05_model-comparison.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ch 5. Model Comparison\n",
    "\n",
    "1. Posterior predictive checks\n",
    "2. Occam's razor—simplicity and accuracy\n",
    "3. Overfitting and underfitting\n",
    "4. Information criteria\n",
    "5. Bayes factors\n",
    "6. Regularizing priors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pathlib import Path\n",
    "\n",
    "import arviz as az\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import plotnine as gg\n",
    "import pymc3 as pm\n",
    "import seaborn as sns\n",
    "from scipy import stats\n",
    "\n",
    "%config InlineBackend.figure_format = 'retina'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior predictive checks (PPC)\n",
    "\n",
    "- a way to evalutate a model in the context of the purpose of the model\n",
    "- with multiple models, can use PPC to compare them"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAABGIAAANaCAYAAADCverRAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAB7CAAAewgFu0HU+AABwk0lEQVR4nOzdeXhV5bk34GcnYRaQSdEEAYcqOKCCaEVxwKooouKEWrVqFa3a1rFaPXUeWgvWnjrPigOK4oRTnRUnlFonVAQRE6CAYJgRkvX94UeOlBASzV6bJPd9XbnOdq9nrf1DTmP48a71ZpIkSQIAAACArMvLdQAAAACAhkIRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFTB3Vq1evKCoqil69euU6CgAAAFBNBbkOwI8zffr0KCkpyXUMAAAAoAasiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUlKQ6wD1zaxZs+Ktt96KDz74ICZNmhRz5syJvLy8aN++fWyxxRYxYMCA6Ny5c65jAgAAADmQSZIkyXWI+mLmzJnx61//On74r7Rp06ZRVlYWS5cujYiI/Pz8OP7442PAgAE/6bOKioqipKQkCgsLo7i4+CddCwAAAEiHFTG1qLy8PJIkiW222SZ233332GqrraJNmzZRVlYWkyZNittuuy0++eSTuPnmm2O99daLnj175joyAAAAkCIrYmrRggULYvr06bHRRhtVenzp0qVxxhlnxFdffRVbbrllXH755T/6s6yIAQAAgLrHw3prUYsWLVZZwkRENGrUKHbdddeIiJg4cWJKqQAAAIA1hSImZU2aNImI729jAgAAABoWRUzKPvroo4gIOycBAABAA6SISdGECRPirbfeioiIX/ziFzlOAwAAAKRNEZOSefPmxdVXXx3l5eXxs5/9LPr165frSAAAAEDKFDEpWLJkSVxxxRUxffr0aNWqVZx11lmRn5+f61gAAABAygpyHaC+W7p0aVx55ZXx8ccfR4sWLeLiiy+Ojh07VuvcYcOGxbBhwyo9Nm3atNqMmVVTpkyJW2+9Nd5///0oLy+PzTbbLI4//vjo1q1brqMBAABAqhQxWbR06dK46qqrYty4cdG8efO4+OKLq9ze+r/NnTs3SkpKspgwu5YuXRq/+93v4qabblphl6jRo0fH0KFD46CDDoo77rgjWrZsmcOUAAAAkB5FTJYsW7Ys/vznP8fYsWOjadOm8ac//Sl+9rOf1egarVq1isLCwkqPTZs2bY3eAru8vDyOOuqoGDFixCpnHn744fjPf/4Tzz//fMW23gAAAFCfZZIkSXIdor5ZtmxZ/OUvf4m33norGjduHBdeeGFsueWWtfoZRUVFUVJSEoWFhVFcXFyr164No0aNikGDBlVrdtiwYXH66adnOREAAADknof11rKysrL461//WlHCXHDBBbVewtQF1113XbVnr7/++jV6dQ8AAADUFkVMLSorK4thw4bFG2+8EY0aNYrzzjsvtt5661zHSt3ixYvjxRdfrPb8F198ERMnTsxiIgAAAFgzeEZMLRo/fny89tprERGRJElce+21Vc4PHTo0OnTokEa0VM2fPz9qesdbaWlpltIAAADAmkMRU4t+WD4sW7Ysvv322yrn6+vtOK1atYqCgoJYtmxZtc9p3759FhMBAADAmkERU4u23HLLePzxx3MdI+caN24cAwcOjEceeaRa8z179ozOnTtnORUAAADknmfEkBWnnXZatWdPPfXUyGQyWUwDAAAAawZFDFmx6667xh/+8IfVzg0ePDiOPvroFBIBAABA7iliyJorr7wyhg0bFm3btl3pWIsWLeLcc8+N4cOHR16e/zcEAACgYcgkNd3ehjVCUVFRlJSURGFhYRQXF+c6TpUWLVoUDz/8cPzrX/+KJEli0003jcGDB0fr1q1zHQ0AAABSpYipo+pSEQMAAAB8zz0hAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApKQg1wGA1SsrK4vRo0fHnXfeGZMmTYrGjRvH9ttvH0OGDIktttgi1/EAAACopkySJEmuQ1BzRUVFUVJSEoWFhVFcXJzrOGTRxIkTY+DAgfHJJ59UevzYY4+NG2+8MRo3bpxyMgAAAGrKihhYg02bNi122223+Prrr1c5c8cdd8TixYvj3nvvjUwmk2I6AAAAasozYmANdskll1RZwix3//33x4svvphCIgAAAH4KRQysoebOnRv33HNPteevv/76LKYBAACgNihiYA01duzYWLBgQbXnrYgBAABY8yliYA1VkxLmx8wDAACQPkUMrKHWW2+9rM4DAACQPkUMrKF69uwZG2+8cbXnjzjiiCymAQAAoDYoYmANlZeXF7/73e+qNdu4ceMYMmRIlhMBAADwUyliYA32m9/8JgYPHlzlTF5eXtx1113RpUuXdEIBAADwoyliYA2Wl5cXw4cPj0svvTTatWu30vEePXrE008/vdqyBgAAgDVDJkmSJNchqLmioqIoKSmJwsLCKC4uznUcUrB48eJ48skn48svv4xGjRrF9ttvHzvssENkMplcRwMAAKCaCnIdAKiepk2bxsEHH5zrGAAAAPwEbk0CAAAASIkiBgAAACAlbk2iQVm6dGm8/fbbMXv27GjTpk307t07mjRpkutYAAAANBCKGBqERYsWxV/+8pe48cYbY/r06RXvd+jQIU444YQ477zzYq211sphQgAAABoCuybVUXZNqr758+fHXnvtFW+88cYqZ3r27BnPP/98rL322ukFAwAAoMHxjBjqvZNOOqnKEiYi4r333otjjz02pUQAAAA0VIoY6rWvvvoq7r///mrNPvroo/HZZ59lOREAAAANmSKGeu2ee+6J8vLyas/feeed2QsDAABAg6eIoV778ssvazQ/efLk7AQBAACAUMRQzzVq1Cir8wAAAFATihjqte23375G8717985SEgAAAFDEUM8ddthh1d6Sunnz5nHUUUdlNxAAAAANmiKGeq158+Zx6aWXVmv2wgsvjNatW2c5EQAAAA2ZIoZ675RTTonLLrusypk//vGPcfbZZ6eUCAAAgIZKEUO9l8lk4vzzz49///vfMWTIkFhnnXWioKAg2rdvH8cdd1y8++67cfnll0cmk8l1VAAAAOq5TJIkSa5DUHNFRUVRUlIShYWFUVxcnOs4AAAAQDVYEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKSkINcBgDVLWVlZTJw4MRYsWBAdOnSIoqKiXEcCAACoN6yIASIiYuHChfGXv/wlNt5449h0001j2223jU6dOsVOO+0UDz30UCRJkuuIAAAAdV4m8aerOqmoqChKSkqisLAwiouLcx2HOm727Nmx1157xbvvvrvKmZNOOimuv/76yGQyKSYDAACoX6yIgQYuSZI47LDDqixhIiJuvPHGuPrqq1NKBQAAUD8pYqCBe+edd+L555+v1uzVV18dixcvznIiAACA+ksRAw3crbfeWu3ZWbNmxWOPPZbFNAAAAPWbIgYauE8//TSr8wAAAPwfRQw0cHl5Nfs2UNN5AAAA/o8/UUED16NHj6zOAwAA8H8UMdDAnXDCCdWeLSwsjH322SeLaQAAAOo3RQw0cFtuuWUMHjy4WrMXX3xxFBQUZDkRAABA/aWIAeK2226Lvffeu8qZSy+9NI4//viUEgEAANRPihggmjdvHk8++WTce++90adPn4r3GzVqFIcddli8/vrrccEFF+QwIQAAQP3gHgNooJIkiddffz1uu+22mDBhQuTn58e2224bt9xyS2ywwQaxYMGCWHvttaNx48a5jgoAAFBvZJIkSXIdgporKiqKkpKSKCwsjOLi4lzHoY6ZMWNGHHTQQfH6669XevyYY46Jm266KZo0aZJyMgAAgPrNihhoYObOnRv9+vWLjz76aJUzd911V8ydOzdGjhwZeXnuYAQAAKgt/oQFDczQoUOrLGGWGzVqVDzxxBMpJAIAAGg4FDHQgCxdujRuvvnmas9fd911WUwDAADQ8ChioAH56KOPYvr06dWef+GFF6KsrCyLiQAAABoWRQw0IAsWLKjRfHl5eSxevDhLaQAAABoeRQw0IOuss06N5lu0aBHNmzfPUhoAAICGRxEDDcgmm2wSW2+9dbXnBw8eHJlMJnuBAAAAGhhFDDQgmUwmfve731V79tRTT81yIgAAgIZFEQMNzDHHHBPHHHPMaueGDRtWo9UzAAAArJ4iBhqYTCYTt99+e1xyySXRpk2blY537tw5hg8fHr///e/TDwcAAFDPZZIkSXIdgporKiqKkpKSKCwsjOLi4lzHoY5atGhRPProozFhwoTIz8+PbbfdNvbcc8/Iz8/PdTQAAIB6qSDXAYDcadasWRx++OG5jgEAANBguDUJAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAFo4MrKymLevHlRXl6e6ygAAFDvKWIAGqAkSeK5556L/fffP5o2bRqtWrWK5s2bx+DBg2PMmDG5jgcAAPWWIgaggSkrK4sTTjgh9tprr3j88cdj2bJlERGxZMmSGDFiROy0005x3nnnRZIkOU4KAAD1T0GuA9Q38+fPj48++igmTpxY8TVnzpyIiPjjH/8YO+ywQ44TAg3dH//4x7jtttuqnLnqqquiQ4cOccYZZ6SUCgAAGgZFTC17++2349prr811DIBKTZ8+Pa655ppqzV5yySUxZMiQaNGiRZZTAQBAw+HWpCxo06ZN9OzZMw499NA499xzcx0HoMIdd9wRS5curdZsaWlpPPjgg1lOBAAADYsVMbVs1113jX79+uU6BkClxo0bV6P5f/3rX3HsscdmKQ0AADQ8VsTUsvz8/FxHAFilsrKyrM4DAABVU8QANCA/+9nPajS/ySabZCkJAAA0TIoYgAakJrcZNW7cOI488sgspgEAgIZHEQPQgGy66aZxyCGHVGv2xBNPjA4dOmQ5EQAANCyKGIAG5rbbbos+ffpUOTNgwIAYOnRoSokAAKDhUMQANDAtW7aM559/Pv7yl79Ely5dVjjWrVu3uO6662LUqFHRuHHj3AQEAIB6zPbVa7Bhw4bFsGHDKj02bdq0lNMA9UnTpk3j7LPPjjPOOCPGjx8fpaWl0bZt29hss80ik8nkOh4AANRbipg12Ny5c6OkpCTXMYB6LD8/P7bYYotcxwAAgAZDEbMGa9WqVRQWFlZ6bNq0aVFeXp5yIgAAAOCnUMSswc4444w444wzKj1WVFRktQwAAADUMR7WCwAAAJASK2KyYO7cuZW+v2jRohWONW/ePAoK/BYAAABAQ5FJkiTJdYj6ZuDAgdWau/zyy2PLLbf8UZ+x/NakwsLCKC4u/lHXAAAAANJlOQaQmjlz5sSdd94ZTz75ZHz77bfRtm3bOPDAA+Ooo46Kli1b5joeAABA1lkRU0dZEUNdc99998WJJ54YCxYsWOlY69at46677or9998/B8kAAADS42G9QNY9+OCDceSRR1ZawkRElJaWxkEHHRRPP/10yskAAADSpYgBsmrx4sVxyimnrHaurKwsTj755CgrK0shFQAAQG4oYoCseuihh2LWrFnVmv3qq6/iqaeeynIiAACA3FHEAFn1/PPPZ3UeAACgLlHEAFm1cOHCGs2v6jkyAAAA9YEiBsiqddddt0bzHTt2zFISAACA3FPEAFk1ePDgrM4DAADUJYoYIKv69OkTvXr1qtZsv379YosttshyIgAAgNxRxABZlclk4v7771/tLUqdO3eOO++8M51QAAAAOaKIAbJu4403jjfffDMGDBgQmUxmhWP5+flx8MEHxxtvvBFFRUU5SggAAJCOglwHABqGrl27xhNPPBFffvlljB49OkpLS6Nt27ax3377KWAAAIAGI5MkSZLrENRcUVFRlJSURGFhYRQXF+c6DgAAAFANbk0CAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASElBrgMA0DAtXbo0Hn300XjooYdi5syZ0apVq+jfv38ceeSR0bJly1zHAwCArMgkSZLkOgQ1V1RUFCUlJVFYWBjFxcW5jgNQI2+++WYcdthh8fXXX690rFWrVnHjjTfG4YcfnoNkAACQXVbEAJCqd999N/bYY49YuHBhpcfnzp0bRxxxRESEMgYAgHrHM2IA1hBlZWUxevToGDRoUHTr1i26d+8ehx9+eLz00ktRXxYvJkkSQ4YMWWUJ80Mnn3xyzJ8/P4VUAACQHrcm1VFuTYL6Zdq0abH//vvH2LFjKz2+++67x8iRI6NNmzYpJ6tdb7/9duywww7Vnr/pppvixBNPzGIiAABIlxUxADk2d+7c2GOPPVZZwkREvPjii7HvvvvGkiVLUkxW+5555pmszgMAwJpOEQOQY3//+9/jk08+We3cm2++GXfddVcKibJn7ty5NZqfN29elpIAAEBuKGIAcqisrCxuuummas/fcMMNWUyTfR06dMjqPAAArOkUMQA5NGnSpBo95+n999+P0tLSLCbKroMPPrhG84ceemiWkgAAQG4oYgByaNGiRTU+pzo7Dq2pNt5449h3332rNdulS5cYMGBAlhMBAEC6FDEAOdSxY8cazTdp0iTatm2bpTTpuPnmm6Nz585VzrRo0SJGjBgRBQUFKaUCAIB0KGIAcmidddaJPffcs9rzhx56aDRp0iSLibJv/fXXjzfeeCMGDBgQmUxmpeO9e/eO1157LXr37p2DdAAAkF2ZJEmSXIeg5oqKiqKkpCQKCwtr9HwJYM3z7LPPxt57773auUwmE++880706tUrhVTpmDhxYjzyyCMxc+bMaNWqVey999716tcHAAD/TRFTRylioH658MIL45JLLqly5u9//3ucdtppKSUCAACywa1JAGuAiy++OO64447YaKONVjq2+eabx8MPP6yEAQCAesCKmDrKihion8rLy+Pll1+OTz/9NDKZTGy11Vax4447VvosFQAAoO5RxNRRihgAAACoe9yaBAAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAACkpSOuDysrKYsyYMfHWW2/FBx98EJMnT47Zs2fHokWLolmzZtG2bdvo0qVL9OjRI3bYYYfYcccdIz8/P614AAAAAFmXSZIkyeYHPPfcc3HXXXfF6NGjY968edU+r2XLlrHvvvvGMcccE3vuuWcWE9ZNRUVFUVJSEoWFhVFcXJzrOAAAAEA1ZKWIWbZsWdx+++0xbNiwmDBhQkRE/JiPyWQyERGx8cYbx5lnnhnHHXdcFBSktohnjaaIAQAAgLqn1ouYESNGxPnnnx9ffvllRfmSl5cXm2++eeywww7x85//PLp16xbt2rWLtm3bRqtWrWLu3Lkxe/bs+Oabb2L8+PHx1ltvxZtvvhmffPJJlJWVfR80k4muXbvGFVdcEYceemhtRq6TFDEAAABQ99RqEdOvX794+eWXKwqYHXfcMY455pg48MADo3379jW+3uzZs2PUqFFx1113xeuvv/594Ewmdt1113jhhRdqK3adpIgBAACAuqdWi5i8vLwoKCiIwYMHxx/+8IfYfPPNa+vSMX78+Ljqqqvi/vvvj7KysoqVMg2VIgYAAADqnlrdvvrggw+OTz75JO6+++5aLWEiIrp16xZ33XVXjB8/Pg4++OBavTYAAABAGrK+axLZYUUMAAAA1D21uiIGAAAAgFVTxAAAAACkRBEDAAAAkBJFDAAAAEBKCmrzYhtuuGFtXq5CJpOJiRMnZuXaAAAAAGmp1SJm8uTJkclkojobMWUymYrXSZKs9M+rmgUAAACoq2q1iNlggw2qLE2WLl0a06ZNiyRJKsqWtddeO1q0aBELFiyIb7/9tmI2k8nEeuutF40aNarNiAAAAAA5U+srYlaluLg4DjnkkJg6dWr07t07zjzzzOjXr1+0bdu2Ymb27Nnx/PPPx9/+9rd46623YoMNNoiHHnooCgsLazMmAAAAQE5kkurcR/QTLV68OLbffvv46KOP4vTTT4+//vWvqz3n7LPPjqFDh0aPHj3izTffjKZNm2Y7Zp1SVFQUJSUlUVhYGMXFxbmOAwAAAFRDKrsmXX/99fHhhx9Gr169qlXCRERcffXV0atXr/jggw/ixhtvzHJCAAAAgOxLpYh58MEHI5PJxBFHHFGj84488shIkiQeeOCBLCUDgJqZMWNGvPPOOzFu3LhYsGBBruMAAFDHpFLELN96ev3116/RecvnbV0NQK6NGTMm9t9//1hvvfVi++23j549e0bHjh3jlFNOia+++irX8QAAqCNSKWIWLlwYERElJSU1Om/q1KkrnA8AuXDLLbdE37594/HHH4/y8vKK9+fPnx/XX3999OzZM957770cJgQAoK5IpYjp1KlTRETcd9991T4nSZK49957VzgfANL20ksvxZAhQ1YoYP7bN998E/vss0988803KSYDAKAuSqWI6d+/fyRJEu+9916cccYZ1Trn7LPPjnfffTcymUzss88+WU4IAJW76qqrojobDM6YMSNuu+22FBIBAFCXpbJ9dUlJSXTv3j3mz58fERG9evWKM844I/r16xft27evmPvmm2/i+eefj2uuuSbGjh0bSZJEq1at4pNPPqnx82XqO9tXA2TflClTonPnztWe32STTeLzzz/PYiIAAOq6gjQ+pLCwMO6777446KCDYunSpfHuu+9W7KDUqlWraN68eSxcuDDmzp1bcU6SJNG4ceO47777lDAA5MSECRNqNP/FF19EeXl55OWlsuAUAIA6KLWfFPfdd994+eWXY9NNN40kSSq+SktLY/r06VFaWrrC+926dYtXXnnFbUkA5Ex+fn6N5jOZTJaSAABQX6SyIma5HXbYIT766KMYPXp0PPLII/HOO+/E1KlTY/78+bHWWmtFYWFh9O7dOw488MDYd999/Y0iADm1+eabR0FBQSxbtqxa81tvvbX/dgEAUKVUi5iIiLy8vNhvv/1iv/32S/ujAaBGOnToEAcddFCMGDGiWvMnnXRSlhMBAFDX+Ws7AKjC+eefH82bN1/tXLdu3eLII49MIREAAHWZIgYAqrDlllvGqFGjYq211lrlzKabbhrPPPNMtQobAAAattRvTYqIGDt2bDz77LPxySefxOzZs2Pp0qXxwgsvrDAza9as+O6776Jp06bRtm3bXMQEgIiI2HPPPePjjz+O66+/Pm6//faYOXNmRER07949TjrppDj22GOrLGoAAGC5TJIkSVof9sUXX8Rxxx0XY8aMqXgvSZLIZDJRVla2wuxZZ50V11xzTXTo0CFKSkpqvHNFfVdUVBQlJSVRWFgYxcXFuY4D0GAkSRLz5s2LgoICK2AAAKix1G5NGjduXPTq1SvGjBmzwjbVq3LqqadGkiQxc+bM+Oc//5lWTACoUiaTiVatWilhAAD4UVIpYhYtWhQHHHBAzJ07NwoKCuL888+Pzz77LB588MFVntOlS5fo2bNnRIQiBgAAAKgXUilibrnlliguLo68vLx46KGH4tJLL41NNtkkGjVqVOV5O+20UyRJEmPHjk0jJgAAAEBWpVLEPPbYY5HJZGKfffaJgQMHVvu8bt26RcT3z5YBAAAAqOtSKWI+/vjjiIjYZ599anTe8t2Svv3229qOBAAAAJC6VIqYOXPmRETEOuusU6Pzli5dmo04AAAAADmRShHTunXriKj5ypavvvoqIiLatWtX25EAAAAAUpdKEdOlS5eIiHjnnXdqdN4zzzwTERGbb755bUcCAAAASF0qRUy/fv0iSZJ48MEH45tvvqnWOS+++GK8+uqrkclkYo899shyQoDcSpIkXnvttbjwwgvjrLPOiquvvjomT56c61gAAEAtS6WIOeGEE6KgoCBKS0vj8MMPj4ULF1Y5/+abb8bhhx8eERHNmzeP4447Lo2YADkxZsyY6NGjR/Tt2zcuueSSGDp0aJxzzjmx4YYbxqBBg2LGjBm5jggAANSSVIqYDTfcMM4666xIkiReeOGF6N69e1x99dXx4YcfVsx89NFHcf/998chhxwSO++8c8ycOTMymUxccsklFbsnAdQ3L774YvTr12+F74fLJUkSo0aNqvieCAAA1H2ZJEmSND4oSZI4+uij4957741MJrPa2YiIIUOGxA033JBGvDqnqKgoSkpKorCwMIqLi3MdB/gRFi5cGF26dKlWyTJ48OC4//77U0gFAABkUyorYiIiMplM3HPPPXHDDTdEx44dI0mSVX6ts846ceONNyphgHptxIgR1V7pMnLkyJg6dWqWEwEAANlWkPYHDhkyJI499th47rnn4tVXX43JkyfHt99+G2uttVYUFRXFrrvuGv37949mzZqlHQ0gVQ899FC1Z5ctWxaPPfZYnHzyyVlMBAAAZFvqRUxEROPGjWPAgAExYMCAXHw8wBqhps998ZwYAACo+1K7NQmAFbVq1Sqr8wAAwJpHEQOQI/3796/R/F577ZWlJAAAQFoUMQA5cuyxx0bTpk2rNbv77rtHt27dspyIXCorK4snnngijjrqqNhrr73i4IMPjptvvjnmz5+f62gAANSiWt2+evfdd6+tS60gk8nECy+8kJVr11W2r4b64ZZbbokTTzyxypm11147xowZE927d08pFWkbN25cHHrooTFx4sSVjrVu3Tquv/76OOKII3KQDACA2larD+t9+eWXI5PJ1OYlI0mSWr8mwJrihBNOiLy8vPjd734XCxYsWOn4xhtvHCNHjlTC1GMffvhh7LrrrjFv3rxKj5eWlsaRRx4ZSZLEkUcemXI6AABqW62uiMnLy86dTplMJsrKyrJy7brKihioX0pLS+Oee+6J559/PubPnx/rrrtuHH744dG/f//Iz8/PdTyyaKeddooxY8asdm6ttdaKkpISD20GAKjjarWIIT2KGIC67/33349tttmm2vP/+Mc/4pRTTsliIgAAss3DegEgR55++umszgMAsOZRxABAjsydOzer8wAArHkUMQCQIx06dKjRfPv27bOUBACAtChiACBHDjzwwBrtDHjIIYdkMQ0AAGmo1e2rq6usrCw++OCDKC4ujrlz51ZrR6Sjjz46hWQAkJ6uXbvGfvvtF48//vhqZ9dbb70YNGhQCqkAAMimVHdNKikpiYsvvjjuv//+WLhwYbXPy2QysWzZsiwmq3vsmgRQP0ydOjX69OkTkydPXuVM06ZN47nnnoudd945vWAAAGRFarcmjR07Nrbeeuu47bbbYsGCBZEkSY2+AKA+Wn/99WPMmDGxzz77VHp8q622ipdeekkJAwBQT6Rya9KCBQviwAMPjG+++Sby8vLil7/8ZfTp0ydOOumkyGQyceqpp8amm24aX375ZTz99NPxySefRCaTiV/+8pex++67pxERAHJm/fXXj9GjR8eECRNi5MiRMWPGjGjZsmXsueee0adPnxo9RwYAgDVbKrcmXXvttXH66adHJpOJe+65J4444oiIiMjLy4tMJhOjRo2KgQMHVsw/8MADcdJJJ8XChQvjjjvuiCOPPDLbEesctyYBAABA3ZPKrUlPPfVURET06dOnooSpyuDBg2PUqFFRVlYWQ4YMiYkTJ2Y7IgAAAEDWpVLEfPjhh5HJZGLAgAGVHq9s16TddtstBg4cGIsWLYqbbrop2xEBAAAAsi6VImb27NkREdGlS5cV3i8o+P4RNYsWLar0vL333juSJImnn346q/kAAAAA0pBKEZOfn7/C/12uZcuWERExffr0Ss9r06ZNRHy/7TUAAABAXZdKEbPuuutGRMS33367wvudOnWKiO9vXarMV199FRGrXjEDAAAAUJekUsR07949IiI+//zzFd7v2bNnJEkSTzzxRCxYsGCFY+Xl5XH33XdHRERhYWEaMQEAAACyKpUipk+fPpEkSbzxxhsrvH/wwQdHRMScOXNi0KBBMX78+Pjuu+/ik08+iYMOOig+/vjjyGQy8Ytf/CKNmAAAAABZlUmSJMn2h/z73/+ObbbZJgoKCmLKlCnRsWPHimM77bRTvPHGG5HJZFY6L0mSaNGiRfz73/+ODTfcMNsx65SioqIoKSmJwsLCKC4uznUcAAAAoBoK0viQHj16xMUXXxwLFy6MkpKSFYqYhx9+OPbaa6/44IMPVjqvZcuWMWLECCUMAAAAUC+ksiJmdcrKymLEiBHx3HPPxfTp06NFixax3XbbxfHHHx8dOnTIdbw1khUxAAAAUPesEUUMNaeIAQAAgLonlYf1AgAAAKCIAQAAAEhNKg/rXbJkSfzlL3+JJEmif//+sd122632nHfeeSeeeeaZyMvLi/POOy/y8/NTSAoAAACQPak8I2bEiBFx+OGHR6NGjWLy5Mmx3nrrrfacadOmRefOnaOsrCxGjhwZBx54YLZj1imeEQMAAAB1Tyq3Jo0ePToiInbZZZdqlTAREeutt17stttukSRJPPHEE9mMBwAAAJCKVIqY9957LzKZTOy88841Oq9v374RETF27NhsxAIAAABIVSpFzJQpUyIiYqONNqrReV27dl3hfAAAAIC6LJUi5rvvvouIiEaNGtXovOXzixYtqvVMAAAAAGlLpYhp27ZtRERMnTq1Ructn2/dunWtZwIAAABIWypFzPJbkp577rkanbd8fvktSgAAAAB1WSpFzO677x5JksSzzz4bb731VrXOeeONN+KZZ56JTCYT/fr1y3JCAAAAgOxLpYg54YQTolGjRpEkSRxwwAHx9ttvVzn/1ltvxUEHHRRJkkR+fn6ccMIJacQEAAAAyKqCND6kU6dOcfbZZ8cVV1wRM2fOjJ122in233//OOCAA6J79+6x1lprxfz58+OTTz6JRx99NB577LEoKyuLTCYTp59+emy44YZpxAQAAADIqkySJEkaH5QkSRxxxBExYsSI7z84k6lyNiLikEMOiQceeKDK2YaqqKgoSkpKorCwMIqLi3MdBwAAAKiGVG5Nivi+eLn//vvjmmuuiQ4dOkSSJKv8at++fVxzzTUxYsQIJQwAAABQb6S2IuaHFi1aFE8//XS89tpr8fXXX8fcuXOjVatWUVRUFH379o3+/ftHs2bN0o5Vp1gRAwAAAHVPTooYfjpFDAAAANQ9qd2aBAAAANDQpbJrUk3MnTs3li1bFm3bts11FACgAZgxY0b861//iu+++y66du0am2++uWfUAQBZk8qKmGXLlsW4ceNi3Lhx8c0331Q68+KLL0aPHj2iTZs20aFDh+jcuXPcfPPNacQDABqgTz/9NA4//PAoKiqKvffeOwYOHBhbbrllbLfddvHggw/mOh4AUE+lsiLmhRdeiP79+0cmk4mPP/442rVrt8Lxd955J/r37x/Lli2r2Lr666+/jpNPPjlmz54d5557bhoxAYAG4o033oj+/fvH3LlzVzr23nvvxWGHHRYffPBBXHbZZTlIBwDUZ6msiHnuueciIqJHjx6x2WabrXT8zDPPjKVLl0aSJNGhQ4fYeuutIy8vL5IkiYsuuigmTpyYRkwAoAGYPXt2DBw4sNIS5ocuv/zyGDFiREqpAICGIpUi5q233opMJhO77bbbSsc+//zzGDNmTGQymTjkkEOipKQkxo0bFy+99FI0atQoli5dGrfddlsaMQGABuC2225b5a3S/+0vf/lL2GASAKhNqRQx//nPfyIiolu3bisde+aZZyIiIpPJxNChQ6Og4Pu7pXbeeecYMGBAJEkSL7/8choxAYAG4M4776z27Lhx4+Kjjz7KXhgAoMFJpYiZOXNmRES0adNmpWOvvvpqRERsu+22UVRUtMKx5StoJkyYkOWEAEBDMWnSpBrNf/nll1lKAgA0RKkUMYsXL46IiAULFqx07PXXX49MJhO77LLLSsfWWWediIjV3sMNAFBdjRs3rtF8o0aNspQEAGiIUililq+EKSkpWeH98ePHx4wZMyIi4uc///lK5y1btiwiouJ2JQCAn2r77bev9mxBQUFsu+22WUwDADQ0qRQx3bt3jyRJYtSoUSu8/8ADD1S83nnnnVc6r7i4OCIiOnTokN2AAECDcdJJJ1V7dtCgQbHuuutmMQ0A0NCkUsTsu+++ERHx3nvvxR/+8If49NNP4957741hw4ZFJpOJPn36VFq2jBs3LiIiNt100zRiAgANwP777x99+/Zd7VzLli3jwgsvTCERANCQpFLEnHjiiRV/m/TXv/41Nt988zj66KMrnhlz7rnnrnTO0qVL49lnn41MJhM77bRTGjEBgAYgPz8/Hn300SrLmDZt2sTo0aOje/fuKSYDABqCVIqYli1bxpNPPhnrr79+JElS8ZXJZOKCCy6IffbZZ6VzHnvssSgtLY2I/9s9CQCgNrRp0yZeeOGFePjhh2OPPfaItdZaK5o0aRKbbrppXHXVVfH5559Xets0AMBPlUmSJEnrwxYtWhRPPfVUfPHFF9GiRYvYY489YrPNNqt09n//939j3LhxkZeXFzfddJMH9v6XoqKiKCkpicLCwopn6QAAAABrtlSLGGqPIgYAAADqnlRuTQIAAABAEQMAAACQmlotYmbMmFGbl1ul6dOnp/I5AAAAALWpVouYjTfeOC655JKK3Y5q26xZs+LMM8+MjTfeOCvXBwAAAMimWn1Yb15eXmQymWjZsmUMGTIkTjzxxNhoo41+8nU/+uijuPPOO+Pmm2+OBQsWREREWVnZT75uXeZhvQCworKyshg3blzMmDEjWrVqFb169YpmzZrlOhYAwApqdUXM8OHDo2PHjjF37tz461//Gptuumn07ds3rr322nj//fejvLy8WtcpLy+Pf//733HNNdfEtttuGz169Ihrrrkm5s+fHx07dox77723NmMDAHXYsmXLYtiwYbHJJptE7969Y8CAAdG3b98oKiqKs88+O+bMmZPriAAAFWp9++r58+fH1VdfHX/7299i3rx5kclkKo41a9YsevbsGd26dYu2bdtG27Zto1WrVjF37tyYPXt2zJ49Oz799NN47733YuHChRXnJUkSLVu2jDPPPDPOOOOMWGuttWozcp1kRQwARHz33XcxaNCgGD169CpnunXrFi+99FKsu+66KSYDAKhcrRcxy82ZMyeuu+66uOmmm6KkpOT/PvAHxcyq/DBSp06d4uSTT46TTjop1l577WxErZMUMQAQceaZZ8awYcNWO7fzzjvHK6+8Uq2fQwAAsilrRcxySZLEP//5z3jkkUfiueeei8mTJ6/2nA033DD23nvvGDRoUOy2225+aKqEIgaAhu7bb7+NwsLCFVbRVuXNN9+MHXbYIcupAACqVpDtD8hkMrHnnnvGnnvuGRERM2fOjA8++CAmT54cs2fPjiVLlkSTJk2iXbt20aVLl9hqq62iffv22Y4FANRxDz74YLVLmIiI22+/XREDAORc1ouY/9ahQ4fo169f2h8LANQzkyZNyuo8AEA21OquSQAAaWnUqFGN5gsKUv/7JwCAlShiAIA6qXfv3lmdBwDIBkUMAFAn9e/fPzp16lSt2by8vDjhhBOynAgAYPUUMQBAnVRQUBB//vOfqzX7+9//vtqlDQBANiliAIA66/DDD49//OMfkZe36h9pTjjhhPjLX/6SYioAgFVTxAAAddopp5wSH3/8cZx22mmx7rrrRl5eXrRu3ToOPfTQeOWVV+Lmm2+O/Pz8XMcEAIiIiEySJEmuQ1BzRUVFUVJSEoWFhVFcXJzrOAAAAEA12McxS0pLS2PkyJHxzjvvxDfffBNNmjSJjTbaKPbZZ5/YYYcdch0PAAAAyAFFTBZMmTIlzj///CgtLY2IiGbNmsWCBQvi/fffj/fffz/2228/OzcAAABAA6SIqWVLly6Nyy67LEpLS6Nz585xxhlnRNeuXWPJkiXx+OOPx/Dhw+OJJ56Irl27xh577JHruAAAAECKPKy3lj377LMxffr0aNq0afzpT3+Krl27RkREkyZN4pBDDol99903IiKGDx8ey5Yty2VUAAAAIGWpFDHl5eVpfMwa4eWXX46IiL59+0aHDh1WOj5o0KDIZDIxe/bs+PDDD1NOBwAAAORSKkVMp06d4k9/+lNMmTIljY/LmUWLFsWECRMiImLbbbetdKZ9+/bRqVOniIj497//nVo2AOqPL774Ii688MI49thjY8iQIXHXXXfFokWLch0LAIBqSKWImTZtWlx++eWx0UYbxYABA+KJJ56ol6tkiouLY/lu4BtssMEq55Yf+/rrr1PJBUD9MGfOnDjooINik002iUsuuSTuvPPOuPnmm+NXv/pVFBYWxq233prriAAArEYqRUyrVq0iSZIoKyuLp59+Og444IDo3LlzXHzxxVFcXJxGhFTMnj274nXbtm1XOdeuXbuI+P4HagCojnnz5kW/fv3ikUceqfT4nDlz4oQTTohhw4alnAwAgJpIbUXMrbfeGr17944kSSJJkpg6dWpccskl0bVr19h///3jqaeeqlhNUlctXry44nWTJk1WObf8mGXkAFTXxRdfHP/6179WO3f22WdX3CYLAMCaJ5UiplmzZnHcccfFW2+9Fe+//36cdNJJ0bJly4pVMk8++WTst99+0aVLl7jsssti6tSpacTKmeoWTsOGDYuioqJKv6ZNm5bllACsKRYuXBi33XZbtWbLy8vjxhtvzHIiAAB+rNS3r95qq63i+uuvj2nTpsUtt9yywiqZ4uLiuPDCC6NLly4xaNCgePbZZ9OO95M0bdq04vWSJUtWObf8WLNmzaq83ty5c6OkpKTSr/r4jB0AKvfqq6/Gt99+W+35UaNGZS8MAAA/SepFzHLNmjWL448/vtJVMsuWLYvHHnss9tlnn+jatWtceeWVMX369FxFrbYfPhfmh8+L+W/Lj7Vp06bK67Vq1SoKCwsr/crLy9lvHQApq+q/KZXxDDIAgDXXGvGn+eWrZKZOnRq33nprbLfddhWrZL766qu44IILonPnznHYYYfFmDFjch13lYqKiiKTyUREVLlV9/Jjy7exXpUzzjgjiouLK/1ab731ai84AGu01RX3P3UeAID0rBFFzHJ5eXmRl5dXUWYs/79JksTSpUtj5MiR0bdv39h3332rLDpypVmzZrHJJptERMS4ceMqnZk1a1bFttVbbbVVatkAqLv69u0brVq1qvb8wIEDs5gGAICfYo0oYj788MM47bTTYr311ovjjz8+xo4dGxHfFzC77LJLXH755dGzZ8+KVTLPPPNM9O7du6LQWJP07ds3Ir6/n3/mzJkrHX/kkUciSZJo27atIgaAamnRokUcd9xx1ZrNZDJx8sknZzkRAAA/Vs6KmMWLF8edd94ZO+64Y2y99dZx/fXXR2lpaSRJEq1atYrTTjstPvnkk3jppZfivPPOi7Fjx8abb74Ze+yxRyRJEjNnzoyLL744V/FXae+994511lknFi9eHJdeeml8+eWXEfH9A3pHjhwZo0ePjoiII444IgoKCnIZFYA65KKLLoott9xytXNXXHFFbLrppikkAgDgx8gk1d1LuZZ89NFHcdNNN8W9994bpaWlEfF/2zlvs802cfLJJ8cRRxwRzZs3X+U1DjjggHj88cejS5cuMWnSpFRy18TkyZPjggsuiLlz50ZERPPmzWPJkiVRVlYWERH77LNPnHTSST/pM4qKiqKkpCQKCwujuLj4J2cGYM33zTffxDHHHFNR6v9Qq1at4oorrohTTjklB8kAAKiuVIqYxYsXx4gRI+Kmm26Kt99+OyL+r3xp2rRpHHrooXHyySfH9ttvX63rPfDAAxUrSr777rus5f4pvv322xg5cmS888478c0330TTpk1jww03jP79+8eOO+74k6+viAFouMaPHx933313fPXVV9GkSZPYcccd4/DDD4+11lor19EAAFiNVIqYtm3brrT6ZeONN44hQ4bEcccdV+PdHZ599tno379/ZDKZilUmDY0iBgAAAOqeVB5S8u2330ZERH5+fgwYMCB+85vfxC9+8Ysffb3CwsI45phjaikdAAAAQDpSWRFTWFgYv/71r+PEE0+MwsLCbH9cg2BFDAAAANQ9qayI+eqrr+wQBAAAADR4qWxfrYQBAAAASKmIAQAAAEARAwAAAJAa9wwBQD2SJElMnjw5Zs6cGa1bt45NNtkk8vL8vQsAwJrCT2YAUA+Ul5fHnXfeGT179owNN9wwtt9++9hss83iZz/7WQwdOjQWL16c64gAAERK21dT+2xfDcByy5Yti6OOOioeeOCBVc706dMnnnrqqWjVqlWKyQAA+G9WxABAHfc///M/VZYwERFjxoyJX/3qV+kEAgBglRQxAFCHlZaWxt///vdqzY4aNSo+/vjjLCcCAKAqihgAqMMeeOCBWLhwYbXnb7vttiymAQBgdRQxAFCHffbZZ1mdBwCgdiliAKAOy8/Pr9G8rawBAHLLT2MAUIf16NGjRvNbb711doIAAFAtihgAqMMOOuigaNu2bbVmM5lM/PrXv85yIgAAqqKIAYA6rFmzZvGnP/2pWrNDhgyJzp07ZzkRAABVUcQAQB3329/+Ns4777wqZw499NBqb3MNAED2KGIAoI7LZDJxxRVXxCuvvBKHHHJINGrUqOL9fv36xSOPPBIPPPBAxfsAAOROJkmSJNchqLmioqIoKSmJwsLCKC4uznUcANYgS5cujblz58Zaa60VTZo0yXUcAAB+oCDXAQCA2tWoUaNo165drmMAAFAJtyYBAAAApEQRAwAAAJASRQwAAABASjwjBgCgjlq4cGFMmDAhli1bFp07d4727dvnOhIAsBpWxAAA1DFTpkyJ0047LTp27Bhbb7119OrVKzp27BiDBg2KN998M9fxAIAq2L66jrJ9NQA0TOPGjYu99torZs2aVenxvLy8uOWWW+K4445LORkAUB1WxAAA1BGzZ8+OffbZZ5UlTEREeXl5nHDCCfHKK6+kmAwAqC5FDABAHXHrrbfGf/7zn9XOlZeXx1VXXZVCIgCgphQxAAB1xK233lrt2WeeeSa+/vrrLKYBAH4MRQwAQB1QXl4eEyZMqNE5NZ0HALJPEQMAUEfk5dXsR7eazgMA2ee/zgAAdUBeXl5stdVW1Z4vKCiI7t27ZzERAPBjKGIAAOqIIUOGVHt20KBBsc4662QxDQDwYyhiAADqiKOOOio23XTT1c41a9Yszj///BQSAQA1pYgBAKgjWrRoEc8880z87Gc/q3Jm1KhRNbqNCQBIjyIGAKAO6dKlS7z77rtxzTXXrLA6pl27dnHWWWfFRx99FHvttVcOEwIAVckkSZLkOgQ1V1RUFCUlJVFYWBjFxcW5jgMA5Mi8efNi2bJl0bp1a7skAUAdUJDrAAAA/HgtW7bMdQQAoAb8tQkAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKCnIdAAAAqP/KysriqaeeisceeyzmzJkTbdu2jf333z/69+8f+fn5uY4HkBpFDAAAkFWvv/56HHXUUTF58uQV3r/11luja9euce+998bPf/7z3IQDSJlbkwAAgKwZM2ZM/OIXv1iphFnuyy+/jN133z3efPPNdIMB5IgiBgAAyIry8vI45phjYvHixVXOLV68OH71q19FeXl5SskAckcRAwAAZMWzzz4bEydOrNbs559/Hi+88EKWEwHknmfEAABQ75SXl8dzzz0Xr776aixatCiKiopi8ODBUVhYmOtoDcoTTzxRo/nHH388fvGLX2QpDcCaQREDAEC9Mnr06Pjtb38bkyZNWuH9P/zhDzF48OC4/vrro1WrVjlK17B8++23NZovLS3NThCANYhbkwAAqDcefPDBGDhw4EolTMT32yffe++9sfvuu8f8+fNzkK7hadu2bVbnAeoiRQwAAPXCjBkzqvXA1/feey8uuOCClFI1bIMGDcrqPEBdpIgBAKBeuO2222LRokXVmr399ttj3rx5WU7EbrvtFt27d6/W7JZbbhk777xzlhMB5J4iBgCAemHkyJHVnp03b14899xzWUxDREQmk4nhw4dHy5Ytq5xr1apV3H333ZHJZFJKBpA7ihgAAOqFmTNn1mh+1qxZWUrCD22zzTbxyiuvxFZbbVXp8R49esSrr74aW2+9dbrBAHLErkkAANQLNd0Jyc5J6dlmm23i/fffjzFjxsRjjz0Wc+bMiTZt2sQBBxwQO+64o5UwQIOiiAEAoF7YZ5994uOPP67WbKNGjWL33XfPciJ+KJPJxE477RQ77bRTrqMA5JRbkwAAqBeGDBkSeXnV+/H20EMPjXXXXTfLiQBgZYoYAADqhY022iguu+yy1c4VFhbGn//85xQSAcDKFDEAANQb5557bgwdOjSaNm1a6fFtttkmXnvttSgsLEw5GQB8L5MkSZLrENRcUVFRlJSURGFhYRQXF+c6DgDAGmX27Nlx5513xquvvhqLFi2KoqKiOProo6Nv374eDAtATili6ihFDAAAANQ9bk0CAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQU5DoAAABQ/02aNCluv/32+PTTTyOTycRWW20Vxx13XBQWFuY6GkCqMkmSJLkOQc0VFRVFSUlJFBYWRnFxca7jAABApRYtWhRDhgyJ4cOHx3//0SM/Pz9OPvnkGDZsWDRq1ChHCQHSZUUMAACQFUuXLo39998//vnPf1Z6vKysLP7xj3/EzJkz47777ou8PE9OAOo/3+kAAICsuPXWW1dZwvzQiBEjYtSoUSkkAsg9RQwAAFDrkiSJ6667rtrz119/fRbTAKw5FDEAAECt++qrr+Ljjz+u9vyLL74Y8+fPz2IigDWDIgYAAKh1paWlNT5n3rx5WUgCsGZRxAAAALWuXbt2NZrPZDLRunXrLKUBWHMoYgAAgFpXVFQUvXr1qvb8PvvsE82bN89iIoA1gyIGAADIit/+9rfVnj311FOzmARgzaGIAQAAsuLII4+Mww47bLVzp5xySuy1114pJALIPUUMAACQFXl5eTF8+PA466yzomnTpisdb9myZVx22WXxv//7v5HJZHKQsHKzZ8+Ojz/+OCZNmhRlZWW5jgPUM5kkSZJch6DmioqKoqSkJAoLC6O4uDjXcQAAoEqzZ8+O++67L8aPHx+ZTCZ69OgRgwcPjpYtW+Y6WoWXXnophg0bFqNHj47lf0zq1KlTDBkyJE477bRo1apVjhMC9YEipo5SxAAAQO256qqr4rzzzlvl8W7dusXzzz8f66+/foqpgPrIrUkAAECD9sADD1RZwkREjB8/PgYMGBDLli1LKRVQXyliAACABitJkrjkkkuqNfuvf/0rRo8eneVEQH2niAEAABqsN998M8aPH1/t+VtuuSWLaYCGQBEDAAA0WJ988kmN5mtS2gBURhEDAAA0WDXdNntN2mYbqJsUMQAAQIO15ZZb1mh+iy22yFISoKFQxAAAAA3WdtttFz169Kj2/JAhQ7KYBmgIFDEAAECDlclk4uKLL67W7I477hh77bVXlhMB9Z0iBgAAaND233//uO6666p8/su2224bjz76aOTl+SMU8NP4LgIAADR4v/nNb+Ltt9+OX/7yl9G4ceOK97t16xZ///vf4/XXX48OHTrkMCFQX2SSJElyHYKaKyoqipKSkigsLIzi4uJcxwEAgHpj8eLFMWvWrGjWrFm0bdvWTklArSrIdQAAAIA1SdOmTaOoqCjXMdY4ixcvjpEjR8a9994b06ZNi+bNm8duu+0WQ4YMiQ022CDX8aDOsCKmjrIiBgAASMvbb78dgwYNiqlTp650LC8vL/70pz/Fn/70J6uHoBqsiAEAAGCVPvzww/jFL34R8+bNq/R4eXl5XHTRRZEkSVx00UXphoM6yIqYOsqKGACA2vPJJ5/E448/HrNnz442bdrEwIEDY/PNN891LFgj7LHHHvHCCy+sdi4vLy8mTpwYXbp0yX4oqMMUMXWUIgYA4KebOHFinHjiifHiiy+udGzXXXeNm2++OTbZZJMcJIM1w2effRabbbZZtefPPffcuPLKK7OYCOo+21cDANAgTZgwIX7+859XWsJERLz88sux4447xqeffppyMlhzrOp/H6tSnZUz0NApYgAAaHCSJIlf/vKXMXPmzCrnZs2aFUceeWRYRE5DtXDhwhrNL1iwIEtJoP5QxAAA0OC888478c4771Rrdty4cfHmm29mORGsmTp27Fij+fXWWy9LSaD+UMQAANDgPPjgg1mdh/piv/32ixYtWlR7/ogjjshiGqgfFDEAADQ4q7sl6b/NmDEjS0lgzdaqVas4/vjjqzW7zjrrxODBg7OcCOo+RQwAAA1Oy5YtszoP9cmVV14ZO+64Y5UzzZs3j0ceeSSaN2+eUiqouxQxAAA0OHvttVdW56E+ad68efzzn/+MU089tdKiZeedd47XXnst+vTpk4N0UPdkEo+Ar5OKioqipKQkCgsLo7i4ONdxAADqlLKysthoo43iq6++Wu1sUVFRfPnll1FQUJBCMlizlZaWxmOPPRbTpk2L5s2bx2677RZbbLFFrmNBneK/JgAANDj5+flx6623Rv/+/WPZsmVVzt1yyy1KGPj/WrduHUcffXSuY0Cd5tYkAAAapD322COeeOKJaN++faXH27VrF4899ljsvffeKScDoD5T7QMA0GDtvffeMWXKlHjooYfi0UcfjTlz5kSbNm1i4MCBcdhhh0WzZs1yHRGAesYzYuooz4gBAACAusetSQAARETE4sWLY9GiReHv6QAgexQxAAANWGlpaQwbNiw23XTTaNasWTRv3jw6d+4cl156acyYMSPX8QCg3nFrUh3l1iQA4Kf6/PPPY6+99orJkydXerx9+/YxevTo6N27d7rBAKAesyIGAKABmjNnTuy5556rLGEiImbNmhX9+/evcgYAqBlFDABAA3TTTTfFV199tdq52bNnx9ChQ1NIBAANgyIGAKCBSZIkbrrppmrP33XXXbFo0aIsJgKAhkMRAwDQwHz77bc1ut1o3rx5MXHixOwFAoAGRBEDANDAlJWVpXIOALAyRQwAQAPTtm3baNeuXbXnGzVqFJ07d85iIgBoOBQxAAANTF5eXvzqV7+q9vxBBx0Ua6+9dtbyAEBDoogBAGiATjvttGjZsuVq5xo1ahRnnXVWCokAoGFQxAAANECdO3eOUaNGRYsWLVY5U1BQEHfffXf07NkzxWQAUL8pYgAAGqh+/frF2LFj45hjjokmTZpUvJ+fnx8HH3xwvPHGGzF48OAcJgSA+ieTJEmS6xDUXFFRUZSUlERhYWEUFxfnOg4AUMd9++238dlnn0WSJLHRRhtFhw4dch0JAOqlglwHAAAg99Zee+3Yfvvtcx0DAOo9tyYBAABARCxevDjuvvvu2H333aNr166x6aabxjHHHBNvvvlmuJmE2uLWpDrKrUkAAADfKy8vj+eeey5Gjx4dc+fOjfbt28dBBx0UP//5zyOTyVTrGh9++GEMGDAgpkyZUunxgw8+OO6+++5o1qxZbUanAVLE1FGKGAAAgIjXXnstjjvuuPjiiy9WOtazZ8+4++67o3v37lVeY/LkydG7d++YOXNmlXMHHnhgPPzww9Uud6Aybk0CAACgTnrllVdijz32qLSEiYh47733Yuedd45PP/20yutceOGFqy1hIiJGjRoV//znP39UVlhOEQMAAECds3Tp0vjlL38Z3333XZVzs2fPjuOPP36Vx7/55psYMWJEtT/3+uuvr/YsVEYRAwAAQJ3z2GOPVfsxDW+88UaMGzeu0mNjx46NJUuWVPtzX3vttWrPQmVsXw0AQL0we/bsuPPOO2PMmDGxZMmS2GCDDeLoo4+O7bffvl4+z+Gzzz6LO++8MyZNmhQFBQXRu3fvOProo6NNmza5jgapePTRR2s8v+222670/qJFi2p0nZrOw39TxAAAUKclSRJXX311XHjhhbF48eIVjt1www2x4447xoMPPhiFhYU5Sli7SktL49hjj41Ro0at8P59990X5557bpx//vlx/vnn18vyCX5o9uzZNZqfM2dOpe8XFRXV6Dr15XsJuePWJAAA6rRLLrkk/vCHP6xUwiz3xhtvRN++fWPGjBkpJ6t9CxYsiF/84hcrlTDLLV68OP7nf/4nzj777JSTQfpquvpr7bXXrvT9Xr16xaabblrt6xx11FE1+lz4b4oYAADqrPHjx8dFF1202rlJkybF//zP/2Q/UJZdffXVMXbs2NXODR06NN56660UEkHuDBw4sEbz+++/f6XvZzKZOP3006t1jRYtWsQJJ5xQo8+F/6aIAQCgzrrhhhuqPTt8+PD49ttvsxcmy5YuXRo33XRTteft7EJ9d+CBB8Z6661XrdnevXtHr169Vnn8xBNPjOOOO67KazRu3DhGjBhR7c+EVVHEAABQZz311FPVnl24cGG88sorWUyTXe+9915Mnz692vOPP/54FtNA7jVu3DjuvvvuaNSoUZVzrVu3jttuu63KmUwmE7fccktcc801lT4zZpdddomXXnop9t1335+UGSI8rBcAgDqstLQ0q/NrklU9aHRVSktLI0kSD+2lXttjjz3imWeeiWOPPTamTJmy0vEtttgi7r333thiiy1We628vLz4/e9/H6eeemq8+OKL8eWXX0bjxo1jhx12iG7dumUjPg2UIgYAgDqrffv2MWvWrBrN11Xt2rWr0XybNm2UMDQIu+++e0ycODFGjx4dTz31VJSWlkb79u3joIMOil133bXG/zsoKCiIPffcM0tpQREDAEAddtBBB8Xll19erdk2bdrErrvumt1AWbTttttGUVFRFBcXV2v+wAMPzHIiWHMUFBTE/vvvv8oH8sKaxDNiAACos4YMGbLa50Msd8IJJ0Tz5s2znCh7CgoK4uSTT672/CmnnJLFNAD8WIoYAADqrE6dOsWNN9642rnevXvHn/70pxQSZdeZZ54Zu+yyy2rnLrrooth2221TSARATSliAACo04477rh48MEHK93pJD8/P375y1/G888/Hy1atMhButrVpEmTeOqpp+KYY46J/Pz8lY63bt06rr322npROgHUV5kkSZJch6DmioqKoqSkJAoLC6t9nzAAQH22bNmyGD16dIwZMyYWL14cG2ywQRx++OFRWFiY62hZUVxcHPfcc09MmjQpGjVqFNttt10cdthhdfr2K4CGQBFTRyliAAAAoO5xaxIAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKSnIdYD6ZuLEifHZZ5/FpEmT4osvvogpU6bEsmXLomvXrnHttdfmOh4AAACQQ4qYWnbllVfGjBkzch0DAAAAWAMpYmpZQUFBdO3aNTbaaKPYaKON4vPPP4+XXnop17EAAACANYAippZdd911kZ+fX/HPpaWlOUwDAAAArEk8rLeW/bCEAQAAAPghRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkJIGv2vS008/HTfccMOPOrddu3Zxxx131HIiAAAAoL5q8EXMmmzYsGExbNiwSo9NmzYt5TQAAADAT9Xgi5g999wz+vXr96POzWQytZxmRXPnzo2SkpKsfgYAAABk05w5c+KOO+6I2267LSZOnBj5+fnRq1evOOmkk+Kggw6Kxo0b5zpiqhp8EZOfnx/5+fm5jlGpVq1aRWFhYaXHpk2bFuXl5SknAgAAgOobO3ZsDBgwIGbMmLHC+6+++mq8+uqr0atXrxg9enSss846OUqYPg/rXYOdccYZUVxcXOnXeuutl+t4AAAAsEqTJk2Kvfbaa6US5ofefffd2HfffWPJkiUpJsstRQwAAABQ66644oqYM2fOaufefffdeOCBB1JItGZQxNSyJUuWxNy5cyu+lrd65eXlK7y/YMGCHCcFAACA7CgtLY377ruv2vM/djfjuqjBPyOmtj388MOVNnlfffVV/PKXv6z45y222CKuuOKKNKMBAABAKj788MNYtGhRtefHjh0b5eXlkZdX/9eL1P9fIQAAAJCqpUuX1mi+vLy8wWxIk0mSJMl1CGquqKgoSkpKorCwMIqLi3MdBwAAACpMnjw5unbtWu35oqKi+Prrr7OYaM1hRQwAAABQq7p06RK77rprteePPfbY7IVZwyhiAAAAgFp3zjnnVGuuZcuWcdJJJ2U5zZpDEQMAAADUuv79+8ef//znKmeaN28eo0aNivXXXz+lVLmniAEAAACy4pxzzonHH388+vTps8L7+fn5cfDBB8ebb74Z/fr1y1G63PCw3jrKw3oBAACoSz799NOYOHFiFBQURI8ePaJjx465jpQTBbkOAAAAANR/m222WWy22Wa5jpFzbk0CAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUlKQ6wAAAABA3fLdd9/FBx98EPPmzYt11lknunfvHplMJtex6gQrYgAAAIBqmTt3blxwwQXRqVOn2G677WL33XePLbbYIrbYYou46aabory8PNcR13iZJEmSXIeg5oqKiqKkpCQKCwujuLg413EAAACo52bMmBH9+vWLjz76aJUzhx56aNx7771RUOAGnFWxIgYAAACoUpIkccghh1RZwkREPPjgg3HRRRelE6qOsiKmjrIiBgAAIDfef//9GD58eHz99dfRtGnT6Nu3bwwePDhatGiR62hZ88Ybb0SfPn2qNduyZcuYOnVqrLXWWllOVTdZEQMAAADVMH369OjXr19ss802MXTo0HjwwQfj7rvvjl//+tdRWFgYt9xyS64jZs3tt99e7dl58+bFyJEjs5imbnPTFgAAAKzGrFmzom/fvjFhwoRKj5eWlsaJJ54YCxcujN/97ncpp8u+L774okbzEydOzFKSus+KGAAAAFiN8847b5UlzA+deeaZMXny5OwHSllNH76bn5+fpSR1nyIGAAAAqjBnzpy49957qzVbVlYWN998c5YTpa9nz541mu/Vq1eWktR9ihgAAACowgsvvBCLFi2q9vzjjz+exTS5ccIJJ1R7tlOnTtG/f/8spqnbFDEAAABQhTlz5tRo/ttvv81OkBzaeOON48QTT6zW7OWXX+7WpCooYgAAAKAKbdu2zep8XfGPf/wjDj/88FUez2QyMWzYsDjqqKNSTFX3KGIAAACgCnvssUe0aNGi2vMHHnhgFtPkTqNGjeLee++Np556Kvbdd99o1KhRRES0atUqTjjhhPjXv/4Vp59+eo5TrvkySZIkuQ5BzRUVFUVJSUkUFhZGcXFxruMAAADUa7/5zW/ihhtuWO1co0aNYtKkSVFUVJRCqtxKkiS+++67aNKkSa6j1ClWxAAAAMBqXHHFFbH55puvdu66665rECVMxPe3Iilhak4RAwAAAKux9tprxyuvvBIDBw6s9Pg666wT9957b412F6JhKsh1AAAAAKgL2rVrF4899lhMmDAhhg8fHl9//XU0bdo0+vbtG4MGDYrGjRvnOiJ1gGfE1FGeEQMAAAB1j1uTAAAAAFKiiAEAAABIiSIGAAAAICUe1gsAAJADS5cujcmTJ8fSpUujsLAwWrdunetIQAqsiAEAAEjRjBkz4o9//GMUFhbGz372s9h8882jffv2MXjw4Bg7dmyu4wFZZtekOsquSQAAUPd8+umn8Ytf/GKVP8Pn5+fHLbfcEscee2zKyYC0WBEDAACQgvnz50f//v2r/IvUsrKy+PWvfx0vv/xyesGAVCliAAAAUnDPPffE5MmTVztXXl4el19+efYDATmhiAEAAEjBLbfcUu3Z559/PiZNmpTFNECuKGIAAABSMH78+BrNf/rpp1lKAuSSIgYAACAFmUwmq/NA3aCIAQAASMGWW25Z7dlMJhObb755FtMAuaKIAQAASMGQIUOqPbvPPvvEBhtskMU0QK4oYgAAAFJw+OGHx2abbbbauUaNGsUFF1yQQiIgFxQxAAAAKWjWrFk8/fTTsckmm6xypnHjxnHffffFDjvskGIyIE2KGAAAgJR06dIlxo4dG3/+85+ja9euFe+3aNEihgwZEu+//34cfPDBOUwIZFsmSZIk1yGouaKioigpKYnCwsIoLi7OdRwAAKCGkiSJWbNmxdKlS6N9+/bRuHHjXEcCUlCQ6wAAAAANUSaTiQ4dOuQ6BpAytyYBAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoKch0AAACA3Bs/fnzcdttt8dlnn0Umk4mtt946jj/++OjcuXOuo0G9kkmSJMl1CGquqKgoSkpKorCwMIqLi3MdBwAAqKPmzZsXxx57bDz88MMrHcvLy4sTTzwxrr322mjcuHEO0kH9Y0UMAABAA7VkyZLYd99947XXXqv0eHl5edx4440xe/bsuP/++yMvz9Mt4KfyvyIAAIAG6oYbblhlCfNDDz74YDz66KPZDwQNgCIGAACgASovL4/rr7++2vPXXXddFtNAw6GIAQAAaIAmTpwYEyZMqPb8Sy+9FIsXL85iImgYFDEAAAAN0Ny5c2s0nyRJzJs3L0tpoOFQxAAAADRA7du3r9F8QUFBtG7dOktpoOFQxAAAADRAG2ywQfTs2bPa8wMHDrSFNdQCRQwAAEADlMlk4rTTTqv2/KmnnprFNNBwKGIAAAAaqKOOOioOP/zw1c6dc845sdtuu6WQCOo/RQwAAEADlZeXF/fcc0+cd9550aJFi5WOt23bNoYNGxZXXXVVDtJB/ZRJkiTJdQhqrqioKEpKSqKwsDCKi4tzHQcAAKjjSktL44EHHojPPvssMplMbL311nHwwQdHs2bNch0N6hVFTB2liAEAAIC6x61JAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAAClRxAAAAACkRBEDAAAAkBJFDAAAAEBKFDEAAAAAKVHEAAAAAKREEQMAAACQEkUMAAAAQEoUMQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAACnJJEmS5DoENde4ceNYunRp5OXlxXrrrZfrOAAAAFCvdezYMd59992ffJ2CWshCDpSVlUVERHl5eZSUlOQ4DQAAAFAdipg6qmnTprF48eLIz8+PddZZJ9dxgEpMmzYtysvLrVwDqs33DeDH8L0D0tGxY8dauY5bkwCypKioKEpKSqKwsDCKi4tzHQeoA3zfAH4M3zugbvGwXgAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJTYvhogS84444yYO3dutGrVKtdRgDrC9w3gx/C9A+oW21cDAAAApMStSQAAAAApUcQAAAAApEQRAwAAAJASRQwAAABAShQxAAAAACmxfTVAiiZOnBifffZZTJo0Kb744ouYMmVKLFu2LLp27RrXXnttruMBOVJaWhojR46Md955J7755pto0qRJbLTRRrHPPvvEDjvskOt4wBpm/vz58dFHH8XEiRMrvubMmRMREX/84x9934A1nCIGIEVXXnllzJgxI9cxgDXIlClT4vzzz4/S0tKIiGjWrFksWLAg3n///Xj//fdjv/32ixNOOCHHKYE1ydtvv+0vcKAOU8QApKigoCC6du0aG220UWy00Ubx+eefx0svvZTrWECOLF26NC677LIoLS2Nzp07xxlnnBFdu3aNJUuWxOOPPx7Dhw+PJ554Irp27Rp77LFHruMCa5A2bdrEhhtuGBtttFFsuOGGcdVVV+U6ElBNihiAFF133XWRn59f8c/L/wYcaJieffbZmD59ejRt2jT+9Kc/RYcOHSIiokmTJnHIIYfEnDlz4sknn4zhw4fHrrvuGgUFfnQDInbdddfo169frmMAP5KH9QKk6IclDMDLL78cERF9+/atKGF+aNCgQZHJZGL27Nnx4YcfppwOWFP5eQLqNkUMAEAOLFq0KCZMmBAREdtuu22lM+3bt49OnTpFRMS///3v1LIBANmjiAEAyIHi4uJIkiQiIjbYYINVzi0/9vXXX6eSCwDILkUMAEAOzJ49u+J127ZtVznXrl27iIiKrWkBgLpNEQMAkAOLFy+ueN2kSZNVzi0/tmjRoqxnAgCyz6P3Aarw9NNPxw033PCjzm3Xrl3ccccdtZwIaGiW374EANQPVsQAAORA06ZNK14vWbJklXPLjzVr1izrmQCA7LMiBqAKe+65Z/Tr1+9HnZvJZGo5DVCf/PC5MLNnz47mzZtXOrf8WTJt2rRJJRcAkF2KGIAq5OfnR35+fq5jAPVQUVFRZDKZSJIkpkyZEkVFRZXOTZkyJSKiYhtrAKBuc2sSAEAONGvWLDbZZJOIiBg3blylM7NmzarYtnqrrbZKLRsAkD2KGACAHOnbt29ERLz66qsxc+bMlY4/8sgjkSRJtG3bVhEDAPWEIgYgRUuWLIm5c+dWfC1/CGd5efkK7y9YsCDHSYE07L333rHOOuvE4sWL49JLL40vv/wyIr7/XjFy5MgYPXp0REQcccQRUVDgjnLg//zw54a5c+dWvL9o0aIV3l+2bFkOUwKVyST2RARIzX333RcPPPDAaue22GKLuOKKK1JIBOTa5MmT44ILLqj4g1Tz5s1jyZIlUVZWFhER++yzT5x00km5jAisgQYOHFitucsvvzy23HLLLKcBasJfrQAA5FCXLl3iH//4R4wcOTLeeeed+Oabb6J58+ax4YYbRv/+/WPHHXfMdUQAoBZZEQMAAACQEs+IAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBAAAASIkiBgAAACAlihgAAACAlChiAAAAAFKiiAEAAABIiSIGAAAAICWKGAAAAICUKGIAAAAAUqKIAQAAAEiJIgYAAAAgJYoYAAAAgJQoYgAAAABSoogBANYY9913X2QymVhrrbVi+vTpuY6TdZlMJjKZTOy66665jrKCLl26RCaTiS5dulR6/JBDDolMJhO77bZbusEAoB5QxAAAa4R58+bFWWedFRERZ555ZnTs2DHHiViVK664IgoKCuLll1+O+++/P9dxAKBOUcQAAGuEv/71rzFt2rRo2bJl/P73v891HKqwySabxODBgyMi4vzzz4/vvvsux4kAoO5QxAAAOTd79uy45pprIiLixBNPjDZt2uQ4Eavzhz/8ISIivvzyy7j99ttznAYA6g5FDACQc9dff33MmzcvMplMDBkyJNdxqIYtttgidtxxx4iIGDZsWJSXl+c4EQDUDYoYACCnysvL48Ybb4yIiB133DE22WSTHCeiuo455piIiJgwYUI899xzOU4DAHWDIgYAiIiIt99+Oxo1ahSZTCbat28fxcXFq5z97rvvYtttt63Y9efmm2/+0Z/7z3/+M0pKSiIi4qCDDlrt/Ny5c2Po0KGx2267xbrrrhuNGzeOVq1axUYbbRQ77rhjnHHGGfHMM8+s9rklU6ZMif/5n/+JPn36RMeOHaNx48ax1lprRffu3eOoo46KBx54IBYvXlzpue+//35cccUVse+++0bXrl2jefPm0aRJk1hvvfVizz33jL/97W8xf/78mv/LqMLEiRPj3HPPje222y46dOgQjRs3jnXXXTd23333uPbaa2PhwoXVuk5xcXGcfvrpsemmm0bz5s2jffv2sf3228fQoUNj0aJFNcp04IEHRl7e9z9O3nXXXTX+NQFAg5QAAPx/V111VRIRSUQkffv2TZYtW1bp3O9+97uKuYMPPvgnfeaJJ55Yca333nuvytl333036dixY8V8VV9jx46t9BplZWXJ+eefnzRq1Gi117joootWOv/iiy+u1uevv/76ydtvv13lr2f57C677LLKmbKysuS8885LCgoKqvy8oqKi5N13363y85588smkZcuWq7zGFltskUyZMiXp3LlzEhFJ586dq7xekiTJlltumURE0rJly+S7775b7TwANHQFtd7sAAB11jnnnBMvvPBC/POf/4xXX301Lr300rjoootWmBk9enRce+21ERHRuXPnuOWWW37SZy6/paVZs2ax1VZbrXJu4cKFccABB8T06dMjIqJnz55x4IEHRmFhYbRo0SLmzJkT48ePj5deein+/e9/r/I6Rx55ZDzwwAMREZHJZGKvvfaKPffcM9Zff/1YunRpTJw4MV577bV45ZVXIkmSSnPk5+dH7969o0+fPvGzn/0s1l577SgrK4vJkyfHk08+GWPGjImpU6dG//794/33349OnTr96H8/xxxzTAwfPjwiIlq3bh2HHnpo9O7dO9Zee+2YMWNGPPXUU/HUU09FcXFx7LbbbvHuu+/Gz372s5Wu89Zbb8WgQYMqVgr17NkzjjjiiCgsLIypU6fGfffdF++++24ccsghsXTp0mrn22GHHeLDDz+MefPmxZgxY2LXXXf90b9WAGgQct0EAQBrlunTpyfrrrtuEhFJfn5+8sorr1QcKykpSdq3b59ERFJQUJCMGTPmJ33Wf/7zn4rVGDvttFOVsw899FDF7Jlnnlnl7Mcff5zMmDFjpff/9re/VVyjQ4cOyeuvv77KaxQXFydvvfXWSu+/8847SUlJSZWfP3z48CQvLy+JiOT4449f5VysZkXMjTfeWDGz++67V/prSpIkefTRRytW+PTp02el48uWLUu6detWca3f/va3SVlZ2QozZWVlyemnn77CCpnqrIi5/fbbK+avvPLK1c4DQEPnGTEAwArWXXfduPvuuyOTyURZWVkceeSRMXv27CgvL4+jjjoqZs2aFRERF110UcWuOT/WBx98UPG6W7duVc5+8cUXFa+PO+64Kme7d+8eHTp0WOG9hQsXxuWXXx4REXl5efHoo49Gnz59VnmNwsLC2H777Vd6f7vttov111+/ys8/8sgj48gjj4yIiPvvv79GK0yWW7JkSVx88cUREdGpU6d47LHHVvo1Lbf//vvHOeecExERY8aMibfffnuF46NHj47x48dHRESvXr3immuuqXi2y3J5eXkxdOjQ6N27d41y/vD37Ye/nwBA5RQxAMBK9txzzzj77LMj4vuHux577LFxxRVXxIsvvhgREbvttlucd955P/lzJk+eXPG6bdu2Vc62aNGi4vV7771X4896+umnY+bMmRHxfXHxU0uk1Vle8ixcuPBHFRTPPfdcTJs2LSIiTjnllFhrrbWqnD/66KMrXj/77LMrHHvkkUcqXp9++ukrlTDLZTKZOPPMM2uUs127dhWvf/j7CQBUzjNiAIBKXXbZZfHKK6/E22+/HY8//ng8/vjjERHRvn37GD58+Cr/MF8Ts2fPrni9uiJmjz32iEwmE0mSxMknnxwTJkyIwYMHR/fu3av1Wa+99lrF6wMOOOBH5V0uSZJ4+umnY+TIkfHee+/F119/HfPmzYtly5ZVOl9cXBw9e/as0We8+uqrFa+XLFkSjz76aJXzP1x188knn6xw7J133ql4vccee1R5nX79+tUg5Yq/bz/8/QQAKqeIAQAq1ahRo7j//vtjm222idLS0or377zzztXemlNdS5YsqXjdqlWrKme7desWF1xwQVx66aWxYMGCuPTSS+PSSy+NddZZJ3baaafo27dv7L333rHppptWev7XX39d8bq65U1lpk+fHgcffHCMGTOm2ufMnTu3xp/zw9UlF154YY3O/e9CZOrUqRHx/b/jddZZp8pz27VrF2uvvXZ8++231fqsH/6+1XT7awBoiBQxAMAqtW/fPtq1a1dRxHTs2DF22WWXWrt+kyZNKl5Xp6y45JJLonfv3nHVVVdVFCEzZsyIRx55pOL2mz59+sTQoUNXer7LD6+/utt8VmXZsmWx9957V+zK1KZNm9hvv/1iyy23jI4dO0azZs0iPz8/IiJefPHF+N///d+IiCgrK6vxZ1W3CKnM8p2Rlps/f35ERDRv3rxa57do0aLan//Df6/NmjWrXkAAaMAUMQDAKp188skxadKkin+ePn16nHLKKXHXXXfVyvV/+HyR6t7WMmDAgBgwYED85z//iddeey3efPPNeOWVV2LcuHGRJEmMGTMmdt5553jqqadWuA3nhys3lhcTNTVixIiKEqZfv34xatSoaNmyZaWzJSUlP+ozlvthWfT+++9Hjx49ftK1SktLY+HChdWaX7BgQbWvXZPbywAAD+sFAFbhzjvvjHvvvTciIrbYYouKW37uvvvuuO+++2rlM7p06VLxuqbPF1l33XXj4IMPjqFDh8a7774bkydPjoMPPjgivn9eyumnn77CfFFRUcXr/36GSnU999xzFa//9re/rbKEiYj48ssvf9RnLPfDvB999NFPulZhYWFEfL96ZfkDi1flm2++qdFqnG+++abi9Q9/PwGAyiliAICVfP7553HqqadGxPe3m4wYMSIeeOCBiluJTjrppBVWyvxYW221VcXrTz/99Cdda4MNNoj77ruvYovnjz76aIVCoW/fvhWvV/fg21WZPn16xeuNN964ytmnn376R33GcrvuumvF6x/uevRj/HBL6ueff77K2RdeeKFG116+LXZE/KRVOwDQUChiAIAVLFmyJAYPHlxxe8rf/va36N69e2y99dbx5z//OSIi5s2bF4cffvgKO/X8GB06dIgNN9wwIr7fknpVuw5VV6NGjSpWf0TECtfr379/tG/fPiIiHnvssXjjjTdqfP0fbqH9xRdfrHLugQce+NGrbpbr379/xYN1R40aVaOHA/+3Aw88sOL1NddcE0mSVDqXJElcc801Nbr2W2+9VfF6hx12+HEBAaABUcQAACs455xz4l//+ldERBx00EFx4oknVhz73e9+F/vuu29EfL8l8gUXXPCTP2/vvfeOiIiFCxfGhx9+uMq5v//97/HQQw+t9CDaH3rttdfigw8+iIjvb+1ZXrxEfP+g2vPPPz8iIsrLy+PAAw+sstyYOnVqvP322yu8t91221W8Pv/88yt9CO9LL70UQ4YMWeV1q6t58+ZxySWXRMT3BckBBxyw2tUqkydPjjPPPDNmzJixwvv77rtvdOvWLSIixo4dG2eeeWaUl5evMJMkSZxzzjkrFCvV8eabb0ZERMuWLWPHHXes0bkA0BBlklX9lQgA0OA88cQTMXDgwIiI6Ny5c7z//vux9tprrzAza9as6NGjR0ydOjUymUw899xzKzwUt6ZeeOGFivP/+te/xplnnlnp3K9+9au46667onXr1rHXXnvFtttuG0VFRVFQUBAzZsyIl156KZ588smKVTrXX399nHzyyStcI0mSOPTQQ2PkyJEREZHJZGLvvfeOPffcM9Zff/1YunRpfPnll/Haa6/Fiy++GOeff35cdNFFFefPmDEjNt5445g3b15ERGy++eZx9NFHR+fOnWPOnDnx7LPPxmOPPRZ5eXlx+OGHx/DhwyMi4o477ohf/epXK/2aMplMRETssssu8fLLL1f66x4yZEjcfPPNFf+8fJvuzp07R6NGjWL27Nkxfvz4eP311+O9996LiO+36v7hM2Yivl+5sssuu1QUWb169Yojjzwy1l9//Zg6dWrcd999MXbs2Nh+++3j66+/jqlTp0bnzp1X2Eb7v33zzTex7rrrRllZWQwePDjuv//+Vc4CAP9fAgCQJElxcXHSrl27JCKS/Pz85PXXX1/l7AsvvJDk5eUlEZF07NgxmTFjxo/+3LKysqRTp05JRCQ9evRY5dyxxx6bRMRqvxo1apRcdtllq7zOsmXLkrPOOivJz89f7bUuvvjilc5/6qmnkubNm6/ynGbNmiV33XVXcscdd1S8d8cdd1SaZfnxXXbZpcp/R3/961+r/MwffrVv3z6ZOXNmpdd54oknkpYtW67y3C233DKZMmVK0rlz5yQiks6dO1eZ65Zbbqk49+mnn65yFgD4nluTAIAoLy+PX/7ylxU74Fx44YXRp0+fVc7vvvvuce6550bE9w+w/dWvfrXK546sTl5eXsXKlX//+98Vtxb9txtvvDFeeeWVuOiii2KPPfaITp06RdOmTaOgoCDatm0b22+/ffzhD3+Ijz/+uOIWpMrk5+fH1VdfHZ9++mmcc8450bNnz2jbtm3k5+fHWmutFd27d49jjjnm/7V3tyqRhnEYh+80M0VEy6AgjuAUzSaDSUHwBCwWwep8pDmBYYTRKngAJqvnYJ0yzWCZahCbYZPLLurusizPq8t19Rf+zxt/PB+5ubnJYDB48/3+/n4mk0lOTk6ytraWWq2W+fn5bGxspNfrZTKZ5Ojo6K/+xUf6/X4eHh5ydnaW3d3dLC8vp16vp16vp9lsZnt7O51OJ7e3t5nNZj8dyfrRwcFBptNpTk9P026302g0sri4mK2trYzH49zd3WVlZeWP53p9xnx9fT17e3v/ZK0A8L9zNAkAqNzj42NWV1fz9PSUbrebi4uLqkfiN6bTaTY3N5O8fwwMAHifHTEAQOUWFha+3w1zdXX15rJZPp/XF7RarVaOj48rngYAvg4hBgD4FHq9XpaWlvL8/JzRaFT1OPzC/f19rq+vkyTD4TC1Wq3iiQDg6xBiAIBPYW5uLufn50mSy8vLzGaziifiI4PBIC8vL9nZ2cnh4WHV4wDAl+KOGAAAAIBC7IgBAAAAKESIAQAAAChEiAEAAAAoRIgBAAAAKESIAQAAAChEiAEAAAAoRIgBAAAAKESIAQAAAChEiAEAAAAoRIgBAAAAKESIAQAAAChEiAEAAAAoRIgBAAAAKESIAQAAAChEiAEAAAAoRIgBAAAAKESIAQAAAChEiAEAAAAoRIgBAAAAKESIAQAAAChEiAEAAAAo5BuSlqzaVIdZZgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 429,
       "width": 561
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8765699779082)>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dummy_data = pd.DataFrame(np.loadtxt(\"data/dummy.csv\"), columns=[\"x_1\", \"y\"])\n",
    "\n",
    "dummy_data = dummy_data.assign(\n",
    "    x_1s=lambda df: (df.x_1 - df.x_1.mean()) / df.x_1.std(),\n",
    "    x_2s=lambda df: df.x_1s ** 2,\n",
    "    y_s=lambda df: (df.y - df.y.mean()) / df.y.std(),\n",
    ")\n",
    "\n",
    "(\n",
    "    gg.ggplot(dummy_data, gg.aes(\"x_1s\", \"y_s\"))\n",
    "    + gg.geom_point()\n",
    "    + gg.theme_classic()\n",
    "    + gg.labs(x=\"x (scaled)\", y=\"y (scaled)\")\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- example: compare linear and polynomial data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [epsilon, beta, alpha]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:05<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 14 seconds.\n",
      "/usr/local/Caskroom/miniconda/base/envs/bayesian-analysis-with-python_e2/lib/python3.9/site-packages/pymc3/sampling.py:1707: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='2000' class='' max='2000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [2000/2000 00:02<00:00]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with pm.Model() as model_l:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sd=1)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sd=10)\n",
    "    epsilon = pm.HalfNormal(\"epsilon\", 5)\n",
    "\n",
    "    mu = alpha + beta * dummy_data[\"x_1s\"]\n",
    "\n",
    "    y_pred = pm.Normal(\"y_pred\", mu=mu, sd=epsilon, observed=dummy_data[\"y_s\"])\n",
    "    trace_l = pm.sample(2000)\n",
    "    postpredcheck_l = pm.sample_posterior_predictive(trace_l, 2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "arviz.data.io_pymc3 - WARNING - posterior predictive variable y_pred's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.\n"
     ]
    }
   ],
   "source": [
    "az_l = az.from_pymc3(trace=trace_l, model=model_l, posterior_predictive=postpredcheck_l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [epsilon, beta, alpha]\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='6000' class='' max='6000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [6000/6000 00:07<00:00 Sampling 2 chains, 0 divergences]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 2 chains for 1_000 tune and 2_000 draw iterations (2_000 + 4_000 draws total) took 14 seconds.\n",
      "/usr/local/Caskroom/miniconda/base/envs/bayesian-analysis-with-python_e2/lib/python3.9/site-packages/pymc3/sampling.py:1707: UserWarning: samples parameter is smaller than nchains times ndraws, some draws and/or chains may not be represented in the returned posterior predictive sample\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <div>\n",
       "        <style>\n",
       "            /* Turns off some styling */\n",
       "            progress {\n",
       "                /* gets rid of default border in Firefox and Opera. */\n",
       "                border: none;\n",
       "                /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
       "                background-size: auto;\n",
       "            }\n",
       "            .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
       "                background: #F44336;\n",
       "            }\n",
       "        </style>\n",
       "      <progress value='2000' class='' max='2000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
       "      100.00% [2000/2000 00:02<00:00]\n",
       "    </div>\n",
       "    "
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with pm.Model() as model_p:\n",
    "    alpha = pm.Normal(\"alpha\", mu=0, sd=1)\n",
    "    beta = pm.Normal(\"beta\", mu=0, sd=10, shape=2)\n",
    "    epsilon = pm.HalfNormal(\"epsilon\", 5)\n",
    "\n",
    "    mu = alpha + pm.math.dot(beta, dummy_data[[\"x_1s\", \"x_2s\"]].to_numpy().T)\n",
    "\n",
    "    y_pred = pm.Normal(\"y_pred\", mu=mu, sd=epsilon, observed=dummy_data[\"y_s\"])\n",
    "    trace_p = pm.sample(2000)\n",
    "    postpredcheck_p = pm.sample_posterior_predictive(trace_p, 2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "arviz.data.io_pymc3 - WARNING - posterior predictive variable y_pred's shape not compatible with number of chains and draws. This can mean that some draws or even whole chains are not represented.\n"
     ]
    }
   ],
   "source": [
    "az_p = az.from_pymc3(trace=trace_p, model=model_p, posterior_predictive=postpredcheck_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 455,
       "width": 561
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (8765700585232)>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_new = np.linspace(dummy_data.x_1s.min(), dummy_data.x_1s.max(), 100)\n",
    "\n",
    "alpha_l_post = trace_l[\"alpha\"].mean()\n",
    "beta_l_post = trace_l[\"beta\"].mean(axis=0)\n",
    "y_l_post = alpha_l_post + beta_l_post * x_new\n",
    "ppc_l = pd.DataFrame({\"x\": x_new, \"y\": y_l_post, \"model\": \"linear\"})\n",
    "\n",
    "alpha_p_post = trace_p[\"alpha\"].mean()\n",
    "beta_p_post = trace_p[\"beta\"].mean(axis=0)\n",
    "y_p_post = alpha_p_post + beta_p_post[0] * x_new + beta_p_post[1] * (x_new ** 2)\n",
    "ppc_p = pd.DataFrame({\"x\": x_new, \"y\": y_p_post, \"model\": \"polynomial\"})\n",
    "\n",
    "\n",
    "(\n",
    "    gg.ggplot(pd.concat([ppc_l, ppc_p]))\n",
    "    + gg.aes(\"x\", \"y\")\n",
    "    + gg.geom_line(gg.aes(color=\"model\"))\n",
    "    + gg.geom_point(gg.aes(x=\"x_1s\", y=\"y_s\"), data=dummy_data)\n",
    "    + gg.scale_color_brewer(type=\"qual\", palette=\"Set1\")\n",
    "    + gg.theme_classic()\n",
    "    + gg.theme(legend_position=(0.8, 0.6))\n",
    "    + gg.labs(\n",
    "        x=\"x (scaled)\",\n",
    "        y=\"y (scaled)\",\n",
    "        title=\"PPC of linear and polynomial models on dummy data\",\n",
    "    )\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Occam's razor – simplicity and accuracy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Information criteria\n",
    "\n",
    "- tools for measuring how well the model fits the data given the complexity of the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model comparison with PyMC3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Computed from 4000 by 33 log-likelihood matrix\n",
       "\n",
       "          Estimate       SE\n",
       "elpd_waic   -13.90     2.65\n",
       "p_waic        2.46        -"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.waic(az_l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Computed from 4000 by 33 log-likelihood matrix\n",
       "\n",
       "          Estimate       SE\n",
       "elpd_waic    -4.15     2.35\n",
       "p_waic        2.71        -"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.waic(az_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Caskroom/miniconda/base/envs/bayesian-analysis-with-python_e2/lib/python3.9/site-packages/arviz/stats/stats.py:149: UserWarning: \n",
      "The scale is now log by default. Use 'scale' argument or 'stats.ic_scale' rcParam if you rely on a specific value.\n",
      "A higher log-score (or a lower deviance) indicates a model with better predictive accuracy.\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>rank</th>\n",
       "      <th>loo</th>\n",
       "      <th>p_loo</th>\n",
       "      <th>d_loo</th>\n",
       "      <th>weight</th>\n",
       "      <th>se</th>\n",
       "      <th>dse</th>\n",
       "      <th>warning</th>\n",
       "      <th>loo_scale</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>polynomal_model</th>\n",
       "      <td>0</td>\n",
       "      <td>-4.188210</td>\n",
       "      <td>2.747927</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.998221</td>\n",
       "      <td>2.566588</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>linear_model</th>\n",
       "      <td>1</td>\n",
       "      <td>-13.922071</td>\n",
       "      <td>2.487777</td>\n",
       "      <td>9.733861</td>\n",
       "      <td>0.001779</td>\n",
       "      <td>2.156212</td>\n",
       "      <td>2.657495</td>\n",
       "      <td>False</td>\n",
       "      <td>log</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                rank        loo     p_loo     d_loo    weight        se  \\\n",
       "polynomal_model    0  -4.188210  2.747927  0.000000  0.998221  2.566588   \n",
       "linear_model       1 -13.922071  2.487777  9.733861  0.001779  2.156212   \n",
       "\n",
       "                      dse warning loo_scale  \n",
       "polynomal_model  0.000000   False       log  \n",
       "linear_model     2.657495   False       log  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.compare({\"linear_model\": az_l, \"polynomal_model\": az_p})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/Caskroom/miniconda/base/envs/bayesian-analysis-with-python_e2/lib/python3.9/site-packages/arviz/stats/stats.py:149: UserWarning: \n",
      "The scale is now log by default. Use 'scale' argument or 'stats.ic_scale' rcParam if you rely on a specific value.\n",
      "A higher log-score (or a lower deviance) indicates a model with better predictive accuracy.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='Log'>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 152,
       "width": 440
      },
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_compare(az.compare({\"linear_model\": az_l, \"polynomal_model\": az_p}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayes factors[sic]\n",
    "\n",
    "- **Bayes factor**\n",
    "\n",
    "$$\n",
    "BF = \\frac{\\Pr(y | M_0)}{\\Pr(y | M_1)}\n",
    "$$\n",
    "\n",
    "- if $BF > 1$ than model 0 is better at explaining the results than model 1\n",
    "    - 1-3: weak\n",
    "    - 3-10: moderate\n",
    "    - 10-30: strong\n",
    "    - 30-100: very strong\n",
    "    - \\>100: extreme\n",
    "- BF are frequently criticized as  hypothesis tested\n",
    "    - inference based model comparison is generally preferred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Regularizing priors\n",
    "\n",
    "- **regurlaization**: adding a bias to reduce a generalization error without affecting the ability of the model to fit\n",
    "    - common way is to penalize larger parameter values\n",
    "    - a Bayesian method is to use a tighter prior distribution\n",
    "    - a Laplace distribution has a peak at 0 and can be used to introduce sparsity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: 2021-01-04\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.9.1\n",
      "IPython version      : 7.19.0\n",
      "\n",
      "Compiler    : Clang 10.0.0 \n",
      "OS          : Darwin\n",
      "Release     : 20.1.0\n",
      "Machine     : x86_64\n",
      "Processor   : i386\n",
      "CPU cores   : 4\n",
      "Architecture: 64bit\n",
      "\n",
      "Hostname: JHCookMac.local\n",
      "\n",
      "Git branch: master\n",
      "\n",
      "seaborn   : 0.11.1\n",
      "pymc3     : 3.9.3\n",
      "arviz     : 0.10.0\n",
      "numpy     : 1.19.4\n",
      "matplotlib: 3.3.3\n",
      "plotnine  : 0.7.1\n",
      "pandas    : 1.2.0\n",
      "scipy     : 1.6.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -d -u -v -iv -b -h -m"
   ]
  }
 ],
 "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": "3.9.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}