8hITE1m7di3r16/n8OHDnD17FqvVSnBwMAMGDCAiIsLVJUoeduzYwfr169m/fz8HDx4kPj6eXr16MXnyZFeXJr/bu3cv7733Hnv27MFms1G3bl0eeeQRunfv7urSJBdLly5l586d7N+/n6NHj2Kz2fjnP/9J7969XV2a5OHcuXN88803bNq0iePHj3Px4kX8/Pxo1qwZw4YNo3Hjxq4u0SkKj1LkRUZGMmbMGMqVK0fr1q3p1KkTly5dYu3atYwePZrdu3czYcIEV5cpuVi4cCGLFy/Gy8uLatWqER8f7+qS5Do//vgjQ4cOxWKx0K1bN3x9fVmzZg0vvPAC0dHRPPHEE64uUXLw7rvvEh0djb+/P5UrVyY6OtrVJYkTPvnkEz788ENq1qxJmzZtqFChAqdOnWLdunWsW7eO6dOn07VrV1eXeUNa51GKvMOHD/PLL7/QpUsXLBaLo/3ixYs8/PDDREdHM3/+fBo1auTCKiU3+/btw9PTk4CAAPbt20f//v018lhEpKWl8eCDD/Lbb7/x1Vdf0aBBAwDi4+MZMGAAJ06cYOXKldSuXdu1hUo227Zto1atWtSoUYNZs2Yxffp0jTwWA2vWrKF8+fK0aNEiS3tkZCSPPvoo3t7ebN68GavV6qIKnaNrHqXICw4Opnv37lmCI0DFihXp378/kDE1KkVTSEgI9erVw83NzdWlyJ9s376dqKgoIiIiHMERwMfHh6eeeoq0tDQWLVrkwgolN23atKFGjRquLkPyqVOnTtmCI0CLFi0ICwvjypUrHDlyxAWV5Y/CoxRr7u4ZV14omIjk308//QTAvffem23bPffck6WPiNxamX+fZf6/KFN4lGIrPT2dJUuWYDKZaNOmjavLESl2Tp48CUCtWrWybfPz88Pf359Tp07d5qpESp+YmBi2bdtGpUqVCAwMdHU5N6TwKMXWu+++y9GjR+ndu3ex+GUTKWoyb17y9fXNcbuPjw9xcXG3sySRUsdmszFmzBhSU1N54YUXisVMWtEfG5USI/N6DmfNmzePsLCwHLd99dVX/Pe//6VBgwa8/PLLhVWi5KIwz52IiGSw2+38/e9/Z8eOHTz88MP07NnT1SU5ReFRbpuIiAgSEhKc7l+xYsUc2xcuXMirr75KYGAgs2fPxtvbu7BKlFwU1rmTosXHxwcg19HF+Pj4XEclReTmGIbB+PHjWbZsGT169OAf//iHq0tymsKj3DaFsRbjggULmDBhAnXr1mXu3Ln4+/sXQmVyI1pHs2TKXILn1KlTNGzYMMu2q1evEhsbS9OmTV1QmUjJZrfbefnll1m0aBERERFMnjwZs7n4XElYfCqVUm/BggWMHz+egIAA5s6dS/ny5V1dkkix1rJlSwC2bNmSbdvWrVsBCA0Nva01iZR01wfHrl27MnXq1GJxneP1FB6lWJg/f36W4FihQgVXlyRS7LVu3Zo777yTFStWcOjQIUd7fHw8//73v3F3d6dXr14urFCkZLk+OHbp0oVp06YVu+AIesKMFAM//PADf/3rXzEMg/79+1OpUqVsferXr094eLgLqpMbiYyMZMGCBQBcvnyZjRs3UrNmTZo3bw5AQEAAw4cPd2WJpdr27dsZNmwYFouFiIgIfHx8WLNmDWfOnGHkyJE8+eSTri5RcjB//nx27twJwNGjRzlw4ADNmjVzLLsUHh6uPxOLoPfee4+ZM2dSpkwZhgwZkuOajuHh4dSvX98F1TlP1zxKkXf27Fky/43z1Vdf5dinV69e+oOyiIqKimLx4sXZ2qKiooCMaVGFR9dp1aoVn3/+Of/617/45ptvsNls1K1blxEjRtCjRw9Xlye52LlzZ7bfq127drFr1y4AatSooT8Ti6DMZ5AnJibywQcf5NinRo0aRT48auRRRERERJymax5FRERExGkKjyIiIiLiNIVHEREREXGawqOIiIiIOE3hUUREREScpvAoIiIiIk5TeBQRERERpyk8ioiIiIjTFB5FRERExGkKjyJyS1y+fJkZM2bQs2dPWrRoQePGjenYsSMTJkzg6NGjub6uQ4cOBAUF3cZKS4bBgwcTFBTEmTNnCmV/QUFBdOjQIUvbjz/+SFBQEGPHji2UY4hI8aTwKCKFbtu2bXTu3Jn//Oc/nDt3jpYtW9KuXTvc3d35+uuv6dmzJ7NmzXJ1mSIiUgDuri5AREqWvXv3Mnz4cNLS0hg9ejR/+9vfcHf/44+ajRs38uKLLzJ9+nQ8PT0ZMmSIC6uV/GjUqBGrVq3C19fX1aWIiAtp5FFECo1hGIwdOxabzcZzzz3H8OHDswRHgLZt2/L+++9jMpl46623iI6OdlG1kl9eXl7cddddVK5c2dWliIgLKTyKSKHZtGkTx44do0qVKjz22GO59mvZsiVdunQhJSWFzz77LMc+hmEwd+5cunbtSkhICPfddx+vv/46165dy9bXZrPx5Zdf0rdvX8LCwmjcuDEdOnTg8ccfZ+XKldn6p6amMnfuXPr06UPTpk1p0qQJffv2Zf78+RiGka1/5vV/qampzJw5ky5dutCwYUOeeuopZs+eTVBQEG+99Vau7/exxx4jKCiIrVu3Zmm/fPkyU6ZMoXPnzoSEhNCyZUuGDRvGjh07ct3XV199Rffu3R2fyaRJk4iLi8u1f14SExOZNm0a7dq1IyQkhC5dujBnzpwcPwPI+ZrHSZMmERQUxBdffJHrcbp160ZQUBAnTpzI0r57926efPJJWrVqRcOGDenQoQOvvfYa586dy7aPRYsWERQUxHvvvceJEycYNWoUbdq0ITg4mHXr1jn62Ww2PvvsMwYMGOC41rZz586MHz8+x2ttIyMjefrpp2ndurWjhtdff53Lly/f8PMTKa0UHkWk0GzcuBGALl26YLFY8uwbEREBwObNm3PcPmnSJKZNm0bVqlV54IEHsNvtfPLJJwwaNIj4+PgsfceMGcOrr77KmTNnaNq0KR06dKBq1apERkby5ZdfZumbmJjIX//6V958802io6Np3rw5oaGhREVFMX78eF599dUc67Hb7Tz99NN89NFH1KxZkwceeIBKlSrRrVs3zGYzK1euzDF0Xb58mW3btlGpUiVatWrlaD927Bg9e/Zk9uzZ2O122rZtS1BQENu3b2fIkCEsX748276mTJnCK6+8wsmTJ2nVqhVNmzZl+fLlDBkyhNTU1Dw/7z9LTU3lb3/7G//73/9ITk6mffv21KhRg+nTpzNx4kSn99O9e3eAHOsFOHToEL/++ishISHUqVPH0b506VIGDhzIhg0bqFOnDp06dcJisfDFF1/Qu3dvjh07luP+Tpw4Qd++fdm7dy9hYWHcc889jtHtxMREHn30USZOnMiRI0do2rQp7du3x9fXl8WLF7N69eos+5o3bx6DBg1iw4YN1KpViw4dOuDh4cEnn3xCv379OH/+vNOfg0ipYoiIFJIBAwYYgYGBxpIlS27Y9+zZs0ZgYKARHBxspKamOtrbt29vBAYGGs2aNTP27dvnaI+PjzeGDBliBAYGGm+++aaj/fTp00ZgYKDRp08fIzk5OcsxkpKSjF27dmVpe/XVV43AwEDjxRdfNOLj4x3tly5dMvr162cEBgYaGzZsyPKawMBAIzAw0OjYsaPx22+/ZXsvmXXt2LEj27ZPP/3UCAwMNN544w1HW1pamhEREWEEBgYac+fONex2u2PbgQMHjNDQUKNJkybGxYsXHe07d+40AgMDjdDQUOPo0aOO9suXLxvdu3d31Hj69OlsNeTkgw8+MAIDA42+ffsa165dc7Tv37/faNasmREYGGi0b98+y2u2b99uBAYGGi+99FKW9vDwcCMoKMg4c+ZMtuNMmTLFCAwMND7++GNHW0xMjNGoUSOjQYMGxvr16x3t6enpxhtvvOE4n9dbuHCh4z1OnDjRSEtLy3asv//970ZgYKAxePBg4/Lly1m2/fbbb1l+nnbv3m0EBwcb7du3Nw4dOuRot9vtxsyZM43AwEDj2WefzfGzEyntNPIoIoXmypUrAFSoUOGGfcuXLw9kjOhdvXo12/ZBgwbRsGFDx/fe3t688sormEwmFixY4Bhpy5xebNq0KR4eHln24enpSdOmTR3fX7p0iQULFnDHHXfw+uuv4+3tnaWezBG3P49WZnr++eepUqVKtvbM0bdly5Zl27ZixYosfQA2bNjA0aNHiYiIYMiQIZhMJse2Bg0a8NRTT5GYmJhlf5k1/fWvf6VevXqOdn9/f8aMGZNjvXnJnGYeN25clhtg7r77bgYOHJivfUVERGAYRrZLBAzDYNWqVbi5udG1a1dH+/z580lOTqZbt260b9/e0W42m3nhhReoXLky+/btY8+ePdmOVb58eV544QXc3NyytJ8/f57Fixfj6enJ1KlT8ff3z7K9SpUqWX6eZs2ahd1uZ+LEiQQHBzvaTSYTTz31FA0aNGDt2rWavhbJgcKjiBQa4/dpWyOXa+Zy6gtkCU+Zrg8bme666y6Cg4OJj4/n8OHDAAQEBFCmTBkWLVrE119/TWxsbK7H/Omnn7DZbNx3331YrdZs24ODg/H29mb//v3ZtplMpmzrHmbq3LkzHh4erF69GpvN5miPiYlh9+7d1K5dm5CQEEd75rWPDzzwQI77a968OQD79u1ztO3cuROABx98MFv/e++9l3LlyuW4r5zExMRw9uxZqlSpQrNmzbJt79atm9P7gtynriMjIzl79iytW7emUqVKWdqvf931rFYrXbp0ydLvem3atMHLyytb+48//kh6ejpt27alatWqedZrt9v54Ycf8Pb2pnXr1tm2m0wmmjVrht1u58CBA3nuS6Q00lI9IlJo/P39OXHiBJcuXbph38wRHZPJRNmyZbNtr1GjRo6vq1GjBocOHXJcj+bj48OkSZOYMGECEyZM4JVXXqFOnTqEhYXRs2dPmjRp4nht5p3dX3zxRZ43eKSkpGRrq1ChQo6BE8DX15d27dqxevVqNm/e7AiZK1aswDCMbCEps45Ro0YxatSoXOu4PgifP38ek8lEtWrVcuxbrVo1x8jvjWR+dtWrV89xe27tuQkICODuu+/mwIEDHDlyxLHIe2aY/PP7zzx+Xuf4+n7Xy+39nz17FoA777zzhvVeuXKFxMREIGOkNy95/WNEpLRSeBSRQhMcHMyuXbs4cOAAPXv2zLNv5ohOvXr1bnhzzfVyGtWMiIigTZs2fPfdd2zZsoUdO3Y4AuLQoUMd07p2ux3ICAz5fYrNn6fE/6x79+6sXr2aFStWOMJjbuEpPT0dgPvvvz/PKf6AgIB81eisG40M5zQSfCM9evTgwIEDrFixgqCgIGw2G6tXr8bT05Pw8PACHSen7Tc6D87Unvn5e3t706lTpzz75jdIi5QGCo8iUmjuv/9+Pv/8c1avXs2YMWPyDIWZweree+/NcXt0dHSOAS9zhOnPaw2WL1+efv360a9fPwzDYPPmzYwaNYqPPvqI3r17U7duXcf1iqGhoYwbN65A7zE3bdu2pWzZsqxfv56EhARiYmI4evQojRs3platWln6Zk6rDhgwINep6z+rVKkS0dHRnD17Ntv+4I/PxRmZn11MTEyO2wuy9mbXrl2ZOnUqK1as4Pnnn2fLli1cuXKFrl274uPjk+34J06c4MyZM1nuwM6UWdf1U903kjkiGRUVdcO+/v7+WK1WLBYLkydPdvoYIpJB1zyKSKFp27YtderU4dy5c3z44Ye59tuxYwerV6/GYrHkenPGqlWrsrUdO3aMQ4cO4e3tneUmhz8zmUzcf//9tGvXDsCxvl+rVq1wc3Pj+++/d4w+FRar1Urnzp1JSkpi3bp1uY46QsZ1e0CW9QlvJPM6yG+//Tbbtq1btzo9ZQ0Z08JVq1bl3Llz7N69O9v2nD77G6lcuTJhYWHExMSwc+fOHG8UytSiRQsg5+V9UlNTHe8xs58zQkNDcXNzY+PGjTmuE3k9d3d3QkNDuXLlSp5raopIzhQeRaTQmM1mJk+ejMVi4V//+hezZs3KFtI2btzI008/jWEYvPDCC9xxxx057uuzzz7j4MGDju8TExN5/fXXMQyDPn36OK4/PHjwIGvWrMlyowrA1atX+fnnn4E/ph6rVKlCr169OHnyJGPGjMnxTtpdu3Y51qvMr+tvHFm5cmW2u4wzde7cmYCAABYvXsysWbOy1Z6amsqaNWs4cuSIo61///4AzJkzJ8saiFeuXGHatGn5rjVzf1OmTMmybuahQ4dyXbj9RjLf/9dff8369espV64c9913X7Z+ffv2xdPTk5UrV/L999872u12O++88w7nzp0jJCQky/WqN1KlShUeeughkpOTGTt2bLYwfe7cuSw3vzzxxBOYzWZeeumlHG/MOXfuXIE/B5GSTtPWIlKomjRpwr///W+ef/55pk+fzscff0yTJk2wWq0cPXqUY8eOYTabGTFiBI8++miu++nRowcPP/wwYWFh+Pr6EhkZyYULF6hXrx7PPfeco19MTAzPPvssvr6+NGzYkIoVKxIXF0dkZCTx8fF07NgxSwgZP348p0+fZsWKFWzYsIH69etTuXJlLl68yKlTpzh37hxDhgyhbdu2+X7voaGhVK1a1bHw+X333ZfjNY3u7u7MnDmTYcOGMX36dObNm0dQUBA+Pj789ttvHD9+nGvXrvH+++87pu5btGjBI488wty5c+nZsydt2rTBw8ODH3/8kWrVqtGkSZMcl7bJzbBhw/j+++/ZvXs34eHhhIWFkZCQwPbt2+nbt2+eNxTlplOnTrz22mssXboUyDiHOV26UL16dSZOnMi4ceN44oknaNasGdWqVePAgQOcOHGCihUrMmXKlHwf/+WXX+bEiRNs27aNDh060KJFC8qUKUN0dDQHDx7kiSee4O677wYynnL08ssv8+abbzJw4ECCgoKoXbs2KSkpxMTEcOzYMcqUKVRafbgAAAI2SURBVJPvZYtESgO311577TVXFyEiJUutWrXo27cvFouFCxcucPDgQY4dO4aHhwedO3fmzTffzHHJGYC5c+cSFxfH/Pnz8fLy4scff+Tnn3/G09OTXr16MXXq1Cx3Z/v6+lK2bFlSU1M5efIk+/bt49q1a9x1112MHDmS5557DrP5j0kWi8VC9+7dqV69OrGxsRw9epQjR45gs9moWbMmAwcOZMCAAVmu05s5cyZly5blkUceyfN9m0wmLly44JgKfvrpp3OdXi9fvjy9evXC09OTs2fPcvjwYU6ePInZbKZhw4YMHz6cdu3aZbnD+95776VixYpERUWxb98+YmNj6dSpE9OmTWP16tVER0fzyCOP5Hj3+p9ljorabDaOHz/OwYMHMQyDoUOHMnLkSN5///1s7zk6OprFixdTv379HG+CsVqtHD58mF9//RXIWEMytxtOgoODad26NZcuXeLgwYMcOnQIDw8PIiIieOutt7LdNX3o0CG+++47QkNDCQsLy3GfVquVHj16UK5cOc6fP8+BAwc4efIkFouFjh070qdPnyxhvlGjRrRt25akpCROnDjBgQMHuHz5Mj4+PnTq1IkRI0bkeke4SGlmMpxZkE1EREREBF3zKCIiIiL5oPAoIiIiIk5TeBQRERERpyk8ioiIiIjTFB5FRERExGkKjyIiIiLiNIVHEREREXGawqOIiIiIOE3hUUREREScpvAoIiIiIk5TeBQRERERpyk8ioiIiIjT/h+gLc1fnbD1EAAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"execution_count": 136,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"for i in range(d.shape[0]):\n",
" if d.Loc[i] in [\"ID\", \"UT\", \"RI\", \"ME\"]:\n",
" ax.annotate(d.Loc[i], (d.D[i], mu_mean[i]), xytext=(-25, -5),\n",
" textcoords=\"offset pixels\")\n",
"fig"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.17"
]
},
{
"cell_type": "code",
"execution_count": 138,
"metadata": {},
"outputs": [],
"source": [
"N = 100 # number of cases\n",
"# x_real as Gaussian with mean 0 and stddev 1\n",
"x_real = dist.Normal().sample(PRNGKey(0), (N,))\n",
"# x_spur as Gaussian with mean=x_real\n",
"x_spur = dist.Normal(x_real).sample(PRNGKey(1))\n",
"# y as Gaussian with mean=x_real\n",
"y = dist.Normal(x_real).sample(PRNGKey(2))\n",
"# bind all together in data frame\n",
"d = pd.DataFrame({\"y\": y, \"x_real\": x_real, \"x_spur\": x_spur})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.18"
]
},
{
"cell_type": "code",
"execution_count": 140,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 29 entries, 0 to 28\n",
"Data columns (total 8 columns):\n",
"clade 29 non-null object\n",
"species 29 non-null object\n",
"kcal.per.g 29 non-null float64\n",
"perc.fat 29 non-null float64\n",
"perc.protein 29 non-null float64\n",
"perc.lactose 29 non-null float64\n",
"mass 29 non-null float64\n",
"neocortex.perc 17 non-null float64\n",
"dtypes: float64(6), object(2)\n",
"memory usage: 1.9+ KB\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>clade</th>\n",
" <th>species</th>\n",
" <th>kcal.per.g</th>\n",
" <th>perc.fat</th>\n",
" <th>perc.protein</th>\n",
" <th>perc.lactose</th>\n",
" <th>mass</th>\n",
" <th>neocortex.perc</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <td>0</td>\n",
" <td>Strepsirrhine</td>\n",
" <td>Eulemur fulvus</td>\n",
" <td>0.49</td>\n",
" <td>16.60</td>\n",
" <td>15.42</td>\n",
" <td>67.98</td>\n",
" <td>1.95</td>\n",
" <td>55.16</td>\n",
" </tr>\n",
" <tr>\n",
" <td>1</td>\n",
" <td>Strepsirrhine</td>\n",
" <td>E macaco</td>\n",
" <td>0.51</td>\n",
" <td>19.27</td>\n",
" <td>16.91</td>\n",
" <td>63.82</td>\n",
" <td>2.09</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <td>2</td>\n",
" <td>Strepsirrhine</td>\n",
" <td>E mongoz</td>\n",
" <td>0.46</td>\n",
" <td>14.11</td>\n",
" <td>16.85</td>\n",
" <td>69.04</td>\n",
" <td>2.51</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <td>3</td>\n",
" <td>Strepsirrhine</td>\n",
" <td>E rubriventer</td>\n",
" <td>0.48</td>\n",
" <td>14.91</td>\n",
" <td>13.18</td>\n",
" <td>71.91</td>\n",
" <td>1.62</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <td>4</td>\n",
" <td>Strepsirrhine</td>\n",
" <td>Lemur catta</td>\n",
" <td>0.60</td>\n",
" <td>27.28</td>\n",
" <td>19.50</td>\n",
" <td>53.22</td>\n",
" <td>2.19</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" clade species kcal.per.g perc.fat perc.protein \\\n",
"0 Strepsirrhine Eulemur fulvus 0.49 16.60 15.42 \n",
"1 Strepsirrhine E macaco 0.51 19.27 16.91 \n",
"2 Strepsirrhine E mongoz 0.46 14.11 16.85 \n",
"3 Strepsirrhine E rubriventer 0.48 14.91 13.18 \n",
"4 Strepsirrhine Lemur catta 0.60 27.28 19.50 \n",
"\n",
" perc.lactose mass neocortex.perc \n",
"0 67.98 1.95 55.16 \n",
"1 63.82 2.09 NaN \n",
"2 69.04 2.51 NaN \n",
"3 71.91 1.62 NaN \n",
"4 53.22 2.19 NaN "
]
},
"execution_count": 140,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"milk = pd.read_csv(\"../data/milk.csv\", sep=\";\")\n",
"d = milk\n",
"d.info()\n",
"d.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.19"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {},
"outputs": [],
"source": [
"d[\"K\"] = (d[\"kcal.per.g\"] - d[\"kcal.per.g\"].mean()) / d[\"kcal.per.g\"].std()\n",
"d[\"N\"] = ((d[\"neocortex.perc\"] - d[\"neocortex.perc\"].mean())\n",
" / d[\"neocortex.perc\"].std())\n",
"log_mass = np.log(d.mass.values)\n",
"d[\"M\"] = (log_mass - np.mean(log_mass)) / np.std(log_mass)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.20"
]
},
{
"cell_type": "code",
"execution_count": 162,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"{'auto_loc': DeviceArray([nan, nan, nan], dtype=float32),\n",
" 'auto_scale_tril': DeviceArray([[inf, nan, nan],\n",
" [nan, inf, nan],\n",
" [nan, nan, inf]], dtype=float32)}"
]
},
"execution_count": 162,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def model(N, K):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 1))\n",
" bN = npyro.sample(\"bN\", dist.Normal(0, 1))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bN * N\n",
" npyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
"\n",
"m5_5_draft = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_5_draft, elbo, optim.Adam(0.1))\n",
"data = (d.N.values, d.K.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(1000))\n",
"p5_5_draft = svi.get_params(last_state)\n",
"p5_5_draft"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.21"
]
},
{
"cell_type": "code",
"execution_count": 148,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 55.16\n",
"1 NaN\n",
"2 NaN\n",
"3 NaN\n",
"4 NaN\n",
"5 64.54\n",
"6 64.54\n",
"7 67.64\n",
"8 NaN\n",
"9 68.85\n",
"10 58.85\n",
"11 61.69\n",
"12 60.32\n",
"13 NaN\n",
"14 NaN\n",
"15 69.97\n",
"16 NaN\n",
"17 70.41\n",
"18 NaN\n",
"19 73.40\n",
"20 NaN\n",
"21 67.53\n",
"22 NaN\n",
"23 71.26\n",
"24 72.60\n",
"25 NaN\n",
"26 70.24\n",
"27 76.30\n",
"28 75.49\n",
"Name: neocortex.perc, dtype: float64"
]
},
"execution_count": 148,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"neocortex.perc\"]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.22"
]
},
{
"cell_type": "code",
"execution_count": 156,
"metadata": {},
"outputs": [],
"source": [
"dcc = d.iloc[d[[\"K\", \"N\", \"M\"]].dropna(how=\"any\", axis=0).index]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.23"
]
},
{
"cell_type": "code",
"execution_count": 166,
"metadata": {},
"outputs": [],
"source": [
"def model(N, K=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 1))\n",
" bN = npyro.sample(\"bN\", dist.Normal(0, 1))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bN * N\n",
" npyro.sample(\"mu\", dist.Delta(mu), obs=mu)\n",
" npyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
"\n",
"m5_5_draft = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_5_draft, elbo, optim.Adam(0.1))\n",
"data = (dcc.N.values, dcc.K.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(1000))\n",
"p5_5_draft = svi.get_params(last_state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.24"
]
},
{
"cell_type": "code",
"execution_count": 168,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xseq = np.array([-2, 2])\n",
"prior_pred = predictive(PRNGKey(1), model, {}, num_samples=1000, N=xseq)\n",
"mu = prior_pred[\"mu\"]\n",
"plt.subplot(xlim=xseq, ylim=xseq)\n",
"for i in range(50):\n",
" plt.plot(xseq, mu[i], \"k\", alpha=0.3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.25"
]
},
{
"cell_type": "code",
"execution_count": 212,
"metadata": {},
"outputs": [],
"source": [
"def model(N, K=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bN = npyro.sample(\"bN\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bN * N\n",
" npyro.sample(\"mu\", dist.Delta(mu), obs=mu)\n",
" npyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
"\n",
"m5_5 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_5, elbo, optim.Adam(0.03))\n",
"data = (dcc.N.values, dcc.K.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(2000))\n",
"p5_5 = svi.get_params(last_state)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.26"
]
},
{
"cell_type": "code",
"execution_count": 200,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" a -0.03 0.16 -0.03 -0.28 0.25 1085.97 1.00\n",
" bn 0.14 0.24 0.14 -0.29 0.53 1068.97 1.00\n",
" sigma 1.13 0.22 1.11 0.77 1.44 947.94 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"post = m5_5.sample_posterior(PRNGKey(1), p5_5, (1000,))\n",
"npyro.diagnostics.summary(post)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.27"
]
},
{
"cell_type": "code",
"execution_count": 203,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xseq = np.linspace(start=dcc.N.min() - 0.15, stop=dcc.N.max() + 0.15, num=30)\n",
"post = m5_5.sample_posterior(PRNGKey(1), p5_5, (1000,))\n",
"post_pred = predictive(PRNGKey(2), m5_5.model, post, N=xseq)\n",
"mu = post_pred[\"mu\"]\n",
"mu_mean = np.mean(mu, 0)\n",
"mu_PI = np.percentile(mu, q=(5.5, 94.5), axis=0)\n",
"az.plot_pair(dcc[[\"N\", \"K\"]].to_dict(orient=\"list\"))\n",
"plt.plot(xseq, mu_mean, \"k\")\n",
"plt.fill_between(xseq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.28"
]
},
{
"cell_type": "code",
"execution_count": 211,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" a -0.02 0.16 -0.02 -0.27 0.25 1085.97 1.00\n",
" bM -0.26 0.21 -0.26 -0.62 0.07 1067.54 1.00\n",
" sigma 1.09 0.22 1.06 0.73 1.43 948.26 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"def model(M, K=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bM = npyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bM * M\n",
" npyro.sample(\"mu\", dist.Delta(mu), obs=mu)\n",
" npyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
"\n",
"m5_6 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_6, elbo, optim.Adam(0.03))\n",
"data = (dcc.M.values, dcc.K.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(2000))\n",
"p5_6 = svi.get_params(last_state)\n",
"post = m5_6.sample_posterior(PRNGKey(1), p5_6, (1000,))\n",
"npyro.diagnostics.summary(post)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.29"
]
},
{
"cell_type": "code",
"execution_count": 208,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" a 0.00 0.14 0.00 -0.23 0.21 937.10 1.00\n",
" bM -0.66 0.24 -0.64 -1.04 -0.28 919.43 1.00\n",
" bN 0.60 0.27 0.60 0.19 1.04 967.72 1.00\n",
" sigma 0.88 0.16 0.86 0.62 1.13 1046.00 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"def model(N, M, K=None):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.2))\n",
" bN = npyro.sample(\"bN\", dist.Normal(0, 0.5))\n",
" bM = npyro.sample(\"bM\", dist.Normal(0, 0.5))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a + bN * N + bM * M\n",
" npyro.sample(\"mu\", dist.Delta(mu), obs=mu)\n",
" npyro.sample(\"K\", dist.Normal(mu, sigma), obs=K)\n",
"\n",
"m5_7 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_7, elbo, optim.Adam(0.03))\n",
"data = (dcc.N.values, dcc.M.values, dcc.K.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(2000))\n",
"p5_7 = svi.get_params(last_state)\n",
"post = m5_7.sample_posterior(PRNGKey(1), p5_7, (1000,))\n",
"npyro.diagnostics.summary(post)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.30"
]
},
{
"cell_type": "code",
"execution_count": 214,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 600x940 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"coeftab = {\"m5.5\": m5_5.sample_posterior(PRNGKey(1), p5_5, (1000,)),\n",
" \"m5.6\": m5_6.sample_posterior(PRNGKey(2), p5_6, (1000,)),\n",
" \"m5.7\": m5_7.sample_posterior(PRNGKey(3), p5_7, (1000,))}\n",
"az.plot_forest(list(coeftab.values()), model_names=list(coeftab.keys()),\n",
" var_names=[\"bM\", \"bN\"], credible_interval=0.89);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.31"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Typo in the book. The code 5.31 should produce the lower-right plot in Figure 5.8."
]
},
{
"cell_type": "code",
"execution_count": 216,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"xseq = np.linspace(start=dcc.N.min() - 0.15, stop=dcc.N.max() + 0.15, num=30)\n",
"post = m5_7.sample_posterior(PRNGKey(1), p5_7, (1000,))\n",
"post_pred = predictive(PRNGKey(2), m5_7.model, post, M=xseq, N=0)\n",
"mu = post_pred[\"mu\"]\n",
"mu_mean = np.mean(mu, 0)\n",
"mu_PI = np.percentile(mu, q=(5.5, 94.5), axis=0)\n",
"plt.subplot(xlim=(dcc.M.min(), dcc.M.max()), ylim=(dcc.K.min(), dcc.K.max()))\n",
"plt.plot(xseq, mu_mean, \"k\")\n",
"plt.fill_between(xseq, mu_PI[0], mu_PI[1], color=\"k\", alpha=0.2);"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.32"
]
},
{
"cell_type": "code",
"execution_count": 217,
"metadata": {},
"outputs": [],
"source": [
"# M -> K <- N\n",
"# M -> N\n",
"n = 100\n",
"M = dist.Normal().sample(PRNGKey(0), (n,))\n",
"N = dist.Normal(M).sample(PRNGKey(1))\n",
"K = dist.Normal(N - M).sample(PRNGKey(2))\n",
"d_sim = pd.DataFrame({\"K\": K, \"N\": N, \"M\": M})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.33"
]
},
{
"cell_type": "code",
"execution_count": 219,
"metadata": {},
"outputs": [],
"source": [
"# M -> K <- N\n",
"# N -> M\n",
"n = 100\n",
"N = dist.Normal().sample(PRNGKey(0), (n,))\n",
"M = dist.Normal(N).sample(PRNGKey(1))\n",
"K = dist.Normal(N - M).sample(PRNGKey(2))\n",
"d_sim2 = pd.DataFrame({\"K\": K, \"N\": N, \"M\": M})\n",
"\n",
"# M -> K <- N\n",
"# M <- U -> N\n",
"n = 100\n",
"N = dist.Normal().sample(PRNGKey(3), (n,))\n",
"M = dist.Normal(M).sample(PRNGKey(4))\n",
"K = dist.Normal(N - M).sample(PRNGKey(5))\n",
"d_sim3 = pd.DataFrame({\"K\": K, \"N\": N, \"M\": M})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.34"
]
},
{
"cell_type": "code",
"execution_count": 220,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"RangeIndex: 544 entries, 0 to 543\n",
"Data columns (total 4 columns):\n",
"height 544 non-null float64\n",
"weight 544 non-null float64\n",
"age 544 non-null float64\n",
"male 544 non-null int64\n",
"dtypes: float64(3), int64(1)\n",
"memory usage: 17.1 KB\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>height</th>\n",
" <th>weight</th>\n",
" <th>age</th>\n",
" <th>male</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <td>0</td>\n",
" <td>151.765</td>\n",
" <td>47.825606</td>\n",
" <td>63.0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <td>1</td>\n",
" <td>139.700</td>\n",
" <td>36.485807</td>\n",
" <td>63.0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <td>2</td>\n",
" <td>136.525</td>\n",
" <td>31.864838</td>\n",
" <td>65.0</td>\n",
" <td>0</td>\n",
" </tr>\n",
" <tr>\n",
" <td>3</td>\n",
" <td>156.845</td>\n",
" <td>53.041915</td>\n",
" <td>41.0</td>\n",
" <td>1</td>\n",
" </tr>\n",
" <tr>\n",
" <td>4</td>\n",
" <td>145.415</td>\n",
" <td>41.276872</td>\n",
" <td>51.0</td>\n",
" <td>0</td>\n",
" </tr>\n",
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"</table>\n",
"</div>"
],
"text/plain": [
" height weight age male\n",
"0 151.765 47.825606 63.0 1\n",
"1 139.700 36.485807 63.0 0\n",
"2 136.525 31.864838 65.0 0\n",
"3 156.845 53.041915 41.0 1\n",
"4 145.415 41.276872 51.0 0"
]
},
"execution_count": 220,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Howell1 = pd.read_csv(\"../data/Howell1.csv\", sep=\";\")\n",
"d = Howell1\n",
"d.info()\n",
"d.head()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.35"
]
},
{
"cell_type": "code",
"execution_count": 221,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" mu_female 178.21 20.22 178.24 145.65 212.05 9943.61 1.00\n",
" mu_male 178.00 22.38 178.00 142.54 216.06 9552.78 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"mu_female = dist.Normal(178, 20).sample(PRNGKey(0), (int(1e4),))\n",
"mu_male = dist.Normal(178, 20).sample(PRNGKey(1), (int(1e4),)) +\\\n",
" dist.Normal(0, 10).sample(PRNGKey(2), (int(1e4),))\n",
"npyro.diagnostics.summary({\"mu_female\": mu_female, \"mu_male\": mu_male})"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.36"
]
},
{
"cell_type": "code",
"execution_count": 236,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0 1\n",
"1 0\n",
"2 0\n",
"3 1\n",
"4 0\n",
" ..\n",
"539 1\n",
"540 1\n",
"541 0\n",
"542 1\n",
"543 1\n",
"Name: sex, Length: 544, dtype: int32"
]
},
"execution_count": 236,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"d[\"sex\"] = np.where(d.male.values == 1, 1, 0)\n",
"d.sex"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.37"
]
},
{
"cell_type": "code",
"execution_count": 239,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" a[0] 134.72 1.47 134.75 132.44 137.24 1085.97 1.00\n",
" a[1] 142.57 1.79 142.55 139.55 145.43 1065.32 1.00\n",
" sigma 27.26 1.14 27.24 25.46 29.18 967.13 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"def model(sex, height):\n",
" a = npyro.sample(\"a\", dist.Normal(178, 20), sample_shape=(len(set(sex)),))\n",
" sigma = npyro.sample(\"sigma\", dist.Uniform(0, 50))\n",
" mu = a[sex]\n",
" npyro.sample(\"height\", dist.Normal(mu, sigma), obs=height)\n",
"\n",
"m5_8 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_8, elbo, optim.Adam(0.1))\n",
"data = (d.sex.values, d.height.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(2000))\n",
"p5_8 = svi.get_params(last_state)\n",
"post = m5_8.sample_posterior(PRNGKey(1), p5_8, (1000,))\n",
"npyro.diagnostics.summary(post)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.38"
]
},
{
"cell_type": "code",
"execution_count": 241,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n",
"\n",
" mean std median 5.0% 95.0% n_eff r_hat\n",
" a[0] 134.72 1.47 134.75 132.44 137.24 1085.97 1.00\n",
" a[1] 142.57 1.79 142.55 139.55 145.43 1065.32 1.00\n",
" diff_fm -7.85 2.20 -7.82 -11.38 -4.26 1062.52 1.00\n",
" sigma 27.26 1.14 27.24 25.46 29.18 967.13 1.00\n",
"\n",
"\n"
]
}
],
"source": [
"post[\"diff_fm\"] = post[\"a\"][:, 0] - post[\"a\"][:, 1]\n",
"npyro.diagnostics.summary(post)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.39"
]
},
{
"cell_type": "code",
"execution_count": 242,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array(['Strepsirrhine', 'New World Monkey', 'Old World Monkey', 'Ape'],\n",
" dtype=object)"
]
},
"execution_count": 242,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"milk = pd.read_csv(\"../data/milk.csv\", sep=\";\")\n",
"d = milk\n",
"d.clade.unique()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.40"
]
},
{
"cell_type": "code",
"execution_count": 244,
"metadata": {},
"outputs": [],
"source": [
"d[\"clade_id\"] = d.clade.astype(\"category\").cat.codes"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Code 5.42"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"d[\"K\"] = (d[\"kcal.per.g\"] - d[\"kcal.per.g\"].mean()) / d[\"kcal.per.g\"].std()\n",
"\n",
"def model(clade_id, K):\n",
" a = npyro.sample(\"a\", dist.Normal(0, 0.5),\n",
" sample_shape=(len(set(clade_id)),))\n",
" sigma = npyro.sample(\"sigma\", dist.Exponential(1))\n",
" mu = a[clade_id]\n",
" npyro.sample(\"height\", dist.Normal(mu, sigma), obs=K)\n",
"\n",
"m5_9 = AutoMultivariateNormal(model)\n",
"svi = SVI(model, m5_9, elbo, optim.Adam(0.1))\n",
"data = (d.clade_id.values, d.K.values)\n",
"init_state = svi.init(PRNGKey(0), data, data)\n",
"body_fn = lambda state, i: svi.update(state, data, data)\n",
"last_state, losses = lax.scan(body_fn, init_state, np.zeros(2000))\n",
"p5_9 = svi.get_params(last_state)\n",
"post = m5_9.sample_posterior(PRNGKey(1), p5_9, (1000,))\n",
"az.plot_"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.6.9"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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