{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Chapter 14. Adventures in Covariance" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "!pip install -q numpyro arviz networkx" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import math\n", "import os\n", "\n", "import arviz as az\n", "import matplotlib.pyplot as plt\n", "import networkx as nx\n", "import numpy as np\n", "import pandas as pd\n", "from IPython.display import Image, set_matplotlib_formats\n", "from matplotlib.patches import Ellipse, transforms\n", "\n", "import jax.numpy as jnp\n", "from jax import random, vmap\n", "from jax.scipy.special import expit\n", "\n", "import numpy as onp\n", "import numpyro as numpyro\n", "import numpyro.distributions as dist\n", "from numpyro.diagnostics import effective_sample_size, print_summary\n", "from numpyro.infer import MCMC, NUTS, Predictive\n", "\n", "if \"SVG\" in os.environ:\n", " %config InlineBackend.figure_formats = [\"svg\"]\n", "az.style.use(\"arviz-darkgrid\")\n", "numpyro.set_platform(\"cpu\")\n", "numpyro.set_host_device_count(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.1" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "a = 3.5 # average morning wait time\n", "b = -1 # average difference afternoon wait time\n", "sigma_a = 1 # std dev in intercepts\n", "sigma_b = 0.5 # std dev in slopes\n", "rho = -0.7 # correlation between intercepts and slopes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.2" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "Mu = jnp.array([a, b])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.3" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "cov_ab = sigma_a * sigma_b * rho\n", "Sigma = jnp.array([[sigma_a**2, cov_ab], [cov_ab, sigma_b**2]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.4" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray([[1, 3],\n", " [2, 4]], dtype=int32)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "jnp.array([1, 2, 3, 4]).reshape(2, 2).T" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.5" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "sigmas = jnp.array([sigma_a, sigma_b]) # standard deviations\n", "Rho = jnp.array([[1, rho], [rho, 1]]) # correlation matrix\n", "\n", "# now matrix multiply to get covariance matrix\n", "Sigma = jnp.diag(sigmas) @ Rho @ jnp.diag(sigmas)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.6" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "N_cafes = 20" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.7" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "seed = random.PRNGKey(5) # used to replicate example\n", "vary_effects = dist.MultivariateNormal(Mu, Sigma).sample(seed, (N_cafes,))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.8" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "a_cafe = vary_effects[:, 0]\n", "b_cafe = vary_effects[:, 1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.9" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(a_cafe, b_cafe, \"o\", mfc=\"none\")\n", "plt.gca().set(xlabel=\"intercepts (a_cafe)\", ylabel=\"slopes (b_cafe)\")\n", "\n", "# overlay population distribution\n", "# Ref: https://matplotlib.org/gallery/statistics/confidence_ellipse.html\n", "for l in [0.1, 0.3, 0.5, 0.8, 0.99]:\n", " pearson = Sigma[0, 1] / jnp.sqrt(Sigma[0, 0] * Sigma[1, 1])\n", " ellipse = Ellipse(\n", " (0, 0),\n", " jnp.sqrt(1 + pearson),\n", " jnp.sqrt(1 - pearson),\n", " edgecolor=\"k\",\n", " alpha=0.2,\n", " facecolor=\"none\",\n", " )\n", " std_dev = dist.Normal().icdf((1 + jnp.sqrt(l)) / 2)\n", " scale_x = 2 * std_dev * jnp.sqrt(Sigma[0, 0])\n", " scale_y = 2 * std_dev * jnp.sqrt(Sigma[1, 1])\n", " scale = transforms.Affine2D().rotate_deg(45).scale(scale_x, scale_y)\n", " ellipse.set_transform(scale.translate(Mu[0], Mu[1]) + plt.gca().transData)\n", " plt.gca().add_patch(ellipse)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.10" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "seed = random.PRNGKey(22)\n", "N_visits = 10\n", "afternoon = jnp.tile(jnp.arange(2), N_visits * N_cafes // 2)\n", "cafe_id = jnp.repeat(jnp.arange(N_cafes), N_visits)\n", "mu = a_cafe[cafe_id] + b_cafe[cafe_id] * afternoon\n", "sigma = 0.5 # std dev within cafes\n", "wait = dist.Normal(mu, sigma).sample(seed)\n", "d = pd.DataFrame(dict(cafe=cafe_id, afternoon=afternoon, wait=wait))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.11" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = dist.LKJ(dimension=2, concentration=2).sample(random.PRNGKey(0), (int(1e4),))\n", "az.plot_kde(R[:, 0, 1], bw=2, label=\"correlation\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.12" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "c86fe5d3db464a3daa797f983fef1a68", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/1000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "post = m14_1.get_samples()\n", "az.plot_kde(post[\"Rho\"][:, 0, 1], bw=2)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.14" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute unpooled estimates directly from data\n", "a1 = jnp.array(\n", " [jnp.mean(wait[(cafe_id == i) & (afternoon == 0)]) for i in range(N_cafes)]\n", ")\n", "b1 = (\n", " jnp.array(\n", " [jnp.mean(wait[(cafe_id == i) & (afternoon == 1)]) for i in range(N_cafes)]\n", " )\n", " - a1\n", ")\n", "\n", "# extract posterior means of partially pooled estimates\n", "post = m14_1.get_samples()\n", "a2 = jnp.mean(post[\"a_cafe,b_cafe\"][..., 0], 0)\n", "b2 = jnp.mean(post[\"a_cafe,b_cafe\"][..., 1], 0)\n", "\n", "# plot both and connect with lines\n", "plt.plot(a1, b1, \"o\")\n", "plt.gca().set(\n", " xlabel=\"intercept\",\n", " ylabel=\"slope\",\n", " ylim=(jnp.min(b1) - 0.1, jnp.max(b1) + 0.1),\n", " xlim=(jnp.min(a1) - 0.1, jnp.max(a1) + 0.1),\n", ")\n", "plt.plot(a2, b2, \"ko\", mfc=\"none\")\n", "for i in range(N_cafes):\n", " plt.plot([a1[i], a2[i]], [b1[i], b2[i]], \"k\", lw=0.5)\n", "fig, ax = plt.gcf(), plt.gca()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.15" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# compute posterior mean bivariate Gaussian\n", "Mu_est = jnp.array([jnp.mean(post[\"a\"]), jnp.mean(post[\"b\"])])\n", "rho_est = jnp.mean(post[\"Rho\"][:, 0, 1])\n", "sa_est = jnp.mean(post[\"sigma_cafe\"][:, 0])\n", "sb_est = jnp.mean(post[\"sigma_cafe\"][:, 1])\n", "cov_ab = sa_est * sb_est * rho_est\n", "Sigma_est = jnp.array([[sa_est**2, cov_ab], [cov_ab, sb_est**2]])\n", "\n", "# draw contours\n", "for l in [0.1, 0.3, 0.5, 0.8, 0.99]:\n", " pearson = Sigma_est[0, 1] / jnp.sqrt(Sigma_est[0, 0] * Sigma_est[1, 1])\n", " ellipse = Ellipse(\n", " (0, 0),\n", " jnp.sqrt(1 + pearson),\n", " jnp.sqrt(1 - pearson),\n", " edgecolor=\"k\",\n", " alpha=0.2,\n", " facecolor=\"none\",\n", " )\n", " std_dev = dist.Normal().icdf((1 + jnp.sqrt(l)) / 2)\n", " scale_x = 2 * std_dev * jnp.sqrt(Sigma_est[0, 0])\n", " scale_y = 2 * std_dev * jnp.sqrt(Sigma_est[1, 1])\n", " scale = transforms.Affine2D().rotate_deg(45).scale(scale_x, scale_y)\n", " ellipse.set_transform(scale.translate(Mu_est[0], Mu_est[1]) + ax.transData)\n", " ax.add_patch(ellipse)\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.16" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# convert varying effects to waiting times\n", "wait_morning_1 = a1\n", "wait_afternoon_1 = a1 + b1\n", "wait_morning_2 = a2\n", "wait_afternoon_2 = a2 + b2\n", "\n", "# plot both and connect with lines\n", "plt.plot(wait_morning_1, wait_afternoon_1, \"o\")\n", "plt.gca().set(\n", " xlabel=\"morning wait\",\n", " ylabel=\"afternoon wait\",\n", " ylim=(jnp.min(wait_afternoon_1) - 0.1, jnp.max(wait_afternoon_1) + 0.1),\n", " xlim=(jnp.min(wait_morning_1) - 0.1, jnp.max(wait_morning_1) + 0.1),\n", ")\n", "plt.plot(wait_morning_2, wait_afternoon_2, \"ko\", mfc=\"none\")\n", "for i in range(N_cafes):\n", " plt.plot(\n", " [wait_morning_1[i], wait_morning_2[i]],\n", " [wait_afternoon_1[i], wait_afternoon_2[i]],\n", " \"k\",\n", " lw=0.5,\n", " )\n", "x = jnp.linspace(jnp.min(wait_morning_1), jnp.max(wait_morning_1), 101)\n", "plt.plot(x, x, \"k--\", lw=1)\n", "fig, ax = plt.gcf(), plt.gca()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.17" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# now shrinkage distribution by simulation\n", "v = dist.MultivariateNormal(Mu_est, Sigma_est).sample(random.PRNGKey(0), (10000,))\n", "v = v.at[:, 1].add(v[:, 0]) # calculate afternoon wait\n", "Sigma_est2 = jnp.cov(v, rowvar=False)\n", "Mu_est2 = Mu_est\n", "Mu_est2 = Mu_est2.at[1].add(Mu_est2[0])\n", "\n", "# draw contours\n", "for l in [0.1, 0.3, 0.5, 0.8, 0.99]:\n", " pearson = Sigma_est2[0, 1] / jnp.sqrt(Sigma_est2[0, 0] * Sigma_est2[1, 1])\n", " ellipse = Ellipse(\n", " (0, 0),\n", " jnp.sqrt(1 + pearson),\n", " jnp.sqrt(1 - pearson),\n", " edgecolor=\"k\",\n", " alpha=0.2,\n", " facecolor=\"none\",\n", " )\n", " std_dev = dist.Normal().icdf((1 + jnp.sqrt(l)) / 2)\n", " scale_x = 2 * std_dev * jnp.sqrt(Sigma_est2[0, 0])\n", " scale_y = 2 * std_dev * jnp.sqrt(Sigma_est2[1, 1])\n", " scale = transforms.Affine2D().rotate_deg(45).scale(scale_x, scale_y)\n", " ellipse.set_transform(scale.translate(Mu_est2[0], Mu_est2[1]) + ax.transData)\n", " ax.add_patch(ellipse)\n", "fig" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.18" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "73b9de5a25374f75a3cf3dec6d2ea80e", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/1000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# extract n_eff values for each model\n", "post_nc = m14_3.get_samples(group_by_chain=False)\n", "post_nc = Predictive(m14_3.sampler.model, post_nc)(random.PRNGKey(1), link=True, **dat)\n", "post_nc = {k: v.reshape((4, 500) + v.shape[1:]) for k, v in post_nc.items()}\n", "neff_nc = jnp.concatenate(\n", " [effective_sample_size(post_nc[k]).reshape(-1) for k in [\"alpha\", \"beta\"]]\n", ")\n", "post_c = m14_2.get_samples(group_by_chain=True)\n", "neff_c = jnp.concatenate(\n", " [effective_sample_size(post_c[k]).reshape(-1) for k in [\"alpha\", \"beta\"]]\n", ")\n", "plt.plot(neff_c, neff_nc, \"o\", mfc=\"none\")\n", "plt.gca().set(xlabel=\"centered (default)\", ylabel=\"non-centered (cholesky)\")\n", "x = jnp.linspace(0, 1200, 100)\n", "plt.plot(x, x, \"--\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.21" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.5% 94.5% n_eff r_hat\n", "sigma_actor[0] 1.38 0.47 1.29 0.69 2.08 1171.76 1.00\n", "sigma_actor[1] 0.91 0.39 0.84 0.36 1.47 1558.57 1.00\n", "sigma_actor[2] 1.85 0.55 1.76 1.01 2.57 1439.96 1.00\n", "sigma_actor[3] 1.60 0.62 1.47 0.69 2.41 1509.03 1.00\n", "sigma_block[0] 0.42 0.33 0.35 0.00 0.83 1248.16 1.00\n", "sigma_block[1] 0.44 0.33 0.38 0.00 0.87 1217.95 1.00\n", "sigma_block[2] 0.28 0.26 0.20 0.00 0.62 1787.09 1.00\n", "sigma_block[3] 0.47 0.35 0.41 0.00 0.91 1316.58 1.00\n", "\n" ] } ], "source": [ "post = m14_3.get_samples(group_by_chain=True)\n", "pars = {k: post[k] for k in [\"sigma_actor\", \"sigma_block\"]}\n", "print_summary(pars, prob=0.89)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.22" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute mean for each actor in each treatment\n", "pl = d.groupby([\"actor\", \"treatment\"])[\"pulled_left\"].mean().unstack()\n", "\n", "# generate posterior predictions using link\n", "datp = dict(\n", " actor=jnp.repeat(jnp.arange(7), 4),\n", " tid=jnp.tile(jnp.arange(4), 7),\n", " block_id=jnp.repeat(4, 4 * 7),\n", ")\n", "p_post = Predictive(m14_3.sampler.model, m14_3.get_samples())(\n", " random.PRNGKey(1), **datp, link=True\n", ")[\"p\"]\n", "p_mu = jnp.mean(p_post, 0)\n", "p_ci = jnp.percentile(p_post, q=jnp.array([5.5, 94.5]), axis=0)\n", "\n", "# set up plot\n", "ax = plt.subplot(\n", " xlim=(0.5, 28.5),\n", " ylim=(0, 1.05),\n", " xlabel=\"\",\n", " ylabel=\"proportion left lever\",\n", " xticks=[],\n", ")\n", "plt.yticks(ticks=[0, 0.5, 1], labels=[0, 0.5, 1])\n", "ax.axhline(0.5, c=\"k\", lw=1, ls=\"--\")\n", "for j in range(1, 8):\n", " ax.axvline((j - 1) * 4 + 4.5, c=\"k\", lw=0.5)\n", "for j in range(1, 8):\n", " ax.annotate(\n", " \"actor {}\".format(j),\n", " ((j - 1) * 4 + 2.5, 1.1),\n", " ha=\"center\",\n", " va=\"center\",\n", " annotation_clip=False,\n", " )\n", "\n", "xo = 0.1 # offset distance to stagger raw data and predictions\n", "# raw data\n", "for j in [1] + list(range(3, 8)):\n", " ax.plot((j - 1) * 4 + jnp.array([1, 3]) - xo, pl.loc[j, [1, 3]], \"b\", alpha=0.4)\n", " ax.plot((j - 1) * 4 + jnp.array([2, 4]) - xo, pl.loc[j, [2, 4]], \"b\", alpha=0.4)\n", "x = jnp.arange(1, 29).reshape(7, 4) - xo\n", "ax.scatter(\n", " x[:, [0, 1]].reshape(-1),\n", " pl.values[:, [0, 1]].reshape(-1),\n", " edgecolor=\"b\",\n", " facecolor=\"w\",\n", " zorder=3,\n", ")\n", "ax.scatter(\n", " x[:, [2, 3]].reshape(-1), pl.values[:, [2, 3]].reshape(-1), marker=\".\", c=\"b\", s=80\n", ")\n", "\n", "yoff = 0.175\n", "ax.annotate(\"R/N\", (1 - xo, pl.values[0, 0] - yoff), ha=\"center\", va=\"top\")\n", "ax.annotate(\"L/N\", (2 - xo, pl.values[0, 1] + yoff), ha=\"center\", va=\"bottom\")\n", "ax.annotate(\"R/P\", (3 - xo, pl.values[0, 2] - yoff), ha=\"center\", va=\"top\")\n", "ax.annotate(\"L/P\", (4 - xo, pl.values[0, 3] + yoff), ha=\"center\", va=\"bottom\")\n", "\n", "# posterior predictions\n", "for j in [1] + list(range(3, 8)):\n", " ax.plot(\n", " (j - 1) * 4 + jnp.array([1, 3]) + xo, p_mu[(j - 1) * 4 + jnp.array([0, 2])], \"k\"\n", " )\n", " ax.plot(\n", " (j - 1) * 4 + jnp.array([2, 4]) + xo, p_mu[(j - 1) * 4 + jnp.array([1, 3])], \"k\"\n", " )\n", "for i in range(1, 29):\n", " ax.plot(jnp.array([i, i]) + xo, p_ci[:, i - 1], \"k\", lw=1, zorder=4)\n", "x = jnp.arange(1, 29).reshape(7, 4) + xo\n", "ax.scatter(\n", " x[:, [0, 1]].reshape(-1),\n", " p_mu.reshape(7, 4)[:, [0, 1]].reshape(-1),\n", " edgecolor=\"k\",\n", " facecolor=\"w\",\n", " zorder=5,\n", ")\n", "ax.scatter(\n", " x[:, [2, 3]].reshape(-1),\n", " p_mu.reshape(7, 4)[:, [2, 3]].reshape(-1),\n", " marker=\".\",\n", " c=\"k\",\n", " s=80,\n", " zorder=5,\n", ")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.23" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "with numpyro.handlers.seed(rng_seed=73):\n", " N = 500\n", " U_sim = numpyro.sample(\"U_sim\", dist.Normal().expand([N]))\n", " Q_sim = numpyro.sample(\"Q_sim\", dist.Categorical(logits=jnp.ones(4)).expand([N]))\n", " E_sim = numpyro.sample(\"E_sim\", dist.Normal(U_sim + Q_sim))\n", " W_sim = numpyro.sample(\"W_sim\", dist.Normal(U_sim + 0 * E_sim))\n", " dat_sim = dict(\n", " W=(W_sim - W_sim.mean()) / W_sim.std(),\n", " E=(E_sim - E_sim.mean()) / E_sim.std(),\n", " Q=(Q_sim - Q_sim.mean()) / Q_sim.std(),\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.24" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "108efd1941cd4aafaeeb8077c7d048ed", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/1000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ax = plt.subplot(\n", " xlim=(0, 8.6),\n", " ylim=(0, 8.6),\n", " xlabel=\"generalized giving\",\n", " ylabel=\"generalized receiving\",\n", ")\n", "x = jnp.linspace(0, 9, 101)\n", "plt.plot(x, 0 + 1 * x, \"k--\", lw=1.5)\n", "\n", "# ellipses\n", "for i in range(25):\n", " Sigma = jnp.cov(jnp.stack([jnp.exp(g)[:, i], jnp.exp(r)[:, i]]))\n", " Mu = jnp.stack([jnp.exp(jnp.mean(g[:, i])), jnp.exp(jnp.mean(r[:, i]))])\n", " for l in [0.5]:\n", " pearson = Sigma[0, 1] / jnp.sqrt(Sigma[0, 0] * Sigma[1, 1])\n", " ellipse = Ellipse(\n", " (0, 0),\n", " jnp.sqrt(1 + pearson),\n", " jnp.sqrt(1 - pearson),\n", " edgecolor=\"k\",\n", " alpha=0.5,\n", " facecolor=\"none\",\n", " )\n", " std_dev = dist.Normal().icdf((1 + jnp.sqrt(l)) / 2)\n", " scale_x = 2 * std_dev * jnp.sqrt(Sigma[0, 0])\n", " scale_y = 2 * std_dev * jnp.sqrt(Sigma[1, 1])\n", " scale = transforms.Affine2D().rotate_deg(45).scale(scale_x, scale_y)\n", " ellipse.set_transform(scale.translate(Mu[0], Mu[1]) + ax.transData)\n", " ax.add_patch(ellipse)\n", "# household means\n", "plt.plot(Eg_mu, Er_mu, \"ko\", mfc=\"white\", lw=1.5)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.35" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.5% 94.5% n_eff r_hat\n", "Rho_d[0,0] 1.00 0.00 1.00 1.00 1.00 nan nan\n", "Rho_d[0,1] 0.88 0.03 0.88 0.83 0.94 1483.90 1.00\n", "Rho_d[1,0] 0.88 0.03 0.88 0.83 0.94 1483.90 1.00\n", "Rho_d[1,1] 1.00 0.00 1.00 1.00 1.00 89.24 1.00\n", " sigma_d 1.10 0.06 1.10 1.00 1.19 1480.49 1.00\n", "\n" ] } ], "source": [ "predictive = Predictive(\n", " m14_7.sampler.model, m14_7.get_samples(), return_sites=[\"Rho_d\", \"sigma_d\"]\n", ")\n", "link = predictive(random.PRNGKey(1), **kl_data, link=True)\n", "print_summary({k: v.reshape((4, -1) + v.shape[1:]) for k, v in link.items()}, 0.89)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.36" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "predictive = Predictive(m14_7.sampler.model, m14_7.get_samples(), return_sites=[\"d\"])\n", "post_d = predictive(random.PRNGKey(1), **kl_data, link=True)[\"d\"]\n", "dy1 = jnp.mean(post_d[..., 0], 0)\n", "dy2 = jnp.mean(post_d[..., 1], 0)\n", "plt.plot(dy1, dy2, \"o\", mfc=\"none\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.37" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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MlTiSCYaFiTrChMnToHa
Malekula0.00.50.64.41.22.03.22.81.95.7
Tikopia0.50.00.34.21.22.02.92.72.05.3
Santa Cruz0.60.30.03.91.61.72.62.42.35.4
Yap4.44.23.90.05.42.51.61.66.17.2
Lau Fiji1.21.21.65.40.03.24.03.90.84.9
Trobriand2.02.01.72.53.20.01.80.83.96.7
Chuuk3.22.92.61.64.01.80.01.24.85.8
Manus2.82.72.41.63.90.81.20.04.66.7
Tonga1.92.02.36.10.83.94.84.60.05.0
Hawaii5.75.35.47.24.96.75.86.75.00.0
\n", "
" ], "text/plain": [ " Ml Ti SC Ya Fi Tr Ch Mn To Ha\n", "Malekula 0.0 0.5 0.6 4.4 1.2 2.0 3.2 2.8 1.9 5.7\n", "Tikopia 0.5 0.0 0.3 4.2 1.2 2.0 2.9 2.7 2.0 5.3\n", "Santa Cruz 0.6 0.3 0.0 3.9 1.6 1.7 2.6 2.4 2.3 5.4\n", "Yap 4.4 4.2 3.9 0.0 5.4 2.5 1.6 1.6 6.1 7.2\n", "Lau Fiji 1.2 1.2 1.6 5.4 0.0 3.2 4.0 3.9 0.8 4.9\n", "Trobriand 2.0 2.0 1.7 2.5 3.2 0.0 1.8 0.8 3.9 6.7\n", "Chuuk 3.2 2.9 2.6 1.6 4.0 1.8 0.0 1.2 4.8 5.8\n", "Manus 2.8 2.7 2.4 1.6 3.9 0.8 1.2 0.0 4.6 6.7\n", "Tonga 1.9 2.0 2.3 6.1 0.8 3.9 4.8 4.6 0.0 5.0\n", "Hawaii 5.7 5.3 5.4 7.2 4.9 6.7 5.8 6.7 5.0 0.0" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# load the distance matrix\n", "islandsDistMatrix = pd.read_csv(\"../data/islandsDistMatrix.csv\", index_col=0)\n", "\n", "# display (measured in thousands of km)\n", "Dmat = islandsDistMatrix\n", "Dmat.columns = [\"Ml\", \"Ti\", \"SC\", \"Ya\", \"Fi\", \"Tr\", \"Ch\", \"Mn\", \"To\", \"Ha\"]\n", "Dmat.round(1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.38" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# linear\n", "x = jnp.linspace(0, 4, 101)\n", "plt.plot(x, jnp.exp(-1 * x), \"--\")\n", "plt.gca().set(xlabel=\"distance\", ylabel=\"correlation\")\n", "\n", "# squared\n", "x = jnp.linspace(0, 4, 101)\n", "plt.plot(x, jnp.exp(-1 * x**2))\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.39" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "9069397b48c2446eb7b4abf0c09d544a", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/2000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "post = m14_8.get_samples()\n", "\n", "# plot the posterior median covariance function\n", "plt.subplot(\n", " xlabel=\"distance (thousand km)\", ylabel=\"covariance\", xlim=(0, 10), ylim=(0, 2)\n", ")\n", "\n", "# compute posterior mean covariance\n", "x_seq = jnp.linspace(0, 10, 100)\n", "pmcov = vmap(lambda x: post[\"etasq\"] * jnp.exp(-post[\"rhosq\"] * x**2))(x_seq)\n", "pmcov_mu = jnp.mean(pmcov, 1)\n", "plt.plot(x_seq, pmcov_mu, lw=2, c=\"k\")\n", "\n", "# plot 50 functions sampled from posterior\n", "x = x_seq\n", "for i in range(50):\n", " plt.plot(\n", " x_seq, post[\"etasq\"][i] * jnp.exp(-post[\"rhosq\"][i] * x**2), \"k\", alpha=0.15\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.42" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "# compute posterior median covariance among societies\n", "K = jnp.zeros((10, 10))\n", "for i in range(10):\n", " for j in range(10):\n", " K = K.at[i, j].set(\n", " jnp.median(post[\"etasq\"])\n", " * jnp.exp(-jnp.median(post[\"rhosq\"]) * islandsDistMatrix.values[i, j] ** 2)\n", " )\n", "K = K.at[jnp.diag_indices(10)].set(jnp.median(post[\"etasq\"]) + 0.01)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.43" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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MlTiSCYaFiTrChMnToHa
Ml1.000.780.690.000.290.040.000.000.070.0
Ti0.781.000.860.000.290.040.000.000.050.0
SC0.690.861.000.000.150.100.010.010.020.0
Ya0.000.000.001.000.000.010.150.130.000.0
Fi0.290.290.150.001.000.000.000.000.600.0
Tr0.040.040.100.010.001.000.080.540.000.0
Ch0.000.000.010.150.000.081.000.310.000.0
Mn0.000.000.010.130.000.540.311.000.000.0
To0.070.050.020.000.600.000.000.001.000.0
Ha0.000.000.000.000.000.000.000.000.001.0
\n", "
" ], "text/plain": [ " Ml Ti SC Ya Fi Tr Ch Mn To Ha\n", "Ml 1.00 0.78 0.69 0.00 0.29 0.04 0.00 0.00 0.07 0.0\n", "Ti 0.78 1.00 0.86 0.00 0.29 0.04 0.00 0.00 0.05 0.0\n", "SC 0.69 0.86 1.00 0.00 0.15 0.10 0.01 0.01 0.02 0.0\n", "Ya 0.00 0.00 0.00 1.00 0.00 0.01 0.15 0.13 0.00 0.0\n", "Fi 0.29 0.29 0.15 0.00 1.00 0.00 0.00 0.00 0.60 0.0\n", "Tr 0.04 0.04 0.10 0.01 0.00 1.00 0.08 0.54 0.00 0.0\n", "Ch 0.00 0.00 0.01 0.15 0.00 0.08 1.00 0.31 0.00 0.0\n", "Mn 0.00 0.00 0.01 0.13 0.00 0.54 0.31 1.00 0.00 0.0\n", "To 0.07 0.05 0.02 0.00 0.60 0.00 0.00 0.00 1.00 0.0\n", "Ha 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 1.0" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# convert to correlation matrix\n", "Rho = jnp.round(K / jnp.sqrt(jnp.outer(jnp.diagonal(K), jnp.diagonal(K))), 2)\n", "# add row/col names for convenience\n", "Rho = pd.DataFrame(np.asarray(Rho))\n", "Rho.columns = [\"Ml\", \"Ti\", \"SC\", \"Ya\", \"Fi\", \"Tr\", \"Ch\", \"Mn\", \"To\", \"Ha\"]\n", "Rho.index = Rho.columns\n", "Rho" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.44" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "image/png": 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90bt3b0yYMAHOzs4V3HrrNnfuXEs3gYiIiKhSsNmw/eWXXyIuLg4qlQre3t6Ii4sr8li1Wo3hw4cjIiICXbp0Qb9+/RAREYFvvvkG586dw/bt2+Ho6FiBrSciIiIiW2CzZSSffvopjh49itOnT2Po0KHFHrtx40ZERERgzJgx+PrrrzF16lR8/fXXGDNmDK5cuYJvv/22YhpNRERERDbFZsN2p06d4Ovr+9TjRFHE7t27oVQqMW7cOKN948aNg1KpxO7du83VTCIiIiKyYTYbtksqOjoaCQkJCA4OhlKpNNqnVCoRHByMu3fv4v79+xZqIRERERFZqyoftmNiYgAAgYGBhe43bI+Ojq6YBhGVQkhICP7880+z32fs2LFYvny52e9DRERka2z2AcmSSk9PBwC4uLgUut+wPSMjo9jrmGsi9KqAfVe0xMRErF+/HseOHcPDhw/h4eGBxo0b4/XXX0fHjh0B5P2OmrsP5XI5HB0dbea/la28j4rGfjMd+8407DfTse8qjyoftstLVVypKTlFRPhFQBCA4FaAu7tQ6mtwlauixcfH45133oGLiwvGjRuH+vXrQ6vV4vTp05g3bx6+++47AHkfBM3dhxqNBjk5OTbx34q/c6Zhv5mOfWca9pvp2Hem4QqSZuLq6gqg6JFrw/aiRr6rqsh/RQwbIeL/5omY+7GIYSNF/PuvaOlm2ZSlS5cCAL755ht0794dAQEBqFu3LoYNG4Zdu3ZJx6WkpGDGjBno2rUrBg8ejOPHj0v79u/fj549expd988//0RISIj0ev78+Zg+fbrRMcuXL8fYsWOLbNvJkyfRo0cP/P7772V6j0RERLauyoft2rVrAyi6Jtuwvaia7qpq7sciMjMBvV4DvT4X6ek6zJ2vgygycJeH1NRUnD59GoMHD4aTk1OB/dWqVZN+/vrrr9GjRw9s27YNnTp1wscff4zU1FSzte3AgQOYM2cO5s2bhz59+pjtPkRERLagyoftwMBAeHt7Izw8HGq12mifWq1GeHg4/Pz8ULNmTQu1sPLJyRFxLw7QanWAqAFELXRaDWJjtFCrc5GbmwutVgudTge9Xs8AboJ79+5BFEXpw2Bx+vXrh169esHf3x9jx46FWq3G9evXzdKuPXv2YOnSpfj888/RpUsXs9yDiIjIllT5sC0IAl555RWo1WqsXbvWaN/atWuhVqsxZMgQC7WucnJwAJycAEGQ5RVsAwD0cHISYf//nwLQ6/XQ6XTQarXQaDTIzc2FRqMxCuFUtNJ8QKlfv770s5OTE5ydnc1Sq3f06FGsWLECK1euRHBwcLlfn4iIyBbZ7AOSu3fvxoULFwAAkZGR0razZ88CANq0aYNXXnkFAPDWW2/hyJEjCAsLQ0REBJo0aYLr16/jxIkTaN68OV5//XXLvIlKShAEjH8X+Hw5IAiOAHTQ60WMfVeAnZ0dRFEsNCwWtt0QwAVBMPqnqvP394cgCNLUlMWxtzf+31gQBOnDjEwmK9DnWq3W6HVJjgGAoKAgREZG4ueff0bjxo3534mIiKgEbDZsX7hwAXv37jXaFh4ejvDwcOm1IWwrlUps27YNq1atwsGDB3HmzBl4eXlh1KhRGD9+PBQKRYW23RoMfEmAqjpw9A8Z9HoRPboBXToLkMlkUngr7J8niaJY6Ci3IXTLZLIqGcDd3NzQoUMH7NmzB0OGDClQt52Wllai67i7u0OtViMrK0u6huHDZ/5jbt++bbQtMjKyQIj38/PDpEmTMG7cONjZ2WHq1KmlfVtERERVjs2G7UWLFmHRokUlPt7V1RWzZ8/G7Nmzzdgq29L1GQFdnxEgigJ0Oh2AvPKR4kao8wfv4kpJCjvmydFvWw/h06ZNw9tvv41Ro0ZhzJgxqF+/PnQ6Hc6ePYv//ve/2LFjx1Ov0bRpUygUCqxbtw5DhgzBtWvX8Ouvvxod07ZtW2zfvh2//vormjVrhgMHDuD27dsICgoqcL2AgACsWbNGCtxTpkwpt/dLRERki6p8zTaVnWEE2qC4EG041s7ODnK5HA4ODpDL5bC3t4ednZ00kl0YQ/h+shbcVh/G9PX1xebNm9GmTRusXLkSoaGhmDhxIs6fP4+PP/64RNdwc3PDxx9/jL///huhoaE4ePAgRo8ebXRMSEgIRo0ahdWrV2PUqFHIzMzECy+8UOQ1a9eujdWrV+PgwYP48ssvy/IWiYiIbJ4g2lI6sSBOHm9c52tnZ1eiUefiJt43hOviylCK8uTod/4PA7aACxaYjn1nGvab6dh3pmG/mY59ZxpzLWpjs2UkVPHs7OykchKdTleg5re0BCHvgcv8SlML/uT2qlaGQkRERJbHsE3lxhBeDSFXp9MVCMvldY/8yhLA81+zqj6MSURERObDsE3lys7OTionMYRbc4fXkj6MWVQZCh/GJCIiInNh2KZyJ5PJpOBaHuUkpsofkA0j7GUdBc8/+s0ATkRERE/DsE3lLv8820De7CSV5QHF4kbBS/IwZnFzgtvqw5hERERkOoZtMguZTFbo3NuVFR/GJCIiInNg2CazMIzwGkaC9Xp9uT8saW58GJOIiIjKimGbzObJZdsrUzmJqfgwJhEREZUGwzaZlbWVk5iKD2MSERFRYRi2yaxsoZzEVOZ8GNOwPH1JvimIvSvi9GlAZgd06QzU8GFoJyIiqigM22R2+cO2rZSTlEV5PIyp0+mk+cyLKkMRRRHrvxKx/TvAkPm/XAWMfQcYNpSBm4iIqCIwbFOFyL+Ue1UP24Uxx8OYJ04C23YAgAyi+L/rr10vomkToGULBm4iIiJzY+KhCvFkmDQEbyqaoQTHzs4O9vb2kMvlcHBwgFwuh729Pezs7Iqt4/7lNz0EQQ9Rnw1N7j3k5sZBr9fBzg749ffCS1eIiIiofHFkmypMYUu5U+nlD+HFPYyZkgyIekCny8j7QdRD1Gug09khNdXCb4KIiKiK4Mg2Vaj8tcoc3S4/hY2Ct2rtAEFmB1HUAoIMkMkhyBwgCEDTJiwhISIiqggM21ShniwnKWzGDSofr/xHgJNTFmR2AiDYQyZzhr2dgOrVgQH9Ld06IiKiqoFhmypc/ocji1sAhsqmho+AxQuy0a4NIJMBDg5KPPecgA1rBLi5cWSbiIioIrBmmypcVZ57uyJlZ2ejVk09Zs+Uwd5ejurV7WFnx8/XREREFYl/85JFGFZHBP439zaVr6ysLOlnFxdnrkBJRERkAQzbZDEsJzEfrVaLnJwcAHkPpTo6Olq4RURERFUTwzZZjKGcxICj2+VHrVZLPyuVSgu2hIiIqGpj2CaLYjlJ+RNFEdnZ2QDyPtA4OTlZuEVERERVF8M2WRxHt8tXVlaW1I8KhYK12kRERBbEsE0Wx6Xcy1f+ByNZQkJERGRZDNtUKeSf+o9LuZtOo9FAo9EAAORyOeRyuYVbREREVLUxbFOlwaXcyy7/g5Gs1SYiIrI8hm2qNLiUe9no9XrpwUiZTMawTUREVAkwbFOlwrm3TadWq6X+4oORRERElQPDNlUqnHvbdHwwkoiIqPJh2KZKh3Nvl15OTo5U5+7o6Ah7e3sLt4iIiIgAhm2qpFhOUjoleTCSZSVEREQVj2GbKiWWk5ScTqdDTk4OgLwZXRQKhYVbRERERAYM21RpsZykZDIzM6WfOQMJERFR5cKwTZUaR7eLJ4qiNN2fIAh8MJKIiKiSYdimSu3JchIudmMsOztb+hCiUCiM+oqIiIgsj38zU6WXP0ByKXdjXDGSiIiocmPYJqvApdwL0mg00Gg0AAC5XA4HB4cCx/CDCRERkWUxbJNV4FLuBXFUm4iIqPJj2CarkX90u6rPva3X640ejGTYJiIiqpwYtsmqcHaSPFlZWdKHDScnJy5YQ0REVEkxbJNV4dzbefLPrc3p/oiIiCovhm2yOlV9KfecnBzpIVFHR0fY29tbuEVERERUFIZtsjpVfSl3PhhJRERkPRi2ySpV1XISnU6HnJwcAHkPjCoUihKfy7puIiKiisewTVarKo5uc1SbiIjIujBsk9Wqaku5i6KIrKws6TUfjCQiIqr8GLbJqlWlpdyzs7OlEXwnJyej905ERESVE/+2JqtXVZZyz19CwlFtIiIi68CwTVavKizlrtFooNFoAAByuRwODg4WbhERERGVBMM22QRbX8o9f612aR6MtLV+ICIisjYM22QzbHV2Er1eL4VtQRA4CwkREZEVYdgmm2Grc29nZWVJI9ROTk6cL5uIiMiKMGyTTbHFpdw53R8REZH1si+Pi9y6dQu7du3C5cuXkZycjB49emD69OkAgPDwcFy9ehUDBgyAu7t7edyOqEiGubcNo9p6vd6ontva5OTkQKvVAgAcHBxgb18u/8sSERFRBSnz39ybNm3CsmXLpEAgCAKSk5ONjlm4cCEcHBwwdOjQst6O6KlkMpk057ahnMRa56TmqDYREZF1K1MCOXbsGBYvXowaNWpg9erV+Pvvvwt8bR8cHIzq1avjyJEjZWooUWnYwsOSOp0O2dnZAPJmW1EoFBZuEREREZVWmUa2N23aBCcnJ2zatAn+/v5FHteoUSPcuXOnLLciKpUny0l0Op3VlZPkX8SGM5AQERFZpzKNbF+7dg2tWrUqNmgDgEqlwqNHj8pyK6JSs+al3EVRLNcSEs5gQkREZBllCtsajQbOzs5PPS4pKcnqRhXJNljrUu7Z2dnSqLxCobDamnMiIqKqrkx/g/v5+eHGjRvFHpObm4ubN28iMDCwLLciMom1LuXOByOJiIhsQ5nCdvfu3REXF4dNmzYVeczGjRuRlJSEXr16leVWRCaztqXcNRoNcnNzAQD29vZwcHCwcIuIiIjIVGV6QPKtt97Czz//jCVLluDSpUt4/vnnAQCPHz/GoUOHcOjQIfz888/w8/NDaGhouTSYyBTWNPc2R7WJiIhsR5nCtpubGzZt2oSJEyfi999/x4EDBwAAf/31F/766y+Iooj69etjzZo1cHFxKZcGE5nCWube1uv1UtgWBIGzkBAREVm5Mi9qU6dOHfz3v//F0aNHcfLkScTFxUGv16NGjRro1KkTevfuXalHEanqkMlk0kOSer2+QD13ZZCVlSWVuTg5OZWpfZW9XIaIiKgqKJe1n2UyGXr27ImePXuWx+WIzMIalnJnCQkREZFtqXzfoxOZkUwmk0aLDeUklUVOTg60Wi0AwMHBAfb25fJZmIiIiCyoVH+bnzt3rkw3a9euXZnOJyoPlbWchKPaREREtqdUYXvEiBFlCiUREREmn0tUXipjOYlOp0N2djaAvA8DCoXCou0hIiKi8lGqsD1w4MACYTslJQV//PEHBEFAo0aN4OvrCwCIj4+XwvVzzz0Hd3f38mkxUTnIH7YNM5RYcnRbrVZLP3MGEiIiIttRqrC9aNEio9ePHj3CkCFDEBISgjlz5qBevXpG+6OiovDpp5/i5s2b2LlzZ9lbS1SO7OzspHISnU5nsRppURRZQkJERGSjyvSA5LJly5Cbm4t169YVCNoAUK9ePaxZswa5ublYtmxZWW5FVO6erNU2BO+Klp2dLY2yKxQKi5e0EBERUfkpU9j+66+/0K5du2K/9lYqlWjXrh1OnDhRllsRmUX+YGsoJ6loFTGqXRkeACUiIqqKyhS209PTkZ6eXm7HEVlC/pUkK3oqQK1Wi9zcXACAvb09HBwcKvT+REREZF5lCtuBgYE4c+YMbty4UeQxN27cwOnTp1GnTp2y3IrIbCw59zYfjCQiIrJtZQrbI0aMgEajwciRI7F69Wrcvn0bOTk5yMnJwe3bt7FmzRq8/vrr0Ol0GD58eHm1majcPTm6XRHlJPkfjBQEgQ9GEhER2aAyTb8wePBgREdH4+uvv8aaNWuwZs2aAseIoojRo0dj8ODBZbkVkVlZYu5ttVothXonJyfWVRMREdmgMs91NnXqVDz//PPYsWMHLly4gISEBACAl5cX2rZti6FDh6J169ZlbiiRuclkMukhSUM5Sf4R7/LG6f6IiIhsX7lMLNyyZUu0bNmyPC5lcZcvX8aqVatw8eJFaLVaBAUF4Y033kDfvn0t3TSqABW1lHtubi60Wi0AwMHBwSxzfFtiZhUiIiIyZplVPCqp06dP46233oKDgwP69esHZ2dnHDx4EFOmTMGDBw8watQoSzeRzKyiykn4YCQREVHVwLD9/2m1WsyZMweCIGD79u1o3LgxAGD8+PEYPHgwvvjiC/Tu3Vtajp5sl7mXctfpdMjOzpbupVAoyu3aREREVLmUKWwbAmlJCIKA69evl+V2ZnX69GnExsZi0KBBRu/L1dUV7777LmbOnIm9e/diwoQJFmwlVRRzLuX+5Kg2H4wkIiKyXWVKEDVr1ix0uyiKSExMlGpSa9WqVZbbVIizZ88CALp06VJgn2HbuXPnKrRNZDmGWm1D3bNOpyu3chI+GElERFR1lClsHz16tMh9er0ep0+fxmeffYagoCB88cUXZbmV2UVHRwMAateuXWCfl5cXlEolYmJiijxfpVKZq2k2rzL3neEDI5A32l3WUejs7GxUq1YNAKBQKMr03p92bv7Fecw5q4o1qsy/c5UZ+8107DvTsN9Mx76rPMxWsy2TydCpUyesX78eAwYMQFhYGN5++21z3a7MMjIyAOSVjRTGxcWl2CXnk5OTzdIuW6dSqSp13+n1eqPQWtZykqSkJGl59rK895Kcy7BduMr+O1dZsd9Mx74zDfvNdOw705jrA4rZ/wb29/dHq1at8MMPP5j7VkTlLv9S7gDKtJS7VquVgra9vT0cHR3L3L6SYE04ERGR5VTIcJdCocD9+/cr4lYmc3FxAYAiR68zMjKKHPUm21ZeS7lzuj8iIqKqx+xhOy4uDufPn4enp6e5b1UmgYGBAFBoXXZiYiLUanWh9dxk+wxzbxuYMrotiqL0YKQgCAzbREREVUSZClD37dtX5L7MzExER0fjp59+QkZGBoYNG1aWW5ldu3btsGHDBpw4cQL9+vUz2nfixAnpGKqayrqUe1ZWljQi7uTkxBpqIiKiKqJMYXvmzJnF1oMawsXAgQPx3nvvleVWZtexY0f4+/tj//79GDlypDTXdnp6OtavXw+5XI6BAwdatpFkUWVZyp0lJERERFVTmcL2+PHjiwwbcrkcXl5eaNeuHfz9/ctymwphb2+PTz/9FG+99RZCQ0ONlmuPi4vDjBkz4OfnZ+lmkgWZupR7bm6uNIWgg4MD5HK5WdtJRERElUeZwnZlH60urZCQEOzYsQMrV67Er7/+Cq1Wi6CgIEydOhV9+/a1dPOoEjClnCT/IjYVNapt6kOcREREVL7KFLbPnTsHT09P1KlTp9jjoqOjkZiYaBU1zy1atMDGjRst3QyqxJ4sJykubOv1eilsy2QyKBSKCmkjERERVQ5lekprxIgRCAsLe+pxGzduxMiRI8tyK6JK48labUPwLsyTtdqc85qIiKhqKfOUCCX5uppfaZOtyV+rbSgpKUz+EhKlUmn2dhEREVHlUiHzjyUkJDBokM3JH7gLG93Ozs6WtisUihI9TElERES2pdQ120/OrR0bG1vkfNtarRZ37tzBqVOn0LJlS1PaR1RpGcpJDKPaT9ZvW+LBSCIiIqpcSh2288+tLQgCwsPDER4eXuTxoijC0dER48ePN72VRJVUUXNva7Va5OTkAMibVtLR0dGSzSQiIiILKXXYNsytLYoi1qxZg8aNG6NHjx6FHiuXy+Ht7Y3OnTvD29u7zI0l6zV//nz8+uuvePnllzFjxgyjfUuXLsUPP/yAvn37Yu7cuRZqoWkKm3s7JUWG1NRMODmJXJqdiIioiit12M4/t/bevXvRsWNHTJgwoVwbRbbJx8cHhw4dwqRJk6Qp8HJycnDw4EHUqFHDwq0znWHu7fCLeqxZr0dkpB56nRo1a4gIDRUwaKBlwzZnQCEiIrKcMj0gefToUUyfPr282kI2rmHDhvDx8cGxY8ekbQcPHoSPjw+CgoKkbadOncLbb7+Nnj17olevXvjggw9w7949aX98fDxCQkLwxx9/YNy4cejatSuGDx+OK1euSMeEhYVhxIgRRvf//vvvMXDgQOn1hQsXMGrUKDz33HPo2bMnxowZg/v375v03q5cFfDBdBG3bgGimAm9qEf8A2DZcgUOH2HYJSIiqqoqZDYSIoP+/ftj//790usffvgB/fv3NzomKysLr732GjZt2oTVq1dDEATMmDFDKtUwWL9+PUJDQ7F161YEBARgzpw50rLoT6PVajFjxgy0bt0a27ZtQ1hYGAYOHGjyKHDY14AoyiCKgFbzCHpdKgBAJnPCuq9E6HSc/pKIiKgqKlUZyaxZsyAIAt5//314enpi1qxZJT5XEAQsWLCg1A0k29KnTx+sW7dOGkEODw/H//3f/xk9ZNu9e3ejcz766CP06dMHd+7cQb169aTtoaGh6Ny5MwBgzJgxeO2113Dv3j0EBgY+tR2ZmZnIyMhA586d4efnBwBPXQm1KNnZIi5dBgAZdLpUZKnPAaIejk4tIZfXQGIiEBMD1K1r0uWJiIjIipUqbO/duxeCIGDMmDHw9PTE3r17S3wuwzYBgEqlQqdOnfDLL79AFEU899xzcHd3NzomNjYWYWFhuHbtGlJSUqSp9R4+fGgUtuvXry/97OHhAQBITk4uUdh2c3NDv379MHnyZLRr1w7t27dHjx494OnpWcZ3KADIa69W8wCi2Jg100RERFVYqcL2li1bAAC1atUyek1UGi+++CI+//xzAMC8efMK7J82bRpq1KiBWbNmwdPTE6IoYtiwYdBoNEbH2dv/79fXEGgNpSaGhxbze7LEZM6cORgyZAhOnz6Nw4cPY8OGDVi5ciWaNWtWqvejUAho0VzE1WuAvb075A51odM+AgQdtJp41Krli9q1S3VJIiIishGlCtvt27cv9jVRSYSEhEjBt0uXLkhLS5P2paamIiYmBrNmzUKrVq0AAP/880+p7+Hu7o7Hjx9DFEUpiEdGRhY4rmHDhmjYsCFef/11vPXWWzhw4ECpwzYAvP2WgEnvixAEQKEIglqdV7Odm3sb74ypBTu7in08oqjl44mIiKhilSkBnDt3Dnfu3HnqcdHR0Th37lxZbkU2xM7ODt9//z2+//77AkuYu7q6ws3NDfv27cPdu3dx/vx5rFy5stT3CA4ORkpKCrZu3Yp79+5hz549OH36tLQ/Pj4ea9euxZUrV3D//n2cOXMGd+/eLVEJSmFatRSw/HMBDRoAdvbusLf3gIcHMGxoDpo1NW2GEyIiIrJ+pZ5nO78RI0Zg0KBBT63F3rhxI3744QdERESU5XZkQ5ydnQvdLpPJ8Mknn+CLL75AaGgoAgIC8P7772PcuHGlun6dOnUwbdo0bN68GZs2bUK3bt0wbNgw7Nu3DwDg6OiImJgY/Prrr0hNTYWHhwcGDx6Ml19+2eT3FNxawDdfCXj8WERySgPcjkqCIAi4ffs2atWqZbSUOxEREVUNgliG75sbNWqEl19+GQsXLiz2uA8//BA//vijTYft5ORkSzfBKqlUKpvtu3/++QeJiYkA8spVAgICyu3aT+u3/NMkMuQbs+XfOXNiv5mOfWca9pvp2HemUalUZrluhfwtnJCQAKVSWRG3Iqo06uab6+/OnTvQ6XQWbA0RERFZQqnLSAxfwxvExsYW2Gag1Wpx584dnDp1Ci1btjSlfURWq1q1avD29kZCQgJyc3Nx79491Oa0JERERFVKqcP2zJkzpdkdBEFAeHi40YIkTxJFEY6Ojhg/frzprSSyUnXr1kVCQgKAvNFtPz+/Ag+FEhERke0qddgeP348BEGAKIpYs2YNGjdujB49ehR6rFwuh7e3Nzp37gxvb+8yN5bI2ri6usLHxwcPHz6ERqNBbGysyStVEhERkfUpddh+7733pJ/37t2Ljh07YsKECeXaKCJbUrduXTx8+BBA3jSY/v7+RgvymBNXryQiIrKsMv2Nf/To0fJqB5HNcnFxQc2aNXH//n1otVrExsYaPTxJREREtotzghFVgPylIzExMQWWniciIiLbVC7fZZ8/fx5HjhxBTEwMMjMzC10qWhAEbN68uTxuR2R1nJ2dUatWLcTHx0uj2/Xq1bN0s4iIiMjMyhS2RVHE7NmzsW/fPilgGx6eNDC8Zu0oVXV16tRBfHw8gLzR7YCAAMjlcgu3ioiIiMypTGUk3333Hfbu3YumTZti06ZN6NWrFwDg999/R1hYGF5++WXIZDKMHj0ahw8fLpcGE1krpVIJX19fAIBOp0N0dLRlG0RERERmV6aR7b1798LJyQlhYWFQqVT46aefAACBgYEIDAzEM888g65du2LKlClo3bq1FDSIqirD6LYoioiNjUXt2rXh4OBQrvcorIyLiIiILKNMI9tRUVEIDg4usJZ8/mWp+/Tpg6ZNm+Kbb74py62IbIKTk5P0oVOv13N0m4iIyMaVKWyLogh3d3fptZOTEwAgNTXV6LjatWsjMjKyLLcishl16tSRnmG4e/cucnJyLNwiIiIiMpcyhW1vb29pKWoAqFWrFgAgIiLC6Ljo6GguUU30/ykUCvj5+QHg6DYREZGtK1PYbtq0KW7duiWVjXTp0gWiKGLp0qWIiopCRkYGNm7ciGvXrqFJkybl0mAiW1CnTh3IZHn/+929exfZ2dkWbhERERGZQ5nCdvfu3ZGcnIxjx44BABo1aoR+/frhxo0b6N+/P9q1a4dly5bB3t4eU6ZMKY/2EtkER0dH+Pv7A8grx7pz546FW0RERETmUKbZSPr3749evXoZlYgsWrQIDRs2xOHDh5Gamoo6dergrbfeQosWLcrcWCJbEhgYiLt370Kv1yMuLg6BgYHScw9ERERkG8q8guST05bJ5XK8/fbbePvtt8t6aSKb5uDggICAAERHR0uj2+VdbsXFpIiIiCyrTGUkRFQ2tWvXlr4ZiouLg1qttnCLiIiIqDwxbBNZkIODA2rXri29Zu02ERGRbSlVGUmPHj1MvpEgCFyynagQAQEBiImJgU6nQ3x8POrUqQOlUmnpZhEREVE5KFXYjouLM1c7iKosuVyOwMBAREVFAQBu376NZs2aWbhVREREVB5KFbZv3LhhrnYQVWmG0W2tVov79+8jMDAQLi4ulm4WERERlRFrtokqAXt7ewQGBkqvy1K7LYpiObSIiIiIygPDNlElERAQALlcDgB48OAB0tPTLdwiIiIiKiuGbaJKws7ODnXq1JFe375924KtISIiovLAsE1Uifj5+UkLRSUkJCAtLc3CLSIiIqKyYNgmqkQ4uk1ERGRbGLaJKhk/Pz84OjoCABITEzm6TUREZMUYtokqGZlMZjS6fevWLQu2hoiIiMqCYZuoEvL19YVCoQAAPH78GKmpqRZuEREREZmCYZuoEiqP0W1BEMqzSURERGQChm2iSsrX1xdOTk4AgKSkJCQnJ1u4RURERFRaDNtElZQgCEaj21FRURZsDREREZmCYZuoEqtVqxaUSiUAIDk5GUlJSRZuEREREZUGwzZRJSYIAurWrSu95swkRERE1oVhm6iSq1GjBpydnQEAqampePz4sYVbRERERCXFsE1UyZVmdFsUxYpoEhEREZUQwzaRFfDx8YGLiwsAIC0tDQkJCRZuEREREZUEwzaRFXhydPvff/+1YGuIiIiopBi2iayEj48PXF1dAeTVbnN0m4iIqPJj2CayIvXq1ZN+joqKYo02ERFRJcewTWRFvLy8pNHtjIwMjm4TERFVcgzbRFamfv360s8c3SYiIqrcGLaJrIynpydUKhUAIDMzEw8ePLBwi4iIiKgoDNtEVigoKEj6+fbt24WObguCUJFNIiIiokIwbBNZIQ8PD7i7uwMA1Go17t+/b9kGERERUaEYtomsVP7a7aJGt4mIiMiyGLaJrJRKpZJqt7OyshAXF2fhFhEREdGTGLaJrFj+0e07d+5Ar9dbsDVERET0JHtLN4CITOfu7g4PDw88fvwY2dnZiI+Ph6+vr6WbZROSk5Px1Vdf4e+//0ZSUhJcXV3RoEEDjBo1Ci1btiy3+8yfPx8ZGRlYsmRJuVzvwoUL2LZtG65du4acnBzUrFkTHTt2xGuvvQZvb+9yuQcREZUcwzaRlatXrx4eP34MIG/e7Zo1a0Im45dWZTVr1ixoNBrMnTsXtWrVQlJSEs6fP4/U1FRLN61Ie/fuxdKlS9G3b18sXLgQNWvWxMOHD/Hrr79ix44dmDx5coFzdDodBEHg7wwRkZkwbBNZOTc3N3h6euLwkUQcOZqNzHl30TDIH2+8LqBLJ07/Z4r09HT8888/WLt2LYKDgwEANWvWRNOmTY2O27FjB3755RfExcWhWrVq6NKlCyZMmAClUgkA2L9/P1asWIFPP/0Uy5cvR0JCAlq2bImPPvoInp6eCAsLw6+//goACAkJAQCsWbMGbdq0werVq/Hnn38iISEBHh4e6N27N0aPHg17+8L/2E5ISMAXX3yBIUOGGIXqWrVqoXXr1khPTzdq09y5c7F27VrcvXsXu3fvxieffIKgoCBMmTJFOnf69OlwcXHB3LlzcebMGYwcObLAffv27Yu5c+ea2NNERLaPYZvIBtz8ty627chbul0Q7uDGzVqYOVuG+R8D3Z9j4C4tJycnKJVKHD9+HM2aNYODg0Ohx8lkMrz//vuoWbMm4uPjsXTpUqxevRrTp0+XjsnOzsb27dvx8ccfQxAEfPzxx1i5ciXmz5+P0NBQREdHIzMzE3PmzAEAVKtWDQCgVCoxZ84ceHp6IioqCgsXLoRSqcSIESMKbcuRI0eg0WgwfPjwQve7uroatWnr1q2YPXs23NzcUL169af2SevWrfHLL79Ir6Ojo/H++++jdevWTz2XiKgqY9gmsnJarYhtO1xhb+8NjeYBRDEb2dmxcHSsi/VfiejWVcYFbkrJ3t4eH330ERYtWoS9e/ciKCgIwcHB6NmzJxo0aCAdN3ToUOnnWrVq4Z133sHixYuNwrZWq8WMGTPg5+cHABg8eDC++eYbAHmB2tHRERqNBh4eHkZtGDVqlNG1Y2NjcejQoSLD9t27d+Hs7AxPT8+nvj+tVovp06cbvZencXBwkNqYmpqKBQsWoH///njxxRdLfA0ioqqIYZvIyj16DKSkAA6OdaHR5C1uo9M+AhwDERcHZGaKcHISpMCdP3gzhBete/fu6Ny5M/755x9cu3YNp06dwrZt2zBr1iz0798fAHD27Fls2bIFMTExyMzMhE6nQ05ODrKzs6FQKAAACoVCCtoA4OnpieTk5Kfe/9ChQ9i1axfi4uKQlZUFnU4HZ2fnIo8XRbHE/z3lcrnRTDalodVqMXPmTNSoUcOo5ISIiArHJ2KIrJxbNUBuD9jZucLBoT4EwR729nmzTjg7A4YKCFEUIYoi9Hq99I9Op4NOp5NeG46hPI6OjujQoQNGjRqFsLAw9O3bFxs3bgQAxMfHY+rUqahfvz4WLlyIb7/9FlOnTgUAaDQa6RpP1lgLgvDUPr5y5Qo+/vhjdOrUCcuWLcPmzZvxxhtvGF33SQEBAcjIyMCjR49K9L6eDOYymaxAu7RabYFzFy9ejISEBCxYsKDI+nEiIvofhm0iK+fkJKBfX0AmAxRO9eFarSccHAMhCDIMGijA3v7p/5s/GcQZwgtXp04dZGVlAQBu3LgBvV6PiRMnolmzZggICEBiYmKprymXy6HT6Yy2Xb58GTVq1MCbb76Jxo0bIyAgAPfv3y/2Ot27d4dcLse2bdsK3W94QLIo7u7u0qw2QN4sJbdv3zY6ZseOHThy5AiWLFkCNze3Yq9HRER5OCxBZAPeGy8gK0vEwcOAKAL29gJe7Ae8NUoGmcx4BNMQmp/8d2GKOqawUhRbKklJTU3F7Nmz0b9/f9SvXx/Ozs6IiIjAtm3b8OyzzwIA/P39odVqsXv3bnTp0gWXL1/G3r17S32vmjVr4syZM4iJiYGbmxtcXFzg7++PBw8e4NChQ2jcuDFOnjyJP//8s9jr+Pj4YNKkSVi2bBkyMzPxwgsvoGbNmkhISMBvv/0GJycnTJo0qcjz27Ztiy+//BInT56Er68vvvvuO6OA/vfff2PNmjWYOnWqUTB3dHSEi4tLqd83EVFVwbBNZAMcHQXM+VDA2HdF3L8P+PkBKvfCw29R4diUEF7YcU9e3xpDuJOTE5o2bYrvv/8ecXFx0Gq18PHxwUsvvYTXX38dANCgQQNMmjQJW7duxdq1a9G6dWuMGzcO8+bNK9W9XnrpJYSHh+PNN9+EWq3GmjVr8Oyzz2Lo0KH4/PPPodFo0KlTJ4waNUoqYSnK4MGDERAQgB07dmDmzJnIyclBjRo10KVLF7z22mvFnvviiy/i33//xbx582BnZ4fXXnsNbdq0kfZfuHABOp0OixcvxuLFi6XtnPqPiKh4gsjvhstFSR54ooJUKhX7zgQV2W+lCeHFqSwhnL9zpmG/mY59Zxr2m+nYd6ZRqVRmuS5HtomoWMWFY5akEBERFc8mw3ZERAR+++03XLt2DdeuXUNycjLat2+PrVu3FnveTz/9hC1btuDWrVuQy+UIDg7GxIkTC6waR0R5WJJCRERUPJucjeTw4cPYsGEDzpw5Ay8vrxKds27dOkybNg1JSUkYOnQo+vTpg3PnzmHo0KG4cOGCmVtMZFsEIW9eb5lMBplMBjs7O9jZ2UmvDfufhrOkEBGRtbPJke0+ffqge/fuCAoKQkpKCrp06VLs8dHR0Vi9ejUCAwOxZ88eaVnjYcOGYciQIZgzZw72798PmcwmP5sQVRhzl6QUdg+OhhMRkSXZZHps0KABmjZtCrlcXqLjf/zxR2i1WowdO1YK2gDQuHFj9O/fH1FRURzdJjIzjoYTEZEtssmwXVpnz54FAHTu3LnAPsOouOEYIqpYJQ3hTwviDOFERGQJNllGUlrR0dFQKpWF1nfXrl0bABATE1PRzSKiYrAkhYiIrAHDNoCMjAxUr1690H2GldGettSxueZmrArYd0935swZjBw5EufOnUO1atUAlLzfZs6cibS0NKxdu9acTcSPP/6IBQsW4Pz582a9T1kYArXh/3drnzO8ovH/VdOx70zDfjMd+67yqLRhe9GiRcjNzS3x8SNHjkRgYKD5GvQUnDzeNLY48X5ISEix+0ePHo0xY8aU6pqGD3spKSnQ6XSl6rfx48dDFEWz93NmZmaF3KesVCoVUlJSjLYVNrptShC35RBui/+vVhT2nWnYb6Zj35mmyi1qs3PnTqjV6hIf37t3b5PDtouLS5Ej1xkZGQBg9OAkUXF++eUX6efDhw/jq6++wq5du6RtTk5O0s+iKEKn08Hevvz/V9TpdBAEQfp2horGkhQiIjKXShu2L168WGH3CgwMxMWLF5GYmFigbttQq22o3SZ6Gg8PD+lnZ2dnCIIgbbtw4QLGjx+PL774Ahs2bEBUVBS+/PJLNG/eHKtWrcLhw4eRmZmJRo0aYfLkyWjSpInRtS9fvoy1a9fi7t27aNCgAWbPno169eoBAPbv348VK1Zg7ty50jG7d+/Gxo0bkZGRgSVLlgAATp06hU2bNuH27duQyWRo3rw5pkyZAj8/PwBAfHw8Bg0ahIULF2L37t24du0a/P39MWPGDDRv3lxqy/79+xEWFoaUlBSEhISgRYsWZu1XSymPhXuKO64kITw5WcTfp/N+7twRcHdnUCcishacjQRAu3btAAAnT54ssO/EiRMAgPbt21dom8i2rV27FuPGjcP333+P+vXrY/Xq1Th27BjmzJmDzZs3w8/PD5MnT0ZqaqrReatWrcLEiROxZ88euLu7Y+rUqdBqtdL+7OxsbN26FbNnz8aOHTsKfRYhKysLr732GjZt2oTVq1dDEATMmDEDer3e6Lj169cjNDQUW7duRUBAAObMmSPd6+rVq1iwYAEGDx6MrVu3Ijg4GN9++235d1QlVlGzpNy7p0fo63osWKTHwsUiRr4p4v59zppCRGQtGLYBDBo0CPb29li3bp1ROUlERAT279+PevXqoU2bNhZsIdmat99+Gx06dICfnx8cHBzw448/YsKECejUqRPq1KmD2bNnw9HRET///LPReaNHj0aHDh3QsGFDzJ07F0lJSTh27Ji0X6vVYvr06WjRogVq164NhUJR4N7du3dHt27d4O/vj6CgIHz00UeIiorCnTt3jI4LDQ1F586dERAQgDFjxuDBgwe4d+8eAGDXrl0ICQnBiBEjEBAQgFdffRUdOnQo/46yQk+GcFPnDDeE8K826pCYeBtRkc/j1s0euHv3CL75lmGbiMhaVNoykrKIiopCWFgYgLyRPgC4ffs2Zs6cKR2zaNEi6ec6depgwoQJWLFiBV566SX06tULmZmZUu3tJ598wtUjqVw1atRI+vnevXvQarVGZRj29vZo0qQJoqOjjc7LX8bh5uaG2rVrGx0jl8tRv379Yu8dGxuLsLAwXLt2DSkpKVJZw8OHD6WSFABG1zGUwSQnJyMwMBDR0dHo2rVrgbadPn36Ke+8ajOlJCXxEaDOuAidLgkAcD/uUxw5fBETJ4zlsyRERFbAJsP2o0ePsHfv3mK35Q/bADB27Fj4+vpi8+bN+O677yCXy9G2bVtMmjQJTZs2rZB2U9WR/yHJ8uTo6PjUEdNp06ahRo0amDVrFjw9PSGKIoYNGwaNRmN0XP6HNg3XfLLUhMpHcSE8uDUQfvEZpCTXRm5uDAANMtL/woQJ1zBu3Dh+o0BEVMnZZNju0KEDbt68WerzBgwYgAEDBpihRURF8/Pzg1wux+XLl1GzZk0AeeUg169fx9ChQ42OvXr1KmrUqAEASEtLQ2xsbKlm4UlNTUVMTAxmzZqFVq1aAQD++eefUrc5MDAQ165dK9A2Kl+CIOCNkTLE3/fGdzt6Iif7JuztwuHjk/ctw2effYYePXpgzJgxUCqVlm4uEREVwibDNpE1cXJywqBBg7B69WpUq1YNNWrUwNatW5GTk4MXX3zR6NhvvvkGbm5uCAwMxJIlS+Du7l6gnKM4rq6ucHNzw759++Dh4YGHDx+atNjNkCFD8Pbbb2P79u145plncObMGZaQmIlcLuD/PrJDowa1EBurQU5ODWRmZkofdo4cOYJLly5h0qRJaNmypYVbS0RET2IhMlElMG7cODz33HOYN28eXn/9ddy7dw8rVqyQVovMf9zy5csxaNAgPH78GEuXLoVcLi/xfWQyGT755BPcuHEDoaGhWLFiBSZMmFDq9jZr1gyzZs3Czp07MWLECJw5cwZvvPFGqa9DJRcQUAv29gKcnZ0xYsQIjB8/XnoA9tGjR5gzZw42bNiAnJwcC7eUiIjyE0RT1ysmI1ypyTRc5co07DfTWWvfxcTE4McffwQAtGzZEt27d8eDBw+wYsUKXL9+XTquZs2amDx5Mho3blyu97fWfqsM2HemYb+Zjn1nGnOtIMmRbSIiK2Co1QeA+/fvS9sWLlyI0aNHS99w3L9/HzNnzsSmTZsKPPRKREQVj2GbiMgKODo6SlMwJiYmSkFaEAS89NJLWLFiBYKCggDkzWKyd+9eTJkyBVFRURZrMxERMWwTEVkNw2w1oiji4cOHRvv8/f2xePFijBgxAnZ2dgDy5lT/4IMP8N133xmtNEpERBWHYZuIyEr4+vpKP8fFxRXYb2dnh1deeQXLli2TpoTU6/X47rvvMH36dMTGxlZUUyXz58/H9OnTpddjx47F8uXLzXrPirgHEVFJceo/IiIrYRjZBv5Xt12YunXr4osvvsCOHTvwww8/QBRF3Lp1C5MnT8bw4cMxcODAclkVNyQkpNj9o0ePxvvvv4+Kfg5/0aJFRosyERFZEv80IiKyEiqVCgqFAtnZ2cWGbSBvBdCRI0eiffv2WLFiBeLj46HVavHtt9/i9OnTmDJlilF4N8Uvv/wi/Xz48GF89dVX2LVrl7TNycnJIovtuLm5Vfg9iYiKwjISIiIrYgjI2dnZSEpKeurxjRo1wooVK/Diiy9Ky8HfuHED7733Hn755ZcyjTp7eHhI/zg7O0MQBKNtSqWyQBnJk06ePIkePXrg999/BwDcunUL48ePR9euXdGrVy8sXLgQarVaOt5wvY0bN6JPnz7o3r07Fi9ebDTzypNlJL/99hveeOMNdO/eHX379sXcuXNL1HdEROWBYZuIyIrUqlVL+vlpo9sGCoUCY8aMwWeffQYfHx8AQG5uLlatWo/eL3yEeZ/EIzm54pdcOHDgAObMmYN58+ahT58+yMrKwuTJk+Hq6opvvvkGCxYswLlz5/D5558bnXf+/HlER0dj7dq1+OSTT3Ds2DFs3LixyPtotVq8/fbb2Lp1K5YsWYL79+/jk08+MffbIyICwLBNRGRV8oft+Pj4Up3brFkzfPnll+jVqxcAIPLfXFw4/wNWr+qLyR/8W67tfJo9e/Zg6dKl+Pzzz9GlSxcAeeE7NzcX//d//4d69eqhbdu2mDp1Kn7//Xc8fvxYOtfe3h4fffQR6tati86dO2PMmDHYvXs39Hp9ofd68cUX0alTJ/j6+qJZs2Z4//33cerUKaMRcyIic2HNNhGRFfHx8YEgCBBFsdRhGwCUSiUmTJiADh06YODLMwFRD71OjRs3TiMpyRPu7u7l8vBkcY4ePYrk5GR89dVXaNKkibQ9Ojoa9evXh5OTk7StRYsW0Ov1iI2NleYZb9CggbRUPQA0b94carUaDx8+LLQO/caNGwgLC8OtW7eQnp4uhfKHDx+iTp065nqbREQAOLJNRGRV5HI5vLy8AABJSUnIzs426Trt2rVDp07PwcExEA6Kugh9rT2ysrKQkJCAnJyc8mxyAUFBQVCpVPj555/NPlNJVlYWJk2aBGdnZ8ybNw/ffPMNFi9eDABcYZOIKgTDNhGRlclfSvLgwQOTrpGWloZaNR+hf7/GePONZ/HK4LwZPHQ6HR49eoTk5GSzBWE/Pz+sWbMGf/31F5YtWyZtDwwMxK1bt5CVlSVtu3z5MmQyGQICAqRt//77r9GHjKtXr0KpVEr16PnFxMQgNTUV48ePR6tWrRAYGMiHI4moQjFsExFZmZLOt12cmzdvAgCUSqBTxxbw9vaGo6OjtF+tViMxMRG5ublla2wRAgICsGbNGvzxxx/SzCF9+vSBg4MD5s+fj6ioKFy4cAHLli1Dnz59pBISIO+BxwULFuDOnTv4+++/ERYWhsGDBxda/uLj4wO5XI5du3YhLi4Ox48fx6ZNm8zynoiICsOwTURkZcrykKSBIWwDedMD2tnZwdMzr2bbMEWgRqNBYmIi0tLSytbgItSuXRurV6/GwYMH8eWXX0KhUGDFihVIS0vDqFGjMGvWLOkhyfzatm0Lf39/vPvuu/joo4/wzDPP4K233ir0HiqVCnPmzMHRo0fx2muvYevWrXjvvffM8n6IiAojiBW9tJeNSk5OtnQTrJJKpWLfmYD9Zjpb6buvvvoKmZmZkMvlGD9+vBSQS0IURcyZMwfp6elwdHTEggULjFZc1Gg0SElJMRrV9vb2hiAIFl+Zcf78+cjIyMCSJUss2o7SsJXfuYrGfjMd+840KpXKLNflyDYRkRUylJJoNBo8evSoVOfGx8cjPT0dAFC/fv0CAdrwEKarq6u0LTc3FwkJCdJ5RERUMgzbRERWyJTFbQxu3Lgh/dyoUaMij6tWrRq8vLykMC6KItLS0vDo0SPodLpStpiIqGriPNtERFboyYckW7RoUeJz89drN2zYsNhjHRwcpMCdkpICAMjJyUFCQgLc3NygVCpL1/Aymjt3boXej4iorDiyTURkhXx8fGBnZwegdCPbGo0GUVFRAPLqE729vZ96jkwmg5ubGzw9PaV76vV6JCcnIykpqciVG4mIiGGbiMgq2dnZSfNKJycnl3jp8Vu3bkGr1QLIG9UuzYOVjo6O8Pb2Nlrh0bAQTv65sYmI6H8YtomIrJQp821HRkZKPxdXr10UmUyG6tWrQ6VSSfNa63Q6JCUlmXUhHCIia8WwTURkpUwJ24aHIwVBQIMGDUy+t1KphLe3NxQKhbRNrVZXyHLvRETWhGGbiMhK5Q/bJVncJi0tTTrO398fLi4uZbq/nZ0dPDw8jBbC0Wq1ePToEdLS0jjKTUQEhm0iIqvl4uKCatWqAQAePHjw1AcVSzrlX2k5OzsXWO49PT0djx49Mtty70RE1oJhm4jIihnm29bpdEhISCj22NJM+Vda9vb28PT0LLAQTmJiItLT0znKTURVFsM2EZEVK2ndtiiKUth2dHREYGCgWdpjWAjHwcFB2paWlobHjx9Ls6AQEVUlDNtERFaspGE7Li5OWmq9QYMGBZZoL08ODg7w9PQ0qgnPyclBYmIiMjMzOcpNRFUKwzYRkRXLv5x6cQ9JmrOEpDCCIEgL4Rjap9frkZKSgqSkJC73TkRVBsM2EZEVk8lkqFGjBoC8hxINo9dPMtfDkU/j6OgILy8vKJVKacaS7OxsJCYmIisri6PcRGTzGLaJiKyc4SFJoPBSktzcXNy+fRtA3hLtXl5eFdY2IO8DgUqlQvXq1aXl3g0L4aSkpHC5dyKyaQzbRERW7ml121FRUdLDiY0aNSrVEu3lSaFQwMvLCwqFQmqDYSGc7OxsjnITkU1i2CYisnJPW9wmfwlJRdRrF8ewEI6bm5vRcu+PHz9GamoqR7mJyOYwbBMRWTknJyeoVCoAQEJCQoEp9gwPRwqCgKCgoApvX2HyL4RjGOXOzMxEYmIicnNzOcpNRDaDYZuIyAYY6rb1ej0ePnwobU9LS5NKSwICAuDs7GyR9hXGzs4Onp6eqFatmjTKrdVqkZiYiIyMDAZuIrIJDNtERDagqFKSylRCUhQXFxdpIRzDKHdaWhoePXoEjUbD0E1EVo1hm4jIBhQ1I4mlpvwrLXt7e3h5ecHZ2VkK3Ibl3rkQDhFZM4ZtIiIbUL16dWmJdEPYrqgl2suTm5sbPDw8IJfLIQgCRFFEamqqtBAOQzcRWRuGbSIiGyAIglRKolarkZqairi4OGRkZADIW6LdMMd1ZVfUQjgJCQlcCIeIrA7DNhGRjchfShIfH281JSSFEQQB7u7u0kI4giBAr9cjOTkZycnJ0Ov1DN1EZBUYtomIbMSTD0kaSkgA6wvbBgqFAt7e3kYL4WRlZSEhIQE5OTkM3ERU6TFsExE9IT4+HiEhIYiMjCzxOWPHjsXy5ctNvueFCxcQEhKC9PR0k69Ro0YN6ee7d+9KS7RXr14dnp6eJl/X0mQyGapXrw53d3fIZDIIglBgIRyGbiKqrBi2icgmzJ8/HyEhIVi8eHGBfUuXLkVISAjmz59vgZZVHEdHR3h4eADIW8gmJycHQN6Uf5Zaor08KZVKLoRDRFaHYZuIbIaPjw8OHTqE7OxsaVtOTg4OHjxoNOprywx124mJicjKygJgvSUkhTEs925YCEcQBGi1Wjx69AhpaWkQRZGhm4gqFYZtIrIZDRs2hI+PD44dOyZtO3bsGHx8fIyWKT916hTefvtt9OzZE7169cIHH3yAe/fuFXvtqKgoTJ48Gd26dcMLL7yAjz/+GCkpKUUef/LkSfTo0QO///57oWUp6enpCAkJwYULFwo9PzU1FXPmzMGLL76Irl27IjQ0FAcPHnxqH+QP22q1GoIgoEGDBk89z9oYFsIxTBEIABkZGUhMTIRWq2XgJqJKg2GbiGxK//79sX//fun1zz//jP79+xsdk5WVhddeew2bNm3C6tWrIQgCZsyYAb1eX+g109PTMWHCBDRs2BCbNm3CihUrkJSUhA8//LDQ4w8cOIA5c+Zg3rx56NOnj0nvIycnB40aNcKyZcuwY8cOvPTSS5g3bx6uXbtW7Hk1a9ZEdnY20tPToVarK90S7eXJsBCOq6srBEGAIAjQaDRGC+EwdBORpTFsE5FN6dOnDy5fvoz79+/j/v37uHLlSoHA2717d3Tr1g3+/v4ICgrCRx99hKioKNy5c6fQa+7evRtBQUEYO3YsAgMD0bBhQ3z00Ue4cOECYmNjjY7ds2cPli5dis8//xxdunQx+X14e3sjNDQUQUFB8PX1xZAhQxASEoIjR44Ue55KpcL5Cym4HqHFP5fS4OlZGzk5OTY92uvq6govLy/Y29sbLYTz+PFjLoRDRBZnb+kGEBGVJ5VKhU6dOuGXX36BKIro1KkT3N3djY6JjY1FWFgYrl27hpSUFCmMPXz4EPXq1StwzVu3buHChQvo1q1bgX337t1DQEAAAODo0aNITk7GV199hSZNmpTpfeh0OmzevBlHjhxBYmIiNBoNcnNzoVAonnpuxA0RgIicHC3uP/RGWloagLy5q2UyGezt7SGTyWBnZwd7e3vY2dlBJrPusRe5XA4vLy+kpqZCrVYDyPt2ICEhAW5ublAqlQBgEw+KEpF1YdgmIpvz4osv4vPPPwcATJs2rcD+adOmoUaNGpg1axY8PT0hiiKGDRsGjUZT6PXUajW6dOmC8ePHF9iXf0q9oKAgREZG4ueff0bjxo2lYGcIsvlHWLVabbHvYfv27di5cycmT56M+vXrQ6FQYMWKFUW2Mb+uzw7Af3+6CoVjbXR77n+16qIoQqfTQafTFQidgiAYhfD8QdxaGBbCcXJyQkpKijSqnZKSguzsbKOpA4mIKgrDNhHZnJCQECnMdujQwWhfcnIyYmJiMGvWLLRq1QoA8M8//xR7vYYNG+LYsWOoWbMm7O2L/mPTz88PkyZNwrhx42BnZ4epU6cCgDSy/vjxY+nYp83hfenSJTz77LN44YUXAAB6vR6xsbGoU6dOsecBwOpVnfHOO7/Ay1MHT08dtFotdDod9Hq9VE6SP/gbSi+KCvKG8J2ZmWkUwitraHV0dIS3tzdSUlKkGVmys7ORmJgINzc36duBytp+IrItDNtEZHPs7Ozw/fffSz/n5+bmBjc3N+zbtw8eHh54+PAh1q5dW+z1Bg8ejJ9++glz587F8OHDUa1aNdy7dw+HDh3C7Nmzje4REBCANWvWSIF7ypQpUCgUaNasGbZs2YKaNWsiOTkZGzZsKPae/v7++OOPP3D58mW4urriu+++Q1JSUonCtp2dgFYtgbw/4u3h6OgI4H8j63q9Xhrh1mq1Rq8LC6A6nQ45OTlScDXIPwqefzS8MpSkCIIAlUoFhUIhLXyj0+mQlJQEpVIJNzc36TgiInOy/J+IRERm4OzsXOgsHDKZDJ988glu3LiB0NBQrFixAhMmTCj2Wl5eXtiwYQN0Oh0mTZqE0NBQLF++HK6uroUGy9q1a2P16tU4ePAgvvzySwDAhx9+CJ1OhzfeeAMrVqzAO++8U+w933zzTTRs2BCTJ0/GuHHj4OHhga5du5aiBwoyzNhhZ2cHuVwOhUIBFxcXVKtWDSqVCh4eHnBzc4OLiwsUCgUcHBykhw4Lo9frodFokJ2djczMTKSlpSEpKQmPHz9GSkqKNCOK4QFNS3BycoKXl5e03LsgCFCr1UYL4fABSiIyJ0HknzLlIjk52dJNsEoqlYp9ZwL2m+nYdwWV5K8BNzc3PHr0qMBoeFHTJRblyZFww2h4RYwwGz4Q5A/Yhg8bgPlGufk7Zxr2m+nYd6ZRqVRmuS7LSIiIqrj8IbOo4C2TySCXy40WkQGKL0kpTFH7DCUphtlS8ofx8uLs7AxHR0ekpKQgNzcXQN5CODk5OXB3d4dcLgfA0hIiKl8sIyEiIomh1KK4wGkYGRZFUQrhhZWkuLu7w9XVFUqlssQlKTk5OdIIdHJyslSSkpaWZlSSYuqXsvb29vD09ISrq6v0fg0L4aSnp0vvz9ZduHABISEh0nt+8vX+/fvRs2dPSzaRyGawjKSc8Osa0/CrLtOw30zHvjONu7t7sf1WmtFgw6wohlFuwz+mlqQ8ORpe0gc0NRoNUlJSpFlYRFGEo6Mj3NzcpFlnymOUW6VSYcqUKcjIyMCSJUvKfL2Sio+Px6BBgwps7927Nz766COkpaWhevXq0geO/K+zs7OhVqtRvXr1Cmvvk/j/qunYd6ZhGQkREVlM/tHuwsZonpxKsDgymQwODg6FXqOwEF6WkpT8UxU+WZIil8vh6emJ9PR0ZGRkQBAE5OTkSFMEKpVKiKJo9WUlq1atQt26daXXjo6OkMvl8PDwkLY9+VqhUJRoASUiejqWkRARUak8rdQkf5lJaa9rKElxdnaWSlI8PT2hUqmkkhRHR8cSl6So1WqpJOXRo0dSSUpmZiZycnKg0+ng6uoKDw8Po2umpKTgwYPH2LZDhzHv6vDOOB1++FGEVmueL4N37NiB0NBQPPfccxgwYACWLFkirYQJAGFhYRgxYoTROd9//z0GDhz41Gu7ubnBw8ND+sfFxYVlJEQViCPbRERksqc9XFmaEe/iFPWw5JMlKYbXRZWkFDUFoUwmg6OjI3Jzc6HRaCAIMnz8iRYRN3IhCNVgZ+eEq9f0uHBRwGfzy/8hSplMhvfffx81a9ZEfHw8li5ditWrV2P69Onleh8iqngM20REVC4qKnjnV1xJimGGlJKUpOj1euj1eql04tjxVFy5qoco6qHJvQBB5gwX547487gDrlwFWjQv37A9dOhQ6edatWrhnXfeweLFi8slbI8ZM8aojn39+vVlviYRlRzDNhERlTtLBO8n729vby896Jhf/qkKn1zGHsirV46Ps4O9XTqys+8iNycSIkTotAlwcWmPK1cD0bxZ+dZynz17Flu2bEFMTAwyMzOlVTuzs7PLXDv96aefIjAwUHrt4+ODK1eulLHFRFRSDNtERGRWlg7eTzKUpDw5Im6YI1yr1aJGDS3s7J0glwvIyb4OAXmj3JkZZxEfF4O0tOByWwwnPj4eU6dOxaBBg/Duu++iWrVquHTpEj777DNoNBooFArIZLICfVfSVTl9fHzg7+9fpjYSken4gCQREVUYcz1cWR4Mc4Y7OTnhxRddoFRWg1JZDyqPN+CkbAN7OxmUzkANn4c4dOgQrl+/Dp1OV+a23rhxA3q9HhMnTkSzZs0QEBCAxMREo2Pc3d3x+PFjo3tFRkaW6b5EVDE4sk1ERBZR2Ua881O5C/hiKfDJAhH37zvD2aUTfLzvo8/z4XB0zIJer8fVq1cRExODNm3awNvb+6ntzMjIKBCQ3dzc4O/vD61Wi927d6NLly64fPky9u7da3RccHAwUlJSsHXrVnTv3h2nT5/G6dOnoVQqy//NE1G5YtgmIiKLK24O7ye3V1TwbtFcwM7tQHQ0ILMDagfUgk7ng+vXr+PmzZsAgPT0dBw7dgyBgYFo0aIFFApFke0LDw/HyJEjjba9+OKL+PDDDzFp0iRs3boVa9euRevWrTFu3DjMmzdPOq5OnTqYNm0aNm/ejE2bNqFbt24YNmwY9u3bZ663T0TlhCtIlhOu1GQarnJlGvab6dh3prFEv5XkrydLLTiTmpqK8+fP4/HjxwDy2urg4IAWLVqgTp06RqUy1vA7d/r0aUyZMgXHjx+HXC63dHMAWEe/VVbsO9OYawVJ1mwTEVGl9LT6bsByNd5ubm7o3r072rRpA7lcDkEQkJubi/Pnz+PYsWNIS0uzSN25KR4/fozjx4/D39+/0gRtIlvCMhIiIqr0nlbf/eT2ihjxFgQB9erVg6+vL/755x/ExsYCABITE3Hw4EE0bNgQTZo0qfSh+/3334darca0adMs3RQim8SwTUREVqWyBW+FQoGQkBAEBgYiPDwcGRkZ0Ov1iIiIQGxsLLp37w4nJyeLlbw8zebNmy3dBCKbxjISIiKyWpWp1KRGjRro3bs3mjRpAjs7OwiCgMzMTBw9ehSnTp2CWq2u9KPcRFT+GLaJiMgmVIbgbWdnh2bNmqFXr17w8vKS2nL37l38/vvvuHXrFvR6vVnuTUSVE8M2ERHZHEsH72rVqqFbt25o3769NB2gRqNBeHg4jh49iuTkZI5yE1URDNtERGTTLBm8AwMDMWDAAAQGBkr3f/z4MQ4dOoR//vkHGo2GoZvIxjFsExFRlWGJ4O3o6Ij27dujW7ducHNzgyAIEEURkZGR+O233xAXF8fATWTDGLaJiKhKqujg7eXlhV69eqFZs2awt8+bDCwrKwsnT57EyZMnkZmZydBNZIM49R8REVV5FTWdoEwmQ5MmTeDv74/w8HA8fPgQoigiLi4ODx8+RNOmTREUFASZjGNhRLbC5sK2RqPB0aNHcfToUVy+fBkPHjwAANSvXx8vv/wyXn31VdjZ2RV67k8//YQtW7bg1q1bkMvlCA4OxsSJE9G0adOKfAtERGRBFRG8XV1d0bVrV8TGxuLixYvIycmBVqvFpUuXEBsbizZt2qB69eqVdm5uIio5QbSx76yioqLQt29fKJVKdOzYEXXq1EF6ejr++OMPJCQkoFu3bli3bl2BP8DWrVuHFStWwNfXF7169UJmZiZ++eUXaDQafPvtt2jTpk2x901OTjbn27JZKpWKfWcC9pvp2HemYb8VHbzzKywcP63vcnNzceXKFURFRRndo379+mjevDkcHBxMa7CV4++c6dh3plGpVGa5rs2F7YcPH+Lw4cN4+eWXoVQqpe1qtRojRozA1atXsWLFCrzwwgvSvujoaPTr1w9+fn7Ys2cPXF1dAQAREREYMmQI/P39sX///mK/1uMvtWn4B4Jp2G+mY9+Zhv1mrDTBu6R99/jxY1y4cAEpKSnS9RUKBVq3bg1/f/8qN8rN3znTse9MY66wbXNFYT4+PggNDTUK2gCgVCrx5ptvAgDOnTtntO/HH3+EVqvF2LFjpaANAI0bN0b//v0RFRWFCxcumL/xRERkFczxcKWHhwd69uyJFi1aSA9QZmdn49SpUzh+/DjS09PLpe1EVLFsLmwXx/CH15M122fPngUAdO7cucA5Xbp0MTqGiIgov/IM3jKZDI0aNUKfPn3g6+srXfPBgwc4cOAAIiIioNPpyrX9RGReVSps//DDDwD+F6ANoqOjoVQq4eXlVeCc2rVrAwBiYmLM30AiIrJq5RW8nZ2d0aVLF3Tq1En6plan0+Hy5cs4dOgQEhMTy73tRGQeNjcbSVF27tyJ48ePIyQkBF27djXal5GRgerVqxd6nouLCwA89es7c9X5VAXsO9Ow30zHvjMN+810Jem7oh6ubNSoES5duoSbN29Cr9dDq9XizJkzqF+/PoKDg+Ho6GiOJlcK/J0zHfuu8qi0YXvRokXIzc0t8fEjR45EYGBgofv++OMPfPLJJ/D19cXSpUvLqYXG+CCCafgQh2nYb6Zj35mG/WY6lUqFlJQU6bUps5rUq1cP1atXx/nz55GUlAQAUgBv2bJlkX//WTP+zpmOfWcac31AqbRhe+fOnVCr1SU+vnfv3oX+YfPnn39i4sSJ8PDwwObNm+Ht7V3gGBcXlyJHrjMyMgDA6MFJIiIiU5k6j7dKpULPnj1x69YtXLlyBRqNBtnZ2Thz5gzu3LmD4OBguLm5mbfxRFRqlTZsX7x4sczXOHbsGN577z2oVCps2bIF/v7+hR4XGBiIixcvIjExsUDdtqFW21C7TUREVF5MCd4NGjSAr68v/vnnH9y9excAkJCQgIMHD6Jx48Zo3LhxkYu3EVHFs9kHJA1B283NDVu2bCk2LLdr1w4AcPLkyQL7Tpw4AQBo3769eRpKRESE0j1cqVQq0alTJzzzzDNwdnYGAOj1ely7dg0HDhzAw4cPK6rZRPQUNhm2//zzT6Og/bRatkGDBsHe3h7r1q0zKieJiIjA/v37Ua9evaeuIElERFRenha8DaG7Zs2a6NOnDxo3biwdm56ejmPHjuHMmTPIzs6uyGYTUSEqbRmJqaKiojBhwgTk5uaiffv2+OWXXwoc4+vri0GDBkmv69SpgwkTJmDFihV46aWXjJZrB4BPPvmk2NUjiYiIzOVppSZ2dnZo3rw5AgICcOHCBTx69AhA3rS28fHxaNGiBerWrStdR6sVkZ4OODsDDg5lX5UyJCSk2P2jR4/GmDFjynwfImtlc2H70aNH0iwmhQVtIK8kJH/YBoCxY8fC19cXmzdvxnfffQe5XI62bdti0qRJaNq0qdnbTURE9DTFBW83Nzd069YNt2/fxuXLl6HRaJCbm4vz588jJiYGDYKC8cPeatj/C5CdDcjlQK+eIsaMFuDpaXrozv937eHDh/HVV19h165d0jYnJyeTr01kC2wubHfo0AE3b9406dwBAwZgwIAB5dwiIiKi8ldY8BYEAfXq1ZMeoDQ85H/vXgLmf3YAGZkN4ejYBIJgD40G+P0AcPaciLANgKeHaYHbw8ND+tnZ2RmCIEjb9Ho9Nm3ahH379iElJQWBgYEYN24cOnbsCACIj4/HoEGDsHDhQuzevRvXrl2Dv78/ZsyYgWeffVa67r59+/DNN98gNTUVISEhaNmyJb755hscPnz4/7+/e/jyyy9x9epVZGdnIzAwEGPHjuXzVlQpsDaCiIjIyj1Z461QKKRF3FxcXHD2PPAoUY8sdQTSUw9Ao7kPANDpgaQkYPPWp8/9bYqdO3dix44dmDhxIrZt24YOHTpg2rRpiI2NNTpu/fr1CA0NxdatWxEQEIA5c+ZAq9UCyJtPfMmSJXj11VexdetWtGvXDt9++63R+VlZWejUqRNWr16NzZs3IyQkBNOmTcODBw/M8r6ISoNhm4iIyIbkD941atRAnz59cCuqMcT//1e+Tp+BjPTjyM6O+P+vgd9+L9liO6W1Y8cOjBgxAs8//zxq166NCRMmICgoCDt37jQ6LjQ0FJ07d0ZAQADGjBmDBw8eSKPyu3fvRseOHREaGoqAgAAMHjxYGhk3aNCgAV5++WXUq1cPAQEBeOedd+Dr64u//vqr3N8TUWnZXBkJERER5REEAfb29hDRHK7VaiNLfR5abSIAICc7GgpFYwB5Ndy5uUB5rvyemZmJxMREtGjRwmh7ixYt8O+//xptq1+/vvSzoQQlKSkJ1atXR2xsLLp27Wp0fJMmTYym61Wr1di4cSNOnjyJx48fQ6fTIScnhyPbVCkwbBMREdk4P19Ara4G+2rdkZNzB5rceDgq6kr7q1cHHBws1z57+//FEUMpjF6vL/H5q1atwtmzZ/Hee+/Bz88Pjo6OmD17tlSKQmRJLCMhIiKycYNeFmCoEnF0rAMX186Qy2sCAAQBGDSw+MV0TOHs7AwvLy9cvnzZaPvly5dRp06dEl8nICAA169fN9oWERFR4Jr9+vXDc889h/r168PDwwP37983vfFE5Yhhm4iIyMb16QV075b3s2HZCEO2btUSeO1V89zX8NDjoUOHEBMTgzVr1iAyMhJDhgwp8TVeeeUVnDp1Cjt27EBsbCz27t2LU6dOGX048PPzw7FjxxAZGYl///0Xc+fOLdXIOJE5sYyEiIjIxtnZCfh4DvBsF2DfTyLi4gFPT+DFfgJe6A3I5eU7qm0wZMgQZGRkYOXKlUhOTkadOnWwdOlSBAQElPgaLVu2xPTp0/H1119jw4YNCAkJwdChQ7Fnzx7pmEmTJuGzzz7DmDFj4O7ujhEjRiAzM9Mcb4mo1ATRHI8fV0HJycmWboJVUqlU7DsTsN9Mx74zDfvNdOw70xTXbwsWLEBMTAw2bNhQwa2yDvydM41KpTLLdVlGQkRERJXa9u3b8e+//+Lu3bvYtWsXfv31V/Tt29fSzSIqEZaREBERUaV2/fp1bNu2DWq1GrVq1cL777+Pl156ydLNIioRhm0iIiKq1D777DNLN4HIZCwjISIiIiIyE4ZtIiIiIiIzYdgmIiIiIjIThm0iIiIiIjNh2CYiIiIiMhOGbSIiIiIiM2HYJiIiIiIyE4ZtIiIiIiIzYdgmIiIiIjIThm0iIiIiIjNh2CYiIiIiMhNBFEXR0o0gIiIiIrJFHNkmIiIiIjIThm0iIiIiIjNh2CYiIiIiMhOGbSIiIiIiM2HYJiIiIiIyE3tLN8BarVq1CqtXry5y/5EjR+Dn51dg+19//YUNGzbg2rVrEAQBTZs2xbhx49CxY0dzNrfSunv3LgYMGAC1Wo1XX30V8+fPL/S4n376CVu2bMGtW7cgl8sRHByMiRMnomnTphXcYsv56aefcODAAdy8eROPHz8GANSqVQudO3fG6NGj4ePjU+R5VbXvNBoNjh49iqNHj+Ly5ct48OABAKB+/fp4+eWX8eqrr8LOzq7Qc6tyvxlERETgt99+w7Vr13Dt2jUkJyejffv22Lp1a7Hnse+Ay5cvY9WqVbh48SK0Wi2CgoLwxhtvoG/fvpZumsX997//xYULF3D16lVERkZCo9Fg4cKFGDRoUKHHZ2RkYNWqVTh48CASExPh7e2N3r17Y8KECXB2dq7g1lvOw4cP8dtvv+H48eO4ffs2Hj16BDc3NwQHB+Ott95Cy5YtC5zDvsuTk5ODL774AlevXkVMTAxSU1NRrVo1+Pv745VXXsGAAQMgl8uNzinPvuPUfyYyhO2XX34Zvr6+Bfa//vrrqFatmtG2//73v5g+fTqqV68u/YH766+/Ijk5GStWrECfPn0qpO2VhV6vx4gRI3D9+vViw/a6deuwYsUK+Pr6olevXsjMzMQvv/wCjUaDb7/9Fm3atLFA6yveu+++i+joaDRt2hTe3t4QRRERERE4c+YMXF1dsWPHDjRo0MDonKred1FRUejbty+USiU6duyIOnXqID09HX/88QcSEhLQrVs3rFu3DoIgGJ1X1fvNwPDnnFwuR506dRAZGfnUsM2+A06fPo233noLDg4O6NevH5ydnXHw4EHExcVhxowZGDVqlKWbaFHdu3dHXFwcVCoVlEol4uLiigzbarUaw4YNQ0REBLp06YLGjRsjIiICJ06cQPPmzbF9+3Y4Ojpa4F1UvM8//xxhYWEICAhA+/btUb16dcTExODw4cMQRRHLli0z+jDHvvufpKQkPPfcc2jRogUCAwNRvXp1pKam4q+//kJcXBy6dOmCsLAwyGR5BR/l3ncimWTlypViUFCQePr06RIdn5KSIrZt21bs0KGDeP/+fWn7/fv3xQ4dOogdOnQQ09PTzdXcSunrr78WmzRpIm7atEkMCgoS58yZU+CYO3fuiE2aNBF79eolpqWlSduvX78uNmvWTHzhhRdEnU5Xkc22mOzs7EK379q1SwwKChLfe+89o+3sO1F88OCBuG3bNjEzM9Noe2Zmpjho0CAxKChI/PXXX432sd/+JzIyUrx69aqYm5srJiQkiEFBQeLw4cOLPJ59J4oajUbs2bOn2KxZM/H69evS9rS0NLFXr15i06ZNxXv37lmwhZZ38uRJqQ82bNggBgUFiT/88EOhx3755ZdiUFCQuHTpUqPtS5cuFYOCgsT169ebvb2VxYEDB8QzZ84U2H7u3DmxadOmYrt27cScnBxpO/vuf3Q6nVHfGGg0GnH48OFiUFCQ+Mcff0jby7vvWLNdQX7//XekpaVh+PDhqFGjhrS9Ro0aGD58OJKTk3H48GELtrBiRUVFYcWKFXj77bfRuHHjIo/78ccfodVqMXbsWLi6ukrbGzdujP79+yMqKgoXLlyoiCZbXFGfol944QUAQGxsrNF29h3g4+OD0NBQKJVKo+1KpRJvvvkmAODcuXNG+9hv/9OgQQM0bdq0wNerRWHf5Y1qx8bGon///kZ/trm6uuLdd9+FRqPB3r17LdhCy+vUqVOh3wg/SRRF7N69G0qlEuPGjTPaN27cOCiVSuzevdtczax0evXqhfbt2xfY3rZtW3To0AGpqam4efMmAPbdk2QyGRwcHApst7e3x/PPPw8AiImJAWCevmPYLqNz587hq6++wsaNG3H48GFkZmYWetzZs2cBAF26dCmwz7DNcIyt0+l0mDlzJmrXro2xY8cWe6yhTzp37lxgX1Xrt6IcO3YMAAqUkLDvimdvn/fIypM12+w307HvSvZn/ZMf8Khw0dHRSEhIQHBwcKEfmIODg3H37l3cv3/fQi2sPAx/nhn+zb4rGb1ej7/++gsAEBQUBMA8fccHJMto1apVRq+rVauGDz/8EAMHDjTaHh0dDQCoXbt2gWsYthk+Vdm6DRs24Pr169i5c2ehnzTzi46OhlKphJeXV4F9Va3fDH799VdERUUhKysLt27dwokTJ+Dn54eJEycaHce+K94PP/wAoGAoYr+Zjn1X/J/1Xl5eUCqVNt8H5cXQT4GBgYXuDwwMxIkTJxAdHY2aNWtWYMsql/j4ePz999/w8vKSAiP7rnC5ubnYsGEDRFFESkoKTp06hdu3b2PQoEHSRBXm6DuGbRM1atQICxYsQPv27eHt7Y3ExEQcO3YMK1euxMyZM+Hq6ooePXpIx2dkZACA0VerBi4uLgCA9PT0imm8Bd24cQNr167F6NGj0axZs6cen5GRgerVqxe6ryr1W36///47Dhw4IL1u1qwZli9fDn9/f6Pj2HdF27lzJ44fP46QkBB07drVaB/7zXTsu+L/rAfy+sHW+6C8GPrJ8LvzJMN2Q59XRRqNBtOnT0dubi6mTp0qfVPHviucRqMxmklOEASMGjUKH3zwgbTNHH1XpcP2okWLkJubW+LjR44cKX3SMdT4GPj5+WH48OGoV68e3nzzTaxYscIobNsSU/stNzcXM2bMQEBAACZMmGDGFlZeZfmdM1i5ciUAIC0tDdevX8eKFSswaNAgrFq1ymankCyPfjP4448/8Mknn8DX1xdLly4tpxZWXuXZd0RUeej1esycORPnzp3DkCFDCnyjTgU5Ozvj5s2b0Ov1SEhIwNGjR7F8+XL8888/CAsLKzJgl1WVDts7d+6EWq0u8fG9e/d+6l9CHTt2REBAACIjI5GRkSH9h8s/qqNSqYzOedpISGVjar999dVXiIyMxPfff//U8hGD4kaBrK3fgPL9natWrRpCQkKwceNG9OnTBzNmzMCRI0ekh9lsqe/Kq9/+/PNPTJw4ER4eHti8eTO8vb0LHGNL/QaY58+5otha35niaSP4GRkZcHNzq8gmWS3D70pRI4iG7eYKSJWZXq/H7NmzsX//fgwYMADz5s0z2s++K55MJkONGjUwbNgwqFQqTJ48GevWrcO0adPM0ndVOmxfvHjRLNdVqVSIiYlBVlaW9B8jMDBQmkz9ybBtqA8qrMavMjK1365fvw69Xo8hQ4YUun/nzp3YuXMnevTogbVr1wLI67eLFy8iMTGxQB2otfUbYJ7fORcXF7Rs2RKHDx9GbGws6tWrB8C2+q48+u3YsWN47733oFKpsGXLlgJlNwa21G+A+f6cK4yt9Z0pDB9UYmJiCpTKJSYmQq1Wo0WLFhZomfUx/K4Y6uCfZNhe1b6J0ev1mDVrFvbt24f+/ftj0aJF0vzQBuy7knvy4W1z9B1nIylnarUa//77L5RKpVGobteuHQDgxIkTBc4xbCtsSh9b0rlzZwwePLjAP4aa2bp162Lw4MFGMxkY+u3kyZMFrldV+q0kEhISAPzvSXSAfZefIWi7ublhy5YtxQY+9pvp2Hcl+7PecAwVLzAwEN7e3ggPDy/w7YxarUZ4eDj8/Pyq1AN++YN23759sWTJkkJXwWXfldyTf3+ao+8Ytk2QkZGBO3fuFNienZ2NOXPmIDMzE3369DEKPi+88AJcXV2xbds2acloAHjw4AG2bdsGlUqFnj17Vkj7LSU0NBSfffZZgX9Gjx4NIO8voM8++wyhoaHSOYMGDYK9vT3WrVtn9LVsREQE9u/fj3r16lWJFekyMjJw+/btQvft2bMHly9fRmBgoFGIZN/l+fPPP42C9tNGI9hvpmPf5ZUS+vv7Y//+/YiIiJC2p6enY/369ZDL5aytLSFBEPDKK69ArVZL33YarF27Fmq1ushvSm2RoXRk37596NOnD5YuXVpo0AbYd0+6desWsrKyCmzPysrCwoULAUAa+DNH33G5dhPcu3cPPXv2RPPmzVGvXj14enri8ePH+Pvvv/HgwQMEBQVhy5YtBcpFiluuffny5dLiJFXNmTNnMHLkSC7XXgzD71yzZs1Qt25d+Pj4IDU1FVevXsW1a9fg4uKCjRs3onXr1kbnVfW+i4qKwsCBA5Gbm4t+/fqhTp06BY7x9fUtsEx0Ve83g6ioKISFhQHIG0z47bff4OnpiWeeeUY6ZtGiRUbnsO+4XPvT7N69W1rcKDIyEteuXUNwcLA0WNCmTRu88sorAPJGEl977TXcuHEDXbp0QZMmTXD9+nVp2ext27ZBoVBY7L1UpFWrVmH16tVQKpUYOXKk0YCeQc+ePaXFlNh3/7Nq1Sps2rQJbdq0ga+vL1xcXPDw4UMcP34cKSkpaNu2Lb7++mupP8q77xi2TZCRkYEvvvgCly9fRlxcHNLS0uDo6Ih69eqhd+/eGD58eJH/EY4fPy7NMw3kTds2duxYdOrUqSLfQqXytLANAD/99BM2b96MW7duQS6XIzg4GJMmTULTpk0ruLWWoVarsXHjRpw9exbR0dFISUmBXC6Hr68vOnfujDfffNNoZdL8qnLfGX63itO+fXts3bq1wPaq3G8GJek/w4p1+bHvgMuXL2PlypW4ePEitFotgoKC8Oabb0oDLVXZzJkzi11F8+WXXzb6EJeeno5Vq1bh4MGDePToEby8vNCnTx+MHz++Sj3g97R+A4CFCxcaDR6w7/JcuXIFu3btwsWLF/Hw4UOo1Wq4uLigYcOG6NevH/7zn/8U+PBSnn3HsE1EREREZCas2SYiIiIiMhOGbSIiIiIiM2HYJiIiIiIyE4ZtIiIiIiIzYdgmIiIiIjIThm0iIiIiIjNh2CYiIiIiMhOGbSIiIiIiM2HYJiIiIiIyE4ZtIqIK0rBhQ3Tv3t3SzSiVytLmH3/8EQ0bNsSqVass3RQiolJh2CYiolI5c+YMGjZsiJkzZ1q6KURElZ69pRtARESV16+//gq5XG7pZhARWS2GbSIiKlK9evUs3QQiIqvGMhIiokrgzz//xJtvvol27dqhefPm6N27Nz7//HOkpaUVOHbVqlVo2LAhfvzxR9y8eRPvvvsu2rVrh1atWmH48OEIDw8v9B4ajQZfffUVevfujebNm+O5557DwoULkZmZiREjRqBhw4a4d++e0TlP1mzPnDkTI0eOBADs3bsXDRs2lP4x1FM/rcxk5syZaNiwIc6cOVNg34ULF/DGG2+gdevWaNu2LUaPHo1Lly4V23darRY7duzAq6++iuDgYLRo0QIvvfQSvv32W2i12mLPJSIyN45sExFZ2IYNG/DFF1/A3t4e7dq1g0qlQnh4OMLCwnDo0CFs374dnp6eBc67evUq5s+fD39/f3Tp0gW3b9/GuXPn8MYbb2DPnj0ICgqSjhVFEVOmTMGhQ4egVCrRuXNnyOVy/Pjjj7hw4QLs7Uv210GbNm2QmJiIEydOICAgAG3atJH2NW7cuEz98Mcff2DChAnQarVo0aIF/P39cePGDYSGhmLQoEGFnpOdnY23334bZ86cgbu7O1q1agUHBwdcvnwZCxcuxJkzZ7BmzRrIZBxbIiLLYNgmIrKgy5cvY8WKFVAqlfj222/RsmVLAEBubi6mTZuG33//HfPnz8fKlSsLnLt9+3Z8+OGH0kgzACxYsACbN2/Gxo0bsWTJEmn7Tz/9hEOHDsHPzw/bt29HjRo1AADJycl48803ceXKlRK195VXXkFAQABOnDiBNm3aYNGiRWV5+5KMjAzMnj0bWq0WCxYswH/+8x8AeR8Sli1bhrCwsELPW7x4Mc6cOYO+ffti/vz5cHV1la73/vvv4+jRo9i5cydee+21cmknEVFp8aM+EZEFbd++HXq9HiNGjJCCNgA4ODhg7ty5UCgUOHToEO7fv1/g3ODgYKOgDQBjx44FAJw/f95o+/fffw8AmDhxohS0AUClUmH69Onl9n5MdeDAASQlJaFdu3ZS0AYAQRAwadIkozYbPH78GLt370bNmjWxcOFCKWgDgIuLCz777DPI5XJ89913FfIeiIgKw7BNRGRBhlD84osvFtjn4eGBzp07Q6/XF1qH3blz5wLbVCoV3N3dkZCQIG3TaDS4cuUKBEFAnz59CpzTqVMnuLu7l+FdlJ2hH/r27Vtgn1wuR+/evQtsP3PmDDQaDZ555hkoFIoC+728vBAYGIjIyEhkZ2eXf6OJiEqAZSRERBZkCMW+vr6F7jdsf/jwYYF9hY32AoCzszNSUlKk1ykpKdBoNKhevTocHR0LPadmzZpG51S0kvZDfnFxcQCAXbt2YdeuXcVePzU1tdBATkRkbgzbRESVmCAIRe6z1of+9Hp9uVxHFEUAeQ9mNmrUqNhjOVc4EVkKwzYRkQV5e3vj3r17iI+PR/369QvsN4ze+vj4mHwPd3d3yOVyJCcnIycnp9DR7cJqwk1lCLZqtbrQ/YXdy9vbG8D/3u+T4uPjC2wz9EmbNm0wZ84ck9pKRGRu1jksQkRkI9q2bQsA2L9/f4F9SUlJOHHiBARBQHBwsMn3kMvlaN68OURRxMGDBwvsP3XqVKlKSAxhuqg5rL28vAAAd+7cKbAvJSUF169fL7DdMIXgb7/9VmCfVqsttN0hISGws7PDH3/8AY1GU+L2ExFVJIZtIiILCg0NhUwmw9atW42m38vNzcUnn3yC7Oxs9OrVCzVr1izTfYYOHQoAWLlypVH9d0pKCpYuXVqqaxlGoQsL0wDg7++PWrVqITIyEocPH5a2q9VqzJ07FxkZGQXO6dOnD9zd3XH27Fns3btX2i6KIlatWlXkyPZ//vMfxMXF4YMPPsCjR48KHBMTE4MDBw6U6v0REZUnlpEQEVlQixYtMGnSJCxfvhxDhw5F+/btpUVt7t+/j8DAQMydO7fM9xkwYAAOHTqEQ4cOoU+fPujYsSPs7Oxw5swZ+Pv7o1WrVvjnn39KVNvs5+eHhg0b4urVqxg8eDAaNGgAmUyG7t27o0ePHgCA8ePH48MPP8TEiRPRtm1bKJVKXLlyBS4uLujRoweOHDlidE3DVH0TJ07EzJkz8d1330mL2sTExGDIkCGFPgT54YcfIi4uDgcOHMBff/2FRo0aoVatWlCr1YiKikJMTAx69OhR6GwmREQVgSPbREQW9u6772LDhg1o164drly5goMHD8LBwQFvvfUWdu3aVejqkaUlCAKWL1+ODz74AN7e3jh+/DguXbqEAQMGYPPmzUhOToYgCHBzcyvR9VatWoWePXvi7t272LdvH/bs2WNUHjJ48GAsXLgQ9erVQ3h4OK5cuYJu3brh+++/R7Vq1Qq9Zs+ePbFlyxZ06NAB//77L44dOwYvLy9s3boVrVu3LvQchUKBsLAwLF68GC1atMDt27dx4MABXL16FdWrV8d7772HadOmlb7DiIjKiSAaHucmIqIq6cGDB+jRowcCAgIKrZkmIiLTcWSbiKiKuHHjRoEHCR89eoSZM2dCq9ViwIABFmoZEZHt4sg2EVEVMXr0aFy5cgWNGjWCp6cnEhMTcfXqVajVajRv3hzbt28vctEbIiIyDR+QJCKqIgYNGgQAuHnzJi5evAg7OzsEBgaid+/eeOONNxi0iYjMgCPbRERERERmwpptIiIiIiIzYdgmIiIiIjIThm0iIiIiIjNh2CYiIiIiMhOGbSIiIiIiM2HYJiIiIiIyE4ZtIiIiIiIzYdgmIiIiIjKT/wfuHVBcIjhxMQAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# scale point size to logpop\n", "psize = d.logpop.values / d.logpop.max()\n", "psize = jnp.exp(psize * 1.5) - 2\n", "\n", "# plot raw data and labels\n", "plt.scatter(d.lon2, d.lat, s=(psize**2) * 20)\n", "plt.gca().set(xlabel=\"longitude\", ylabel=\"latitude\", xlim=(-50, 30))\n", "labels = d.culture.values\n", "pos = [2, 4, 3, 3, 4, 1, 3, 2, 4, 2]\n", "for i in range(len(labels)):\n", " dx = [0, -5, 0, 5][pos[i] - 1]\n", " dy = [-2, 0, 2, 0][pos[i] - 1]\n", " plt.annotate(\n", " labels[i],\n", " (d.lon2[i], d.lat[i]),\n", " (d.lon2[i] + dx, d.lat[i] + dy),\n", " ha=\"center\",\n", " va=\"center\",\n", " )\n", "\n", "# overlay lines shaded by Rho\n", "for i in range(10):\n", " for j in range(10):\n", " if i < j:\n", " plt.plot(\n", " [d.lon2[i], d.lon2[j]],\n", " [d.lat[i], d.lat[j]],\n", " lw=2,\n", " c=\"k\",\n", " alpha=Rho.values[i, j] ** 2,\n", " )\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.45" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# compute posterior median relationship, ignoring distance\n", "logpop_seq = jnp.linspace(6, 14, num=30)\n", "lambda_ = vmap(lambda lp: post[\"a\"] * jnp.exp(lp) ** post[\"b\"] / post[\"g\"])(logpop_seq)\n", "lambda_median = jnp.median(lambda_, 1)\n", "lambda_PI80 = jnp.percentile(lambda_, q=jnp.array([10, 90]), axis=1)\n", "\n", "# plot raw data and labels\n", "plt.scatter(d.logpop, d.total_tools, s=(psize**2) * 20)\n", "plt.gca().set(xlabel=\"log population\", ylabel=\"total tools\", xlim=(6, 14), ylim=(0, 74))\n", "pos = [4, 3, 4, 2, 2, 1, 4, 4, 4, 2]\n", "for i in range(len(labels)):\n", " dx = [0, -0.5, 0, 0.6][pos[i] - 1]\n", " dy = [-2.5, 0, 2.5, 0][pos[i] - 1]\n", " plt.annotate(\n", " labels[i],\n", " (d.logpop[i], d.total_tools[i]),\n", " (d.logpop[i] + dx, d.total_tools[i] + dy),\n", " va=\"center\",\n", " ha=\"center\",\n", " zorder=3,\n", " )\n", "\n", "# display posterior predictions\n", "plt.plot(logpop_seq, lambda_median, \"k--\", lw=1)\n", "plt.plot(logpop_seq, lambda_PI80[0], \"k--\", lw=1)\n", "plt.plot(logpop_seq, lambda_PI80[1], \"k--\", lw=1)\n", "\n", "# overlay correlations\n", "for i in range(10):\n", " for j in range(10):\n", " if i < j:\n", " plt.plot(\n", " [d.logpop[i], d.logpop[j]],\n", " [d.total_tools[i], d.total_tools[j]],\n", " lw=2,\n", " c=\"k\",\n", " alpha=Rho.values[i, j] ** 2,\n", " )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.46" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "fd11d1d7fbb44800803c98c594d64f1e", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/2000 [00:00" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Primates301 = pd.read_csv(\"../data/Primates301.csv\", sep=\";\")\n", "\n", "# plot it\n", "Image(\"../data/Primates301.png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.48" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "d = Primates301\n", "d[\"name\"] = d.name\n", "dpyro = d.loc[d[[\"group_size\", \"body\", \"brain\"]].dropna().index]\n", "spp_obs = dpyro.name" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.49" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "6c0f9ea54c0d45a3a1550ef845e2451b", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/1000 [00:00" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "V = pd.read_csv(\"../data/Primates301_vcov_matrix.csv\", index_col=0)\n", "Dmat = pd.read_csv(\"../data/Primates301_distance_matrix.csv\", index_col=0)\n", "plt.figure(figsize=(8, 6))\n", "plt.plot(Dmat.values.reshape(-1), V.values.reshape(-1), \"o\", mfc=\"none\")\n", "plt.gca().set(xlabel=\"phylogenetic distance\", ylabel=\"covariance\")\n", "set_matplotlib_formats(\"png\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.51" ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "sample: 100%|██████████| 1000/1000 [00:10<00:00, 91.70it/s, 7 steps of size 7.31e-01. acc. prob=0.91] \n", "sample: 100%|██████████| 1000/1000 [00:07<00:00, 136.66it/s, 7 steps of size 7.63e-01. acc. prob=0.91]\n", "sample: 100%|██████████| 1000/1000 [00:07<00:00, 133.15it/s, 3 steps of size 7.70e-01. acc. prob=0.90]\n", "sample: 100%|██████████| 1000/1000 [00:07<00:00, 129.89it/s, 7 steps of size 6.98e-01. acc. prob=0.91]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.5% 94.5% n_eff r_hat\n", " a -0.19 0.17 -0.20 -0.46 0.08 2027.65 1.00\n", " bG -0.01 0.02 -0.01 -0.05 0.02 1862.21 1.00\n", " bM 0.70 0.04 0.70 0.64 0.76 2028.95 1.00\n", " sigma_sq 0.16 0.02 0.16 0.13 0.19 1996.56 1.00\n", "\n", "Number of divergences: 0\n" ] } ], "source": [ "# put species in right order\n", "dat_list[\"V\"] = V.loc[spp_obs, spp_obs].values\n", "# convert to correlation matrix\n", "dat_list[\"R\"] = dat_list[\"V\"] / jnp.max(V.values)\n", "\n", "\n", "# Brownian motion model\n", "def model(M, B, R, G):\n", " a = numpyro.sample(\"a\", dist.Normal(0, 1))\n", " bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n", " bG = numpyro.sample(\"bG\", dist.Normal(0, 0.5))\n", " sigma_sq = numpyro.sample(\"sigma_sq\", dist.Exponential(1))\n", " mu = a + bM * M + bG * G\n", " SIGMA = R * sigma_sq\n", " numpyro.sample(\"B\", dist.MultivariateNormal(mu, SIGMA), obs=B)\n", "\n", "\n", "m14_10 = MCMC(\n", " NUTS(model),\n", " num_warmup=500,\n", " num_samples=500,\n", " num_chains=4,\n", " chain_method=\"sequential\",\n", ")\n", "m14_10.run(random.PRNGKey(0), **{k: v for k, v in dat_list.items() if k in \"MBRG\"})\n", "m14_10.print_summary(0.89)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.52" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "sample: 100%|██████████| 1000/1000 [00:12<00:00, 78.50it/s, 7 steps of size 5.98e-01. acc. prob=0.93] \n", "sample: 100%|██████████| 1000/1000 [00:08<00:00, 112.44it/s, 7 steps of size 6.02e-01. acc. prob=0.92]\n", "sample: 100%|██████████| 1000/1000 [00:08<00:00, 111.29it/s, 7 steps of size 5.06e-01. acc. prob=0.94]\n", "sample: 100%|██████████| 1000/1000 [00:08<00:00, 112.56it/s, 7 steps of size 5.92e-01. acc. prob=0.92]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " mean std median 5.5% 94.5% n_eff r_hat\n", " a -0.07 0.08 -0.07 -0.19 0.06 1969.30 1.00\n", " bG 0.05 0.02 0.05 0.01 0.09 2388.67 1.00\n", " bM 0.83 0.03 0.84 0.79 0.88 2437.23 1.00\n", " etasq 0.03 0.01 0.03 0.02 0.04 2379.81 1.00\n", " rhosq 2.80 0.25 2.79 2.38 3.18 2293.32 1.00\n", "\n", "Number of divergences: 0\n" ] } ], "source": [ "# add scaled and reordered distance matrix\n", "dat_list[\"Dmat\"] = Dmat.loc[spp_obs, spp_obs].values / jnp.max(Dmat.values)\n", "\n", "\n", "def cov_GPL1(x, sq_alpha, sq_rho, delta):\n", " N = x.shape[0]\n", " K = sq_alpha * jnp.exp(-sq_rho * x)\n", " K = K.at[jnp.diag_indices(N)].set(sq_alpha + delta)\n", " return K\n", "\n", "\n", "def model(M, B, Dmat, G):\n", " a = numpyro.sample(\"a\", dist.Normal(0, 1))\n", " bM = numpyro.sample(\"bM\", dist.Normal(0, 0.5))\n", " bG = numpyro.sample(\"bG\", dist.Normal(0, 0.5))\n", " etasq = numpyro.sample(\"etasq\", dist.FoldedDistribution(dist.Normal(1, 0.25)))\n", " rhosq = numpyro.sample(\"rhosq\", dist.FoldedDistribution(dist.Normal(3, 0.25)))\n", " SIGMA = cov_GPL1(Dmat, etasq, rhosq, 0.01)\n", " mu = a + bM * M + bG * G\n", " numpyro.sample(\"B\", dist.MultivariateNormal(mu, SIGMA), obs=B)\n", "\n", "\n", "m14_11 = MCMC(\n", " NUTS(model),\n", " num_warmup=500,\n", " num_samples=500,\n", " num_chains=4,\n", " chain_method=\"sequential\",\n", ")\n", "m14_11.run(\n", " random.PRNGKey(0), dat_list[\"M\"], dat_list[\"B\"], dat_list[\"Dmat\"], dat_list[\"G\"]\n", ")\n", "m14_11.print_summary(0.89)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.53" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "post = m14_11.get_samples()\n", "plt.subplot(\n", " xlim=(0, jnp.max(dat_list[\"Dmat\"]).item()),\n", " ylim=(0, 1.5),\n", " xlabel=\"phylogenetic distance\",\n", " ylabel=\"covariance\",\n", ")\n", "\n", "# posterior\n", "x = jnp.linspace(0, jnp.max(dat_list[\"Dmat\"]), 101)\n", "for i in range(30):\n", " plt.plot(x, post[\"etasq\"][i] * jnp.exp(-post[\"rhosq\"][i] * x), \"b\")\n", "\n", "# prior mean and 89% interval\n", "eta = jnp.abs(dist.Normal(1, 0.25).sample(random.PRNGKey(0), (int(1e3),)))\n", "rho = jnp.abs(dist.Normal(3, 0.25).sample(random.PRNGKey(1), (int(1e3),)))\n", "d_seq = jnp.linspace(0, 1, 50)\n", "K = vmap(lambda x: eta * jnp.exp(-rho * x))(d_seq)\n", "plt.plot(d_seq, jnp.mean(K, axis=1), lw=2, color=\"k\")\n", "plt.fill_between(\n", " d_seq, *jnp.percentile(K, q=jnp.array([5.5, 94.5]), axis=1), color=\"k\", alpha=0.2\n", ")\n", "plt.annotate(\"prior\", (0.5, 0.5), ha=\"center\", va=\"center\", color=\"k\")\n", "plt.annotate(\"posterior\", (0.2, 0.1), ha=\"center\", va=\"center\", color=\"b\")\n", "if \"SVG\" in os.environ:\n", " set_matplotlib_formats(\"svg\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Code 14.54" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "sa = 1\n", "sb = 0.5\n", "rho = -0.7\n", "S = jnp.array([[sa**2, a * sb * rho], [a * sb * rho, sb**2]])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.11.6" }, "widgets": { "application/vnd.jupyter.widget-state+json": { "state": {}, "version_major": 2, "version_minor": 0 } } }, "nbformat": 4, "nbformat_minor": 4 }