Chapter_2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "f594e492-721f-4d23-ae44-2192832c2f67",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stats\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from plotnine import ggplot, aes, facet_grid, labs, geom_point, theme_dark, geom_line, theme, geom_histogram, geom_density\n",
    "import pandas as pd\n",
    "import arviz as az\n",
    "from tqdm import tqdm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9f55d46c-e7a4-4e81-9568-30e4095c2e81",
   "metadata": {},
   "source": [
    "# Posterior via grid approximation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "id": "20ef6468-7b39-4909-9e29-327c14db0db2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def posterior_grid_approx(points=5, success=6, tosses=9, prior=lambda x:1):\n",
    "    \"\"\"\n",
    "    success ~ Binomial(n,p)\n",
    "    p ~ Uniform(0,1)\n",
    "    \"\"\"\n",
    "    grid = np.linspace(0, 1, points)\n",
    "    likelihood = stats.binom.pmf(success, tosses, grid)\n",
    "    unnormalized_posterior = likelihood*prior(grid) \n",
    "    normalized_posterior =  unnormalized_posterior / sum(unnormalized_posterior) \n",
    "    return pd.DataFrame({'param_value':grid, 'p':normalized_posterior})\n",
    "\n",
    "def plot_posterior(posterior):\n",
    "    return (ggplot(posterior, aes(x='param_value', y='p'))\n",
    "            + geom_line()\n",
    "            + geom_point())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "id": "423b7529-ee33-4c21-a3e4-5fba2cba9d17",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314642469)>"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "id": "54235eca-1e9c-4783-b1c1-153622d794ba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314567473)>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(50))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ca26c02c-2845-4f58-a150-d08b4048dc2f",
   "metadata": {},
   "source": [
    "# Quadratic Approximation"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "563e250a",
   "metadata": {},
   "source": [
    "- Under general assumptions, near the mode the posterior is approximately Gaussian. Log-posterior is then a quadratic function we can fit via an optimization procedure.\n",
    "- Uniform prior + Binomial likelihood leads to a Beta Posterior, which kind of matches the beta's parameters interpretation as 'fake trials'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e4d96569",
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "e362deac",
   "metadata": {},
   "source": [
    "# Metropolis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "8e36d169",
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def posterior_metropolis_approx(n_samples=5, success=6, tosses=9):\n",
    "    \"\"\"\n",
    "    Using a half normal distribution as \n",
    "    proposal\n",
    "    \"\"\"\n",
    "    rejections = 0\n",
    "    old_sample = np.array([0.5])\n",
    "    samples = np.zeros(n_samples)\n",
    "    for i,_ in enumerate(range(n_samples)):  \n",
    "        new_sample = stats.norm.rvs(old_sample, 0.1, size=1, random_state=None)\n",
    "        if new_sample < 0:\n",
    "            # this turns normal into half normal.\n",
    "            new_sample = abs(new_sample)\n",
    "        if new_sample > 1:\n",
    "            new_sample = 2-new_sample\n",
    "        p_new_sample = stats.binom.pmf(success, n=tosses, p=new_sample)\n",
    "        p_old_sample = stats.binom.pmf(success, n=tosses, p=old_sample)\n",
    "        # accept with prob p(p_new)/p(p_old)\n",
    "        if stats.uniform(0,1).rvs() < (p_new_sample/p_old_sample):\n",
    "            samples[i] = new_sample\n",
    "            old_sample = new_sample\n",
    "        else:\n",
    "            samples[i] = old_sample\n",
    "            rejections+=1\n",
    "    print(rejections)\n",
    "    return samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "id": "83c7f0fc",
   "metadata": {
    "jupyter": {
     "outputs_hidden": false
    },
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "216\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (316453105)>"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(ggplot(pd.DataFrame({'posterior_samples':posterior_metropolis_approx(1000)}), aes(x='posterior_samples'))\n",
    "+ geom_density()\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "65be5fc4-399b-4826-bae5-4ec5d5542ba4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12dcf3640>]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=np.linspace(0,1,100)\n",
    "success = 6\n",
    "fail = 3\n",
    "plt.plot(x, stats.beta.pdf(x, success+ 1, fail + 1), \"C1\", label=\"True posterior\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "50988d51",
   "metadata": {},
   "source": [
    "- Different scales for the proposal may lead to different shapes of the posterior (exploration/exploitation)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4b7d3b9f",
   "metadata": {},
   "source": [
    "# End of chapter problems"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d7e19f2-a0f5-47f6-b7b9-adf32208d3d9",
   "metadata": {},
   "source": [
    "## 2M1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "7ccb338f-122e-4039-a2d9-dc41d0ad532a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (316478088)>"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(100, 3, 3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "d7fa41ac-e00a-424a-a8ff-a7de9fc12391",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314704589)>"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(100, 3, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "5bb73a72-8863-424e-8464-83104e2e5e86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314235124)>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(100, 5, 7))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0f85f639-923c-454c-b128-bdc816c75ad3",
   "metadata": {},
   "source": [
    "## 2M2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "5a45caea-f1bf-41c2-8890-ee606401140e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314603894)>"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(100, 3, 3, lambda x: np.array([0 if xi<0.5 else 1 for xi in x])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "id": "bd5c8d87-da5f-4ee2-bc10-1cb848cfd921",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (316393960)>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(100, 3, 4, lambda x: np.array([0 if xi<0.5 else 1 for xi in x])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "id": "5f662609-90c2-4bf4-83a3-85b546e548e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Jz6LT6Qo4jX3w9PTEoEGDsHTpUvnZWeQ4WHaIiOyMWq1Gs2bNzJ7y7eTkhKpVq8LHx0dgMts2fPhw/PXXXzh06JDoKFTAWHaIiOzQnDlzoFKp5NflypXDmjVrzJaROX9/f3Tr1g0zZ85EZGQkDh8+zFkeB8ETlImI7FBkZCRCQkKwc+dOpKenIyAgwGymh3IyGo24c+cOfvvtN3z88ccwGAzo2bMnlixZwpKocNwziIjszLVr17BixQpMnz4dwcHBCAwMZNHJhXXr1uHEiRMAHp/bZDKZsGXLFmzdulVwMrI2zuwQEdmB+Ph4zJkzB1evXkVCQgKqV6+Otm3bio5lVy5evJjjsJVarcbFixfRrVs3MaGoQLDsEBHZuMTERLRs2RIPHz6EwWAAAKSmpuLhw4fw9vYWnM5+8K7KjovznkRENm7NmjVISkqSiw7wuOxER0cLTGV/3nrrLRQpUgRarVZe5u/vj759+wpMRQWBZYeIyMbdv38fJpPpmcsp94oUKYIDBw5g0KBBaNKkCdRqNT755BOHfViqI2HZISKycdWrV8+xzGg0olq1agLS2LfixYtjzpw52Lx5M7p168Y7KjsIlh0iIhvXq1cv1KlTBwDg7OwMlUqFvn37omvXroKT2beBAwdi9+7dSEhIEB2FrIwnKBMR2Tij0Yh//vkHvXr1QosWLRAcHIx69eqJjmX3GjZsiJCQEERHR2PcuHGi45AVsewQEdm49evX4/79+5gzZw4KFy4sOo5iqFQqDBw4ECtXrsTYsWN5ryIF48gSEdkoSZKQmZmJBQsW4N1332XRsYLXX38dCQkJOHDggNnVbqQsLDtERDYmJSUFQ4YMQWBgIEJDQ5GYmIi33npLdCxFcnV1RbFixdCvXz+ULFkS/fv3R3JysuhYZGEsO0RENmbIkCHYvXs3dDod9Ho9DAYD5s6dKzqWIr333nv4559/AAAmkwk///wz3n77bcGpyNJYdoiIbMiDBw9w6NAh6PV6eZnRaER0dDSf0G1hRqMR27dvNzt8pdfrceDAAaSlpQlMRpbGskNEZEOeLDlPevoRB2QZzyuQLJbKwrJDRGRDihcvjipVqphdGaTVatGmTRuoVCqByZRHo9Ggbdu2Zo+PcHJyQuPGjXlXZYVRSayvSE5OhouLi8XfV6VSwdnZGTqdTrG/JTg5OSn2CgZHGD+AY2iLLl++jJo1a8qzOS1btsS6detQqFChHOsqefwA649hcnIyBg0ahF27dgEASpYsiZMnT6Jo0aIW/1zPwzHMv9z+7OZ9dgDodDrodDqLv69Go4GzszPS0tIUOwXt5eWFlJQU0TGswhHGD+AY2qItW7agaNGi2LVrFzw8PFCkSBGoVKpnjpOSxw+w/hiqVCp89913SE9Px/fff4+5c+c+92ttLRzD/Mtt2eFhLCIiG5Keno7FixdjzJgxCAoKQtGiRXn4qgC4u7ujZ8+eSE1NxcGDB0XHIQtj2SEisiFRUVEAHj+3iQqWl5cX2rVrh02bNomOQhbGw1hERIJdunQJc+fOxa1bt/Dnn3/ivffeg5ubm+hYDql3794YOnQoUlJS4OXlJToOWQhndoiIBLp69Spat26NnTt34uzZs8jIyMDGjRuRnp4uOppDeu211+Dh4YGffvpJdBSyIJYdIiKBli5dCp1OZ3bi5vXr17F7926BqRyXVqtFt27deChLYVh2iIgEunfvXo4rVDQaDe7fvy8oEfXu3RuHDx/GkiVLcODAAZhMJtGR6BWx7BARCVS7dm2zm9oBQFZWFmrUqCEmEGHz5s0AgFmzZuHNN9/EG2+88dw7W5N9YNkhIhLonXfeQVhYGIDHh1BUKhU++ugj1K1bV3Ayx/Tzzz9jxYoVAACDwQCj0YijR49i5cqVgpPRq+DVWEREAjk5OcFkMqFr167o2LEjwsLCUKlSJdGxHNaFCxfg7OyMzMxMeZler8f58+cFpqJXxbJDRCTQvn37cOXKFWzYsAElSpQQHcfh+fr65jiHSqvVws/PT1AisgQexiIiEmjRokV4/fXXWXRsRLdu3RASEmJ2HpWHhweGDx8uMBW9KpYdIqICZjKZcOfOHezbtw///e9/MWrUKNGR6H/c3d2xe/duDBs2TD5vasWKFQgICBCcjF4FD2MRERWgS5cuoW/fvrh58yaAx0/ZLlmypOBU9CRvb298+umnAIAWLVrg1KlTaNasmeBU9Co4s0NEVEAyMjLQu3dv3LlzR172zz//YObMmQJT0Yt07twZ27dvFx2DXhHLDhFRAbl06RLi4+PNToA1GAz8YWrDunTpgt9//x1XrlwRHYVeAcsOEVEBcXJ69pkDT99UkGxHmTJlULlyZRZSO8eyQ0RUQCpUqICKFStCrf7/b71OTk4YPHiwuFD0Up07d8a2bdtEx6BXwLJDRFRAnJyc5LvzajQaeHl5Yfz48Xj33XcFJ6MX6dy5My5cuIC///5bdBTKJ16NRURUgLZv347g4GDExsZCo9GIjkO5UL58eYSFheGnn37CmDFjRMehfGDZISIqIBkZGVixYgUmTJjAomNnmjRpguXLlyMpKQnNmjVD06ZNRUeiPOBhLCKiAvL9999DkiS88cYboqNQHpw9exZRUVFISEjA0qVL0atXLyxfvlx0LMoDlh0iIitLTEzEpUuXsGTJEgwdOhRubm6iI1EejB8/Hnq9HsDjh4JKkoQpU6bg4cOHgpNRbvEwFhGRlRiNRowfPx5r166Vl1WrVk1gIsqP69evw2QymS0zmUy4ffs2fHx8BKWivODMDhGRlfz73//Ghg0bzJaNGDECiYmJghJRfgQFBZndLgAA1Go1H/NhR1h2iIisZMeOHTAYDGbLsrKycObMGUGJKD8WLFgAZ2dnODs7AwBUKhU+/fRTzurYER7GIiKyEldX1xzLTCaT/EOT7EOtWrVw6NAh/PDDD9i5cyfc3d0xYsQI0bEoDzizQ0RkJUOHDoVKpZJfOzk5oVSpUqhfv77AVJQfZcqUwYQJEzB58mRcuHABGRkZoiNRHrDsEBFZSffu3dGkSRNotVq4u7ujQYMG2Lp1K9zd3UVHo3xq0qQJVCoVjhw5IjoK5QHLDhGRlSQlJeH06dP45ptvcP36dWzZsoUntdo5Nzc3NG/eHLt37xYdhfKAZYeIyErWrFkDHx8fdOrUSXQUsqC2bdtiz549OS5HJ9vFskNEZAV6vR7Lly/H8OHD4eTEa0GUpHXr1khMTMS5c+dER6FcYtkhIrKCn376CY8ePUL//v1FRyELK1asGOrUqYM9e/aIjkK5xLJDRGQhd+7cQY8ePRAaGoqRI0eifv368Pb2Fh2LrCD7UBbZB5YdIiILSEtLQ+fOnXH8+HGkpKRAr9fj4MGD2LFjh+hoZAXt2rXDxYsXcePGDdFRKBdYdoiILCA2Nha3b9+WHxgJAJIkYcWKFQJTkbWUK1cOvr6+GDVqFBYsWIC7d++KjkQvwLJDRGQBWVlZZjcQzMabzymPJEkYNWoU7t+/j9jYWHz55Zdo1qwZ7ty5IzoaPQfLDhGRBdSuXRtardZsmZOTE9q1aycoEVnLyZMnsWnTJkiSBADQ6XR49OgR5syZIzgZPQ/LDhGRBZQoUQLffvut2bLevXtj9OjRghKRtdy4cSNHsTUYDPj7778FJaKX4c0fiIgs5MaNG/Dz80N0dDSKFSuGEiVKiI5EVlC6dGmzc7MAQKvVoly5coIS0ctwZoeIyAKMRiOWL1+OIUOGoGrVqiw6ClanTh0MHDgQGo0GGo0GAFC0aFF89NFHgpPR87DsEBFZwP79+5GQkICBAweKjkIFYN68eVi+fDneeustAMDSpUvh5+cnOBU9D8sOEZEFREREoFevXvD19RUdhQqASqVC586dMWfOHFSpUgX//e9/RUeiF2DZISLKp4SEBERERGDy5Mk4cuQI3n77bdGRSICWLVviwIEDomPQC/AEZSKifPjrr7/Qvn17ZGRkwGAwAABOnTqFihUrCk5GBa1ly5ZYvHgxkpKSUKhQIdFx6Bk4s0NElA/jxo1DamoqdDodTCYTAGDChAm4d++e4GRU0OrWrQsPDw/ExMSIjkLPwbJDRJQPV65cgdFoNFtmNBr5rCQH5OTkhKZNm/JQlg1j2SEiyoeAgIBnPh7C399fQBoSrWXLlvj555/luyqTbWHZISLKh88//xxq9eNvoWq1Gmq1Gu+//z7LjoNq2bIlEhIS8Pvvv4uOQs/AE5SJiPKhXr16qFChAlQqFWrWrIkmTZqge/fuomORIP7+/qhcuTIOHDiAypUri45DT7GJspOamoolS5bgzJkzcHNzQ/fu3dG1a9dnrnvhwgUsW7YMCQkJCAoKwujRo1G6dGkAwIEDB7Bjxw7cuXMHrq6uqFevHt566y24ubkV5OYQkQM4e/YsLl68iOPHj6NMmTKi45ANaNGiBQ4cOIAxY8aIjkJPsYnDWBEREdDr9Vi1ahWmT5+OTZs24fTp0znWS05OxuzZs9GjRw9ER0ejadOmmDVrlvyMkqysLAwZMgRRUVH497//jfj4eKxataqgN4eIHMCKFSvQqlUrFh2S1ahRA8ePH8ekSZOwfft2nr9jQ4SXnczMTBw7dgwDBgyAu7s7QkJC0KZNG+zbty/HurGxsfD390eLFi2g1WrRtWtXSJKEc+fOAQA6dOiAKlWqQKvVwtvbG23btsUff/xRwFtEREr3zz//YMuWLbyJIMn+/vtvjBs3DiaTCZGRkRg2bBimTZsmOhb9j/Cyc/v2bUiShODgYHlZ6dKln3n55o0bN+RDVsDj23WHhIQ891LPCxcuICgoyPKhicihfffddwgJCUHz5s1FRyEbMW3aNKSnpwN4fAsCk8mEpUuX4tKlS4KTEWAD5+xkZmbC3d3dbJmHhwcyMjJyrJuRkQFPT89crXv8+HEcPnwY8+fPz/F38fHxiI+Pl1+7uLggICAgv5vwXNlPw83+rxKpVCrFbp8jjB/AMcytq1evYvTo0fjzzz+RkpKCIUOGwMlJ+LdQRY8fYD/74dWrV+U7aWfTaDS4desWKlWq9MKP5Rhan/A91dXVNUdZSU9Pf+ZJxW5ubnJzzpaWlpZj3XPnzuHrr7/Gxx9//MwSExERgRkzZsivJ0+ejNmzZ7/KZryQt7e31d7bFjg7O4uOYFVKHz+AY/gyiYmJaN++PR49eiT/QPvPf/6DoUOHon79+paI+EqUPn6A7e+HlSpVQlxcnFnhMRqNqFq1Knx8fF768RxD6xJedkqWLAng8SGq7ENOcXFxzzz8FBQUhD179sivJUnCtWvX0L59e3nZr7/+innz5mHixInPvfxvxIgR6NKli/zaxcUFDx8+tMj2PEmj0cDb2xvJyck57rSqFB4eHkhLSxMdwyocYfwAjmFurFu3DsnJyWY/yCRJwpIlS1C+fHlLRM03JY8fYD/74bRp03D48GGkpaVBp9NBpVJh9OjR8Pf3f+nPF45h/uWmSAI2UHZcXV3RqFEjREVFYdy4cUhMTMTevXsxduzYHOuGh4cjMjISBw8eROPGjbFz504Aj8+AB4DffvsNc+fOxQcffIBq1ao993P6+/ub3fjr3r17Vt2JjEajTe+kr0KSJMVuWzYljx/AMcyN9PT0HHdLNplMSEtLE/61c4TxA2x/PyxVqhQOHz6M9evXY+vWrdBqtZg6dWquMnMMrU942QEez7QsXrwYgwcPhpubG3r27InatWsDAPr06YNp06ahcuXK8Pb2xuTJkxEREYElS5YgKCgIU6ZMgVarBQCsX78e6enp+Pzzz+X3LlasGJYsWSJku4hIGRo2bCjf4iKbRqPhCcpkpkSJEnjvvfdQrlw5jBo1Cnq9Xv75RGKpJN4IwGpPKdZoNPDx8cHDhw8V29q9vLyQkpIiOoZVOML4ARzD3PrPf/6DiRMnyq9HjRqFTz755JnPxypISh4/wD73w6SkJJQvXx7btm3L1TldHMP88/X1zdV6NjGzQ0Rk6+7fv4/Q0FB8++238PPzQ4kSJURHIhtVqFAh1KxZE4cPH7aJE9jJBu6zQ0Rk63Q6HSIjI/H222+jevXqLDr0Us2aNcOhQ4dEx6D/YdkhInqJ7du3IyMjA6+//rroKGQnmjVrhtOnTyv68JQ9YdkhInqJFStWoG/fvjluakr0PHXq1IGLiwuOHTsmOgqBZYeI6Jl0Oh1+/fVXREdH47///S+GDh0qOhLZEWdnZzRq1IiHsmwET1AmInpKfHw8evbsib/++gvA4xuPPv0oAKKXadasGVavXi06BoEzO0REOQwfPhxxcXHya71ej379+oF36qC8aN68Of766y/cuXNHdBSHx7JDRPQEk8mEU6dOmc3kmEwmXL9+HYmJiQKTkb0pX748SpQowUNZNoBlh4joCSqVCq6urs/8O3d39wJOQ/YuODgYX375JaZOnSofFqWCx7JDRPQElUqFd999F2r1/3971Gq1vBqL8mzq1Kk4deoUrl+/jhUrVuC1117Dr7/+KjqWQ2LZISJ6yocffoiAgAB4eXkhKCgI77zzDhYsWCA6FtmRuLg4REREwGQyAQAMBgP0ej0+/vhjwckcE6/GIiJ6yoULF3Dr1i3ExsaibNmyouOQHXrWSckmkwm3bt0SkIY4s0NE9JQVK1agefPmLDqUb6VLl87xkFgnJyeUL19eUCLHxrJDRPSE+/fvY/PmzRg+fLjoKGTHAgICMHPmTKhUKmi1WgCAt7c3vvjiC8HJHBPLDhHRE9asWQN/f3+0bNlSdBSycyNGjMC2bdswduxYqFQqLFmyBCEhIaJjOSSes0NEDi8rKwvr1q1DXFwc1q1bh7Fjx0Kj0YiORQrQoEEDNGjQAPv378dvv/2GVq1aiY7kkDizQ0QOLSsrC126dMHHH3+Mb7/9FklJSdi2bRt0Op3oaKQgTZo0wdGjR0XHcFgsO0Tk0NasWYPffvsNer0eRqMRAHDx4kWsWbNGcDJSksaNG+PkyZPIzMwUHcUhsewQkUO7du3aM595df36dQFpSKnq168Pg8GA06dPi47ikFh2iMihBQUF5bhEWKVSISgoSFAiUiIPDw/UqlULR44cER3FIbHsEJFDGzBgAMLCwgAAarUaWq0WlSpVQv/+/QUnI6XheTvi8GosInJorq6u6Nq1K27duoXevXujdOnSGDBgAFxcXERHI4Vp0qQJFi1ahLS0NHh4eIiO41BYdojIoRmNRkRFRWHMmDEYPXq06DikYLVr14aTkxNOnDiBFi1aiI7jUHgYi4gc2r59+3D37l28+eaboqOQwrm6uqJu3bo8lCUAyw4RObQVK1agZ8+eKFKkiOgo5AAaN27Mk5QFYNkhIod1+fJlxMTEYNiwYaKjkINo0qQJzp8/j6SkJNFRHArLDhE5FJ1OhxkzZqBWrVpo164dgoKCUKlSJdGxyEE8evQIkiShVq1a6N27N27evCk6kkNg2SEih/L+++8jIiICN2/eREpKCm7duoV58+aJjkUO4Pjx4+jfvz8kSUJycjKOHj2Kjh07cpanALDsEJHDSE1NxYYNG6DX6+VlJpMJ33zzjcBU5ChWrVpldrdug8GAe/fuYffu3QJTOQaWHSJyGGlpac9cnpWVBZPJVMBpyNGkpqbmeDSJWq1+7r9LshyWHSJyGMWLF0dwcDDU6v//1ufk5IR69eqZLSOyhtdeew1OTua3tzMYDGjUqJGgRI6DezcROQyVSoV169aZ/cAJDQ3Ft99+KzAVOYohQ4aY3c9JrVZj6dKl8uNKyHpYdojI4eh0OnzzzTc4cOAADh06hBIlSoiORA5ArVZj/vz5OHPmDIYNG4by5cuje/fuomM5BJYdInIoK1asQHh4OHr37o1q1apBq9WKjkQOplSpUujTpw/+/PNPPHjwQHQch8CyQ0QOIykpCRs2bMDw4cNFRyEHV7VqVXh6euL48eOiozgElh0ichjR0dHw8fFB+/btRUchB+fk5IT69evj2LFjoqM4BD71nIgUTZIk/PHHH7h9+zYiIiIwZMiQHFfEEInQqFEjbN68WXQMh8CZHSJSLJPJhCFDhqBRo0Z4/fXXcevWLV5iTjajYcOGuHjxIh4+fCg6iuJxrycixVq1ahXWrFkDAPLN3D799FOcO3dOYCqix6pVqwZ3d3ceyioALDtEpFhHjx6FwWAwW+bi4oKTJ08KSkT0/7RaLerVq4fDhw+LjqJ4LDtEpFiFChWCRqMxW2Y0GuHl5SUoEZG5Ro0a4ciRI6JjKB7LDhEp1vDhw6FWq6FSqQA8vgKmWLFi6Nixo+BkRI81bNgQ586d45PPrYxlh4gUq3Llyjh69CjCwsKgUqnQpk0b7N69G97e3qKjEQEAatSoATc3N5w4cUJ0FEVj2SEiRatXrx4mTZoEX19frF69Gv7+/qIjEcm0Wi3Cw8N5krKV8WYTRKR4Op0Ozs7OomMQPVPp0qXxww8/oFChQujatSvKlCkjOpLicGaHiBSPZYds1fr167Fy5Ur8888/WLBgAZo1a8arBa0g32Xn3r17+Pjjj9GqVStUrlwZrVq1wpQpU5CYmGjJfEREr4xlh2xReno63n//ffkeUDqdDjqdDmPHjhWcTHnyVXZOnDiBcuXKYfHixShUqBCaNWuGQoUK4euvv0bZsmV5ohUR2RSWHbJFCQkJ0Ov1ZsskScKNGzcEJVKufJ2zM3LkSFSuXBk7d+40u6ohKSkJ7du3x6hRo3Dq1CmLhSQiehVZWVksO2Rz/Pz84OTkZHbjS5VKhYCAAIGplClfMzsXL17EpEmTcly+WahQIUyaNAkXLlywSDgiIkvQ6/UsO2RzPDw8MGfOHKhUKvnmlxqNBgsXLhScTHnyVXbKli2LR48ePfPvkpKSEBoa+iqZiIgsijM7ZKsGDx6MHTt2YMiQIVCr1Zg7dy4aN24sOpbi5Osw1rx58zBy5EiUKlUKzZo1k5cfOnQI06dPx+LFiy0WsCA4OzvDxcXF4u+bfddWDw8P+QQ0pXFyclLsrfcdYfwAxxhDSZLg7u6uyO1U8vgBjrEftmnTBi1atMDFixdx//59xY2nLYxhvsrOhx9+iKSkJLRo0QKFChVCsWLFkJiYiKSkJPj4+GDixImYOHEigMcb+euvv1o0tKVlnwFvaRqNBs7OzkhLS4PRaLT4+9sCLy8vpKSkiI5hFY4wfoDjjKFarVbkdip5/ADH2A+zx7BevXqIiYlR3HhacwxzO1GRr7JTu3ZtuakREdk6Xo1F9iA8PBzLli1DVlaWVY42OLJ8lZ3IyEgLxyAish6WHbIH9erVg06nw7lz51C/fn3RcRSFd1AmIsVj2SF74OnpiWrVqiE2NlZ0FMVh2SEixWPZIXsRHh7OsmMFLDtEpHgsO2QvwsPDcfLkSbMbDdKrY9khIsVj2SF7Ub9+faSmpuLixYuioygKyw4RKR7LDtmLIkWKoGLFijyUZWEsO0SkeCw7ZE8aNGjAsmNhLDtEpHh8XATZk/DwcBw/fhwmk0l0FMVg2SEixeODQMmehIeH48GDB7h8+bLoKIrBskNEiseZHbInkiTB09MTgwYNwoQJE3D//n3Rkeweyw4RKR7P2SF7cffuXbRo0QJpaWn4+++/sWbNGrRq1QrJycmio9k1lh0iUjydTsdnDZFdWL16NZKTk+Wng+v1ety9excbNmwQnMy+sewQkeLpdDpotVrRMYheKjEx8ZlPBuehrFfDskNEisfDWGQvqlatCpVKZbbMaDSiatWqghIpA8sOESkeyw7ZizfffBPt27eHWq2GWv34R3S/fv3QoUMHwcnsG8sOESkeyw7ZC7VajZUrV2LTpk3o2bMn/P398eWXX+aY7aG8cRIdgIjImgwGA0wmE8sO2Q2VSoUmTZrA19cXGzduxD///AM/Pz/RsewaZ3aISNF0Oh0AsOyQ3QkLC0PhwoVx/Phx0VHsHssOESlaVlYWAJYdsj9qtRr169dn2bEAlh0iUjTO7JA940NBLYNlh4gUjTM7ZM/Cw8Px+++/IykpSXQUu8ayQ0SKxrJD9qxatWpwc3PDyZMnRUexayw7RKRo2Yex+LgIskdarRa1a9fmeTuviGWHiBQte2aHj4sge8Xzdl4dyw4RKRpndsjehYeH49y5c8jIyBAdxW6x7BCRomVlZUGtVkOj0YiOQpQvtWvXhiRJOHPmjOgodotlh4gUTafTcVaH7Jq7uzuqV6/O83ZeAcsOESlaVlYWz9chu9egQQOWnVfAskNEisaZHVICFxcXHDlyBEOGDMH27dtFx7E7LDtEpGic2SF7FxUVhYULF8JoNGL79u0YNmwYvv32W9Gx7ArLDhEpGmd2yJ5JkoSpU6dCkiR5mclkwowZM2A0GgUmsy8sO0SkaJzZIXuWlZWFtLS0HMt1Oh1SUlIEJLJPLDtEpGic2SF75urqisDAQKjV///jWqVSoVixYihUqJDAZPaFZYeIFI0zO2TvVqxYATc3N/nfsbOzM1auXAmVSiU4mf1g2SEiRcvKyuLMDtm12rVr45dffsG8efNQpEgRfPDBBwgPDxcdy644iQ5ARGRNOp2OTzwnuxcQEIA333wTv/zyCy5duiQ6jt3hzA4RKVpWVhbLDilGeHg4by6YDyw7RKRoPEGZlCQ8PBy3bt3CzZs3RUexKyw7RKRoPEGZlCQ0NBTFihXj7E4esewQkaJxZoeURKVS8TlZ+cCyQ0SKxpkdUhqWnbxj2SEiRePMDilNgwYNcPnyZdy7d090FLvBskNEisaZHVKaypUrw8vLCydOnBAdxW6w7BCRonFmh5RGo9GgXr16PJSVByw7RKRonNkhJeJ5O3nDskNEisbHRZASNWjQAOfPn0dqaqroKHaBZYeIFE2n03FmhxSnZs2a0Gq1OHXqlOgodoFlh4gUjTM7pEQGgwHFihXDlClTMGPGDCQmJoqOZNNs4kGgqampWLJkCc6cOQM3Nzd0794dXbt2fea6Fy5cwLJly5CQkICgoCCMHj0apUuXBgBcv34d//nPf3DlyhWkpKRg06ZNfCYOkYPjg0BJabKystC5c2fcuXMHJpMJcXFx2LhxIw4dOgRfX1/R8WySTczsREREQK/XY9WqVZg+fTo2bdqE06dP51gvOTkZs2fPRo8ePRAdHY2mTZti1qxZ0Ov1AB6fod6oUSO89957BbwFRGSr+CBQUpotW7bgzz//hMlkAgDo9Xo8ePAAERERgpPZLuFlJzMzE8eOHcOAAQPg7u6OkJAQtGnTBvv27cuxbmxsLPz9/dGiRQtotVp07doVkiTh3LlzAIDAwEC0adMGQUFBBbwVRGSreOk5KU18fDzUavMf33q9HgkJCYIS2T7hh7Fu374NSZIQHBwsLytdujRiY2NzrHvjxg35kBXw+BkhISEhuHHjBurWrZvrzxkfH4/4+Hj5tYuLCwICAvK5Bc+n0WjM/qtEKpVKsdvnCOMHKH8Ms8/ZUeo2Knn8AMfYD/M6hpUqVYLBYDBbptVqUbFiRZv8OtnCGAovO5mZmXB3dzdb5uHhgYyMjBzrZmRkwNPTM1frvkhERARmzJghv548eTJmz56dp/fIC29vb6u9ty1Q+iECpY8foOwx1Ol08PHxgY+Pj+goVqPk8cum9P0wL2PYr18/7NmzB+vWrQMAmEwm1K9fHxMnTrTpWUyRYyi87Li6uuYoK+np6XBzc8uxrpubG9LT082WpaWlPXPdFxkxYgS6dOkiv3ZxccHDhw/z9B65odFo4O3tjeTkZBiNRou/vy3w8PBAWlqa6BhW4QjjByh/DLOysqDX662yj9sCJY8f4Bj7YX7G8KuvvkKnTp2wdetW/PDDD/j++++Rnp6e42ekLbDmGOb2lxjhZadkyZIAHh+iyj7XJi4u7pnn3QQFBWHPnj3ya0mScO3aNbRv3z5Pn9Pf3x/+/v7y63v37ll1JzIajYrdSSVJUuy2ZVPy+AHKH8Ps++wodRuVPn7ZlLwf5ncMW7RogZo1a2LdunW4ePEiatSoYflwFiRyDIWfoOzq6opGjRohKioK6enpuH79Ovbu3YvWrVvnWDc8PBzx8fE4ePAg9Ho9tm3bBgDyAEuSBJ1OJ1+dpdfrodPpCmxbiMi2ZH9z5U0FSal8fHxQqVKlZ57nSv9PeNkBHh9W0mg0GDx4MD755BP07NkTtWvXBgD06dMHFy9eBPD4eN/kyZPxww8/oG/fvoiJicGUKVPkb2R3795Fr1698O677wIA+vbti169eonZKCISLvuXHVs+j4HoVTVo0IBl5yWEH8YCAE9PT0yaNOmZf/f999+bva5atSoWL178zHX9/Pzk2R4iouyyw5kdUrLw8HBMmDABJpMpxyXp9Bi/KkSkWFlZWQA4s0PKFh4ejocPH+LPP/8UHcVmsewQkWLxMBY5Aj8/P5QpU4aHsl6AZYeIFIuHschRhIeHs+y8AMsOESkWZ3bIUWSXHUmSREexSSw7RKRYnNkhRxEeHo67d+/i77//Fh3FJrHsEJFicWaHHEWpUqUQGBiIX375RXQUm8SyQ0SKpdPpFP+gTKJsDRs2xPHjx0XHsEksO0SkWDqdDi4uLlCpVKKjEFkdby74fCw7RKRYOp3OIZ4ITiRJEuLi4nDz5k2UK1cOI0eORGpqquhYNoNlh4gUK3tmh0jplixZgm+++QYA8OjRI2zZsgWDBw/m1Vn/w7JDRIqVlZXFmR1yCMuWLTN7orher0dMTAxu3rwpMJXtYNkhIsXizA45iuxHozwtMzOzgJPYJpYdIlIsnrNDjqJ58+Zm95NSq9UoUaIEQkJCxIWyISw7RKRYnNkhR7FgwQLUqVNHfu3l5YUNGzaw7P+Pk+gARETWwrJDjsLb2xtbt25FXFwcJk6cCH9/f1SqVEl0LJvBmR0iUiwexiJHolKpEBoaivbt2/Pmgk9h2SEixeLMDjmiRo0aIS4uDnfu3BEdxWaw7BCRYnFmhxxR+fLl4evry+dkPYFlh4gUizM75IhUKhUaNmyIY8eOiY5iM1h2iEixOLNDjqpRo0YsO09g2SEixeLMDjmqxo0b87ydJ7DsEJFicWaHHFW5cuVQrFgxzu78D8sOESkWZ3bIUfG8HXMsO0SkWHwQKDkynrfz/1h2iEixOLNDjqxRo0a4du0abt++LTqKcCw7RKRYLDvkyHjezv9j2SEixeIJyuTI0tLS4OXlhU8++QQDBw7E+fPnRUcShmWHiBSLMzvkqPR6PXr06IHr16/j/v372LNnD9q1a+ewhYdlh4gUizM75KhiYmJw/vx5GI1GAIDJZILRaMSiRYsEJxODZYeIFIszO+SoHj58CCcnJ7NlJpMJiYmJghKJxbJDRIrFmR1yVFWrVoVerzdbptVqUbduXUGJxGLZISLF4swOOaoKFSpg9uzZUKvV8gxPrVq18MEHHwhOJgbLDhEpFmd2yJENGzYMR44cwaxZswAAc+fOhZubm+BUYrDsEJFicWaHHF358uUxdOhQlClTxqHvt8OyQ0SKxZkdoseaNm2KI0eOiI4hDMsOESlWVlYWZ3aIADRr1gxHjx6FwWAQHUUIlh0iUiSj0Qij0ciZHSI8fk5Weno6zp49KzqKECw7RKRIOp0OADizQwSgcOHCqF69Og4fPiw6ihAsO0SkSNn3GGHZIXqsadOmLDtEREqSlZUFADyMRfQ/zZo1w6lTp5CWliY6SoFj2SEiReLMDpG5unXrQqPR4Pjx46KjFDiWHSJSJM7sEJlzdXVF/fr1HfJQFssOESkSZ3aIcnLU83ZYdohIkTizQ5RT1apVceHCBUyZMgV79+4VHafAsOwQkSJxZofI3LVr1zBixAgAwMqVKzFgwAB89tlnglMVDJYdIlKk7Jmd7Cc+Ezm6qVOnIiUlBQBgMBhgMpmwcOFCXLlyRXAy62PZISJF0uv1cHFxgUqlEh2FyCb89ddfOR4XodFocO3aNTGBChDLDhEpUlZWFrRaregYRDYjNDQUGo3GbJnRaERQUJCgRAWHZYeIFEmn0/F8HaInzJw5E+7u7vJJ+yqVCiNGjED58uUFJ7M+HswmIkXS6XS8EovoCWXKlMGRI0ewdu1a7N69G0ajETNnzhQdq0Cw7ODxpanW+A0w+1wBDw8PSJJk8fe3BU5OTvDy8hIdwyocYfwA5Y6hWq2W92slj6FSxy+bI+yHBTmGFSpUwMyZM9G8eXN0794darUanp6eVv2ctjCGLDt4/Btg9hOSLUmj0cDZ2RlpaWkwGo0Wf39b4OXlJZ/drzSOMH6AcscwOTlZPmdHyWOo1PHL5gj7oYgxrF69OpycnLBr1y60a9fOqp/LmmOY24kKnrNDRIrEw1hEz+fi4oImTZrgwIEDoqMUCJYdIlKk7EvPiejZWrVqhf379yv28OCTWHaISJF46TnRi7Vs2RK3bt3C5cuXRUexOpYdIlIkzuwQvVipUqVQvnx5hziUxbJDRIrEmR2il2vVqhXLDhGRveLMDtHLtWzZErGxsUhNTRUdxapYdohIkTizQ/Ry9evXh1arxZEjR0RHsSqWHSJSJD4ugujlnJ2dUaZMGXz66aeYMmWKYk9WZtkhIkXS6XSc2SF6iY8++ggXL17ElStXsHLlSrRo0QK//vqr6FgWx7JDRIrEmR2iF7t69SpWrlwJk8kEADAYDNDr9ZgyZYrgZJbHskNEisQ7KBO92J07d+TnVmUzmUy4ffu2oETWw7JDRIrEskP0YqGhoTmWOTk5oUKFCgLSWBfLDhEpEssO0YuVLFkSn376KVQqlbyveHl5Yc6cOYKTWR7LDhEpEssO0cu988472L59OyZMmAAfHx+8++67CA4OFh3L4pxEByAisga9Xs+yQ5QL9evXR/369fHgwQMcOnQI7733nuhIFseZHSJSpKysLJYdojzo2LEjYmNjce/ePdFRLI5lh4gUiY+LIMqbOnXqoFixYti1a5foKBbHskNEisTHRRDljVqtRocOHbBjxw7RUSyOZYeIFIkzO0R516lTJxw+fBjJycmio1gUyw4RKRJndojyLjw8HJ6enti7d6/oKBbFskNEisTHRRDlnVarRdu2bfHTTz+JjmJRLDtEpEh8EChR/rRt2xZ79+7FokWLcPjwYdFxLIJlh4gUiTM7RHmXmpqKuXPnQq/XY+7cuejduzc++eQT0bFeGcsOESmOyWSCwWDgfXaI8mjBggW4evUqgMcn+ZtMJixbtgwnTpwQnOzVsOwQkeLodDoAYNkhyqPffvsNer3ebJmzszMuX74sKJFlsOwQkeJkf7PmYSyivAkKCoKTk/mTpAwGA/z8/AQlsgyWHSJSnKysLADgCcpEeTRu3Dh4eHjIhUelUiE8PBwtW7YUnOzVsOwQkeJwZocof0qVKoWYmBgMHToUTZs2hSRJ+PLLL6HRaERHeyUsO0SkOJzZIcq/kiVLYtasWdi0aRPCwsKwefNm0ZFeGcsOESkOZ3aIXp1KpUK/fv2wfv16mEwm0XFeCcsOESkOZ3aILKNXr164efMmYmNjRUd5JSw7RKQ42Zeec2aH6NUUL14crVu3xrp160RHeSUsO0SkONllhzM7RK+uX79++Omnn5Camio6Sr6x7BCR4uh0Ojg7O0OlUomOQmT3WrVqBRcXF4wdOxbLly/HnTt3REfKM5YdIlKc7LJDRK9ux44dePToEbZv347p06ejYcOGOH/+vOhYecKyQ0SKw7JDZBnp6ekYNWoUJEmCJEnQ6XTIzMzEqFGjREfLE5YdIlIclh0iy4iPj5evbsxmNBrx999/C0qUPyw7RKQ4LDtEllG8eHGo1Tmrgr09K4tlh4gUh2WHyDK8vLzw8ccfQ6VSyaVHpVJh7ty5gpPljdPLVyEisi8sO0SWM2bMGISGhmLfvn24ffs2Tpw4gVq1aomOlSec2SEixWHZIbKsTp06YdGiRdiwYQMCAgIQEREhOlKesOwQkeLodDreUJDICjQaDcaNG4fly5fj0aNHouPkGssOESmOTqfjoyKIrKRnz54oWrQovvrqK/z666948OCB6EgvxbJDRIrDmR0i69FqtahYsSKWLFmCVq1aoWLFioiMjBQd64VYdohIcTizQ2Q9O3fuxJ49e+TXJpMJEyZMwIkTJwSmejGWHSJSHM7sEFlPTExMjufOOTs74+jRo4ISvRzLDhEpDmd2iKzH3d09x40GJUmCm5uboEQvx7JDRIrDS8+JrOeNN94wu8lgtq5duwpK9HIsO0SkOCw7RNYTFhaGH3/8EZUqVYKPjw9CQ0NhMBhw9epVXLlyBX/99RcMBoPomGYUdwfl1NRULFmyBGfOnIGbmxu6d+9u022TiCyPZYfIuurWrYuDBw/Kr99//3306dMHRqMRAFCuXDls3LgRJUuWFBXRjOJmdiIiIqDX67Fq1SpMnz4dmzZtwunTp4VkSU9PhyRJ8muTyYSMjAyzdTIyMmAymeTXkiQhPT3dbJ2srCyzlvysdXQ6HfR6/Qs/v8FgyPH02qfXMRqNyMzMzHPGzMzMPGeUJAlpaWlWyWgymZ6ZMXtHtJWMT/97yG9Ga421JTM+6+uo0+mskjEjIwNOTor7XY7IZv3+++9m3xfi4uIwaNAgADn3axEUVXYyMzNx7NgxDBgwAO7u7ggJCUGbNm2wb9++As1x7tw51KpVC4GBgfDw8MC3336LmTNnomTJkggKCkLz5s1x6NAhNG3aFEFBQQgMDMScOXOwbNkyBAUFITg4GHXq1MHBgwfRsWNHBAYGIjAwEOPHj8eGDRsQGhqK4OBgVKpUCbt378abb76JwMBAlCxZEoMHD8aOHTtQoUIFBAcHo2zZsti0aRPGjBmDkiVLolSpUujatSsOHDiAmjVrIjg4GMHBwVixYgVmzJiBwMBAlCpVCq+99hoOHTqExo0bIygoCKVKlcLcuXPxzTffyBnr1q2L/fv3o0OHDihVqhQCAwPx4YcfYv369XLGypUrY8+ePejXr5+8HUOGDMGOHTtQsWJFhISEoFy5cti8eTNGjRolZ+zevTsOHDiAGjVqyBn/85//YPr06XLGFi1aICYmJkfGJUuWyBnr1auHgwcPon379ihVqhRKliyJCRMmIDo6Ws5YpUoV7NmzB3379pUzDh06FNu2bUPx4sVRqlQplCtXDlu2bMHIkSPljD169MD+/ftRvXp1OeOqVaswbdq0HBkbNmwoZ5w3bx6+/vprBAUFISgoCPXr18fBgwfRtm1bOePEiROxbt06lC5dGsHBwahatSr27t2L119/Xc44bNgwbN++HWFhYQgODkb58uXx448/4l//+pecsWfPnmYZQ0JCsHr1akydOlXO2LBhQ8TExCA8PFzOuGDBAixatAilSpWSMx46dAht2rSRx/qjjz7CmjVrzDLu27cPffr0kTO+/fbb2LZtG8LCwhASEoLy5ctj69ateOedd1CyZEkEBgaiV69e2LdvH6pVq2aW8eOPP5Yztm7dOkfGhQsXYuHChXLGBg0aICYmBq1bt8b+/fuxbNkyfPTRRzY3nU6kNJmZmTkmFQwGA3799VdUrFgRgYGBKFy4MDZt2iQoIaCSRNctC7p69So++OADbNmyRV529OhRrFu3Dt98881zP+7evXsWy5CQkICGDRsiLS3N7LdPtVotv37yybHZTTj7Mr7s4VCpVPIJYNnfrDUajVlzzv4YjUYjr+Pk5ASj0ZijRTs5OZmtk53lyYxPvr9Go5GX23JGSZJe+HXM/lpbM6MkSWbr5fXrWBAZX/Z1zE/GJ/9NF9TXUZIk+XNm//t7cr/KXpb93lqtFpMmTcK4cePMvp5K4uXlhZSUFNExrEaj0cDHxwcPHz7kGNoog8GAwMDAl46PSqXCli1b0KhRI4t9bl9f31ytp6h53szMTLi7u5st8/DwyDHFHR8fj/j4ePm1i4sLAgICLJLh2LFjyMrKMvshACDHtPvTnv5hkP2N/8l1n/6HlP0xT/7m+rzfYnOzzpPv/6x/tPaY8Vk/6JnRMhmf/ncsIuPTh4mfptfrERkZiQ8++OCZn0MJVCqVWWFVmuxtU/I22vsYajQaDBw4EGvWrJEPXz/9y1D2su3bt6Np06YFnlFRZcfV1TVHsUlPT89x7X9ERARmzJghv548eTJmz55tkQxPly0iEs/b21t0BKtyhJOxOYa2LSIiAkWLFsV3330H4PEVWydPnsxx7qCLiwt8fHwKPJ+iyk72Wd83btxAUFAQgMcnSWX/f7YRI0agS5cu8msXFxc8fPjQIhlq164NrVYLvV7/3Cn5Zx3GUqvVZr+p5uYQUfZ61ji0YSsZX3Ro48l7PDx5KCOvGV/l8Ev2+7zo8Ev239lTxvwcssxe7+mMz5q5yW/Gpw9ZPn0YK3t59jparRZvvvkmkpOTFXsIxMPDA2lpaaJjWI1Go4G3tzfH0A5MnjwZkydPBgBcunQpxwyOyWRC69atLfbzFkCui5OiTlB2dXVFo0aNEBUVhfT0dFy/fh179+5F69atzdbz9/dHrVq15D9+fn4wGo0W+VO8eHFs2rQJfn5+AB639U8//RTDhw+XvxmXLVsWa9euRUhICIDHO/O//vUvTJkyRb7Fvb+/P6KiolC1alUAj7+B9+7dGwsXLpRnqnx8fLBy5Uo0adJE3rYWLVpg+fLlKFSoEIDHM01ff/01unbtKv8Aq1mzJr777jsUK1bMLOOwYcPkjOXKlcuRceTIkZg8ebKcMSAgAJs2bUKVKlXkjK+//jq+/PJLOWORIkWwcuVKNG7cWM7YsmVLfPvtt3JGDw8PLF68GF26dJEz1qpVC5GRkWYZZ86ciSFDhsgZy5cvnyPj6NGj8dFHH8lX4gQEBCAqKgqVKlWSM77xxhtYsGABXF1d5a/jqlWr0LBhQ3mdVq1amX0dszN26tRJzli7dm2sXr1azuji4oJZs2bhrbfeypExODgYwOMf7GPGjMHEiRPljCVLlsSaNWtQsWJF+fP37dsX8+bNkzMWKVIEkZGRCA8Pl9dp06YNli1bBi8vLwCAp6cnlixZgo4dO8oZ69Spg9WrV8vHtV1cXPDZZ59h0KBBcsaKFSti7dq18i8FTk5OGDduHCZMmCBnDAwMxJo1a1ChQgUAj4vFm2++iS+++EK+U7Gvry9Wr16NBg0ayBnbtm1rltHLywtLly5F+/bt5Yz16tVDZGSkWcbPP/8cAwYMkDNWqFABa9euRWBgoJxx/PjxGD9+vFnGtWvXyl9HtVqNAQMGYObMmRbbv23xjyRJwjNY+w8A4Rk4hnn7k/1zLruMuLu7Y/HixWjcuLHF/23khqJOUAYe32dn8eLF8n12evTo8dL77FjyBOVs2ZfjBgYGyr+RGAwGZGZmwtPT0yyvq6ur/A3baDQiPT1d/uEAAGlpadBqtfI0p8lkQmpqKry8vOQfGBkZGVCpVPIPR0mSkJKSYrZO9iXsHh4e8jqpqanw8PCQf6jkNWP2iXWWzGg0GuXDgdnreHp6yhn1ej2ysrLy/HVMTU2Fi4uLXNZellGj0aBw4cK4ceMG3N3dXzljSkoK3NzcXjljeno61Gq1xb6O/v7+8smRtprx6a+ju7u7fI7DizK6urry5FY7xxOU7Vv2z8JSpUohKSnJ4mOY2xOUFVd28sMaZQfgTmrvHGH8AI6hvVPy+AEcQyWw5hjmtuwo6jAWERER0dNYdoiIiEjRWHaIiIhI0Vh2iIiISNFYdoiIiEjRWHaIiIhI0Vh2iIiISNFYdoiIiEjRWHaIiIhI0Vh2iIiISNFYdoiIiEjRWHaIiIhI0fggUCuKj49HREQERowYAX9/f9FxKI84fvaPY2j/OIb2zxbGkDM7VhQfH48ZM2YgPj5edBTKB46f/eMY2j+Oof2zhTFk2SEiIiJFY9khIiIiRWPZsSJ/f39MmzaNx5ntFMfP/nEM7R/H0P7ZwhjyBGUiIiJSNM7sEBERkaKx7BAREZGiOYkOoFSpqalYsmQJzpw5Azc3N3Tv3h1du3YVHYuQ+7H5888/ER0djStXrgAAwsLCMGzYMAQEBAAAfvvtN0yZMgUuLi7yx/Tq1Qt9+vQpmA1xUHnZt7p06QIXFxeoVCoAQKVKlTB9+nT5748dO4bVq1fjwYMHqFChAsaMGYPixYsXxGY4tNyO4aFDh/DNN9/IryVJQlZWFiZNmoSGDRtyH7RxP/30E37++Wdcu3YN4eHh+PDDD4VlYdmxkoiICOj1eqxatQp3797F1KlTERgYiNq1a4uO5vByOzZpaWlo1aoVJkyYAGdnZ6xduxazZs0y++ZbqFAhfPfddwW9CQ4tr/vWwoULERgYmGP5zZs3sWjRInz00UeoVKkSoqKi8MUXX2D+/PnW3gSHl9sxbN68OZo3by6/Pn36NObNm2e2HvdB21WkSBH06dMH586dQ0pKitAsPIxlBZmZmTh27BgGDBgAd3d3hISEoE2bNti3b5/oaA4vL2NTu3ZtNGnSBB4eHtBqtejWrRtu3bqF5ORkAckJsOy+dejQIdSqVQs1a9aEi4sL+vXrh7i4ONy4ccMKySnbq4zhvn370LhxY7OZHLJdDRs2RIMGDeDt7S06Cmd2rOH27duQJAnBwcHystKlSyM2NlZgKgJebWwuXLgAHx8fsx03JSUFAwcOhFarRa1atTBw4EB4eXlZJTvlb/ymTJkCo9GIcuXKYfDgwQgKCgIAXL9+HeXKlZPXc3d3R4kSJXD9+nV5HbK8/O6DycnJOHnyJD777DOz5dwHKTc4s2MFmZmZcHd3N1vm4eGBjIwMQYkoW37HJiEhARERERg2bJi8LDAwEIsWLUJkZCQ+//xz3L9/H1999ZU1YtP/5HX8PvvsMyxfvhwREREIDQ3FJ598gvT0dPm9PDw8cv1eZBn53QdjYmLg7++PChUqyMu4D1JusexYgaura44dNz09HW5uboISUbb8jE1iYiKmTp2Knj17okmTJvJyHx8fBAUFQa1Wo1ixYnj77bdx+vRpZGVlWS2/o8vr+FWpUgVarRbu7u7o378/NBoN/vjjD/m9sotPbt6LLCO/3x/379+Pli1bmi3jPki5xbJjBSVLlgQAs2P/cXFxnBq3AXkdm3v37mHKlClo27YtunXr9sL3VqvVkCQJvE+n9bzqvpV9VRYABAcH4++//5ZfZ2RkICEhwezwCllefsbw6tWruHHjBl577bUXvjf3QXoelh0rcHV1RaNGjRAVFYX09HRcv34de/fuRevWrUVHc3h5GZv79+/j448/RvPmzdGrV68cf3/+/Hn8888/kCQJDx8+xLfffosaNWrA1dW1IDbFIeVl/G7cuIGrV6/CaDQiKysL69atg06nQ1hYGIDHV/qcOXMG586dg06nw7p16xASEsJfSqwsP98fDxw4gNq1a8PHx8dsOfdB22Y0GqHT6WAymWAymaDT6WAwGIRk4eMirCQ1NRWLFy+W7yPRo0cP3mfHRrxobPr06YNp06ahcuXKiI6ORnR0dI5vnEuWLEGxYsXw448/Ytu2bUhOToanpydq1aqFQYMGoVChQiI2y2HkdvzOnz+PpUuX4t69e3B2dkbZsmUxePBglC5dWn6vo0ePYvXq1Xj48CHCwsIwduxY3menAOR2DAFAr9dj8ODBGD16NBo0aGD2PtwHbdu6deuwfv16s2UtWrTAe++9V+BZWHaIiIhI0XgYi4iIiBSNZYeIiIgUjWWHiIiIFI1lh4iIiBSNZYeIiIgUjWWHiIiIFI1lh4iIiBSNZYeIiIgUjWWHiIiIFI1lh4gol0JCQjBq1CjRMYgoj1h2iIiISNFYdojIajIyMkRHICJi2SFydIMHD0aVKlWwa9cuVKlSBa6urqhduzaOHz8ur/Pdd9+hcePGKFKkCHx8fNC8eXOcPHnS7H2mT58OT09PnDx5EuHh4XB1dcWSJUsAAJMmTULVqlXh6emJkiVLom/fvoiPjzf7+ObNm6NTp06Ijo5GuXLl4O7ujs6dO+Phw4e4fv062rZtC09PT1SuXBmHDh3K1balpaXBw8MD8+fPz/F3vXr1Qnh4uLzeqFGjEBYWBnd3d4SEhOCdd95BUlLSC98/O/OTzp07B5VKZZZRkiTMnz8f5cuXh4uLC0JDQ7Fw4cJcbQMRvTqWHSJCfHw83n33XXz44Yf4/vvv4eLigrZt2+Lu3bsAgGvXrmHgwIHYuHEj1q1bh6CgIDRt2hSXL182ex+dTod+/fqhf//+2LVrF9q0aQMAuHv3LiZPnowdO3Zg0aJFuHbtGpo1awaDwWD28WfPnsWiRYswf/58LFu2DEeOHMHw4cPRq1cvdOrUCZs3b0bx4sXRo0cPpKamvnS7PDw80KVLF6xfv95seUpKCnbs2IF+/foBANLT02E0GjF79mzs2rULs2bNQkxMDLp165bfL6mZsWPH4pNPPsGgQYOwY8cODB48GBMnTsSyZcss8v5E9BISETm0QYMGSQCkAwcOyMsePXokeXl5SZMmTcqxvtFolPR6vRQWFiZ99NFH8vJp06ZJAKT169e/8PMZDAbp1q1bEgBpz5498vJmzZpJHh4eUmJiorxs/PjxEgBp6dKl8rLffvtNAiD9+OOPudq+rVu3SgCky5cvy8tWr14taTQaKSEh4Zkfo9frpaNHj0oApEuXLsnLg4ODpZEjR5pl7tixo9nHnj17VgIgHTx4UJIkSbpy5YqkUqmkiIgIs/UmTpwolShRQjIajbnaDiLKP87sEBEKFSqEFi1amL1u1aoVTpw4AQD4448/0L17d/j5+UGj0UCr1eLSpUs5ZnYAoGPHjjmW7dq1Cw0bNkShQoXg5OSEwMBAAMjx8TVq1ICvr6/8unz58gCAVq1a5Vh28+bNXG1bu3btULhwYbPZnfXr1+O1116Dn5+fvCwqKgo1a9aEp6cntFotGjdu/MyMebV//34AQM+ePWEwGOQ/rVq1QkJCQq63g4jyj2WHiFCsWLEcy/z8/BAfH4+UlBS0adMG169fx5dffokjR47g1KlTqF69OjIzM80+xt3dHZ6enmbLTp06hS5duiAgIABRUVGIjY2Vzwd6+uMLFy5s9trZ2TnH8uxlT3/s8zg7O6Nnz55y2bl//z727dsnH8ICgC1btmDgwIGoV68evv/+exw/fhxbtmzJ0+d5nnv37kGSJPj6+kKr1cp/WrduDSD3pY2I8s9JdAAiEi8xMTHHsn/++Qf+/v6IjY3FrVu38NNPP6F69ery3yclJckzNNlUKlWO99myZQsKFSqE77//Hmr149+vrl+/buEteLG+ffti5cqVOH/+PGJjY6HRaNCjRw/57zdu3IgaNWogIiJCXhYTE/PS93V1dYVOpzNb9vDhQ7PXRYoUgUqlwtGjR+Wi9qSwsLC8bg4R5RHLDhEhKSkJP//8s3woKykpCfv378fIkSPly8ef/EH9yy+/4Nq1a6hcufJL3zsjIwNardasCK1du9bCW/BizZs3R4kSJRAdHY3Y2Fi0b98ehQoVMsv4dBHJTcbAwEDs27cPkiTJ27d3716zdVq2bAng8YxS586dX3VTiCgfWHaICEWKFMHQoUMxY8YMFC5cGJ9//jkkScJ7770HAPD09MTIkSMxadIk3L59G9OmTUPJkiVz9d6tW7fGV199hdGjR6N79+6IjY1FVFSUFbcmJ41Ggz59+iAyMhJ3797NcXVW69atMXLkSMycORPh4eHYuXMnDhw48NL37dWrF1auXInRo0ejW7du+OWXX7Bp0yazdcqXL4+RI0diwIAB+PDDD1G/fn3o9XpcvnwZBw8exI8//mjJTSWiZ+A5O0QEf39/LF68GJ9//jl69+6NzMxM7NmzB35+fvDz88PGjRtx9+5ddO3aFV999RUiIiJQtmzZXL13hw4dMHfuXGzduhVdunTB4cOH8dNPP1l5i3Lq27cvEhIS4O7unuPeOCNGjMD48ePx9ddfo0ePHrh58ybWrVv30vds164dvvjiC2zbtg3dunXDhQsXnnk5+b///W/MmjUL69evR8eOHdG/f39s2LABzZo1s9j2EdHzqSRJkkSHICJxBg8ejP/+97+4cOGC6ChERFbBmR0iIiJSNJ6zQ0R2S5IkGI3G5/69Wq2WrwAjIsfF7wJEDi4yMtJuD2GtXr3a7N41T//59NNPRUckIhvAc3aIyG7dv38fcXFxz/37gIAABAQEFGAiIrJFLDtERESkaDyMRURERIrGskNERESKxrJDREREisayQ0RERIrGskNERESKxrJDREREisayQ0RERIr2f/2S+7c6jpfoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (316506408)>"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot_posterior(posterior_grid_approx(100, 5, 7, lambda x: np.array([0 if xi<0.5 else 1 for xi in x])))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "de2b2235-88a7-4e48-98ab-8947f745362b",
   "metadata": {},
   "source": [
    "## 3M1\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "70ccdad1-d8ba-4fc7-9ced-a8496b64c94e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (316742349)>"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior = posterior_grid_approx(100, 8, 15)\n",
    "plot_posterior(posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "b01f917f-d961-463c-b07e-2da23dd34eaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.choice(posterior.param_value, p=posterior.p, size=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "8def14c4-4593-4cd4-a528-5cb462b3f37c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.34343434, 0.72727273])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.hdi(samples, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4cc1ce3c-8b31-4d7b-87bf-0d9b68810ab2",
   "metadata": {},
   "source": [
    "Posterior predictive"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "98d81782-e54b-4be3-a69f-724ba4271ab4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([  379.,  1133.,  8041.,  8342., 25114., 14688., 25454.,  8366.,\n",
       "         7466.,  1017.]),\n",
       " array([ 0. ,  1.5,  3. ,  4.5,  6. ,  7.5,  9. , 10.5, 12. , 13.5, 15. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 117,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ppd = np.random.binomial(n=15, p=samples)\n",
    "plt.hist(ppd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "7d245cd9-3ce0-43ba-bbbd-1464e74d61c0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([78.,  3.,  3.,  2.,  2.,  1.,  2.,  2.,  2.,  5.]),\n",
       " array([0.00000000e+00, 9.48236691e-09, 1.89647338e-08, 2.84471007e-08,\n",
       "        3.79294677e-08, 4.74118346e-08, 5.68942015e-08, 6.63765684e-08,\n",
       "        7.58589353e-08, 8.53413022e-08, 9.48236691e-08]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(stats.binom.pmf(6, n=9, p=posterior.p))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "429e21f3-1717-4824-bdf2-d6a84cd4d0a0",
   "metadata": {},
   "source": [
    "Our data is 8 successes, so at least the expectation matches. It is also true that P(6)>P(8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "fa806604-4f45-4f08-b2a5-37416c2be05d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([1.43489070e-08, 5.02211745e-07, 8.20279184e-06, 8.29393397e-05,\n",
       "        5.80575378e-04, 2.98028694e-03, 1.15900048e-02, 3.47700143e-02,\n",
       "        8.11300333e-02, 1.47235986e-01, 2.06130381e-01, 2.18623131e-01,\n",
       "        1.70040213e-01, 9.15601148e-02, 3.05200383e-02, 4.74756151e-03]),)"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.pmf(np.linspace(0, 15, 16), n=15, p=0.7),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "2f4e0903-7bfb-40cd-89ef-19d56f69016e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (316837765)>"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior = posterior_grid_approx(100, 8, 15, lambda x: np.array([0 if xi<0.5 else 1 for xi in x]))\n",
    "plot_posterior(posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "5c8ce5fc-f566-437e-b2d7-b844bfb4b336",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.choice(posterior.param_value, p=posterior.p, size=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "94fafa41-39e6-43d1-a659-848af0472584",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.50505051, 0.71717172])"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.hdi(samples, 0.9) # HDPI is tighter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "e834d139-2d5a-4131-8fce-20b8f5ad5a52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([8.0000e+00, 7.3000e+01, 1.5500e+03, 3.3290e+03, 1.8457e+04,\n",
       "        1.5784e+04, 3.4186e+04, 1.2968e+04, 1.1993e+04, 1.6520e+03]),\n",
       " array([ 0. ,  1.5,  3. ,  4.5,  6. ,  7.5,  9. , 10.5, 12. , 13.5, 15. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ppd = np.random.binomial(n=15, p=samples)\n",
    "plt.hist(ppd)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "9220d326-5d57-4cb7-b75f-326ff5350714",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.2668279320000001,)"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stats.binom.pmf(6, n=9, p=0.7),"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "6a87042d-933a-47a5-b82d-dab35837b6df",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([86.,  1.,  2.,  1.,  1.,  0.,  1.,  1.,  2.,  5.]),\n",
       " array([0.00000000e+00, 1.93079072e-07, 3.86158144e-07, 5.79237216e-07,\n",
       "        7.72316288e-07, 9.65395360e-07, 1.15847443e-06, 1.35155350e-06,\n",
       "        1.54463258e-06, 1.73771165e-06, 1.93079072e-06]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(stats.binom.pmf(6, n=9, p=posterior.p))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "2c70a51b-a450-4a37-af10-9555f860d7bf",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:04<00:00, 22.25it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:21<00:00,  4.69it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:36<00:00,  2.72it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:47<00:00,  2.09it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:46<00:00,  2.13it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:48<00:00,  2.06it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:44<00:00,  2.27it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:35<00:00,  2.85it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:21<00:00,  4.57it/s]\n",
      "100%|██████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████████| 100/100 [00:02<00:00, 45.84it/s]\n"
     ]
    }
   ],
   "source": [
    "grid = np.linspace(0, 1, 10)\n",
    "\n",
    "trials_for_p = []\n",
    "\n",
    "for p in grid:\n",
    "    number_of_trials = []\n",
    "    for repeat in tqdm(range(0,100)):\n",
    "        successes = 0\n",
    "        tosses = 0\n",
    "        interval = (0,1)\n",
    "        while interval[1] - interval[0] > 0.05:\n",
    "            successes += np.random.binomial(1, p)\n",
    "            tosses += 1  \n",
    "            interval = stats.beta.interval(0.99, successes + 1, tosses - successes + 1)  \n",
    "        number_of_trials.append(tosses)\n",
    "    mean = np.array(number_of_trials).mean()\n",
    "    trials_for_p.append(mean) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "id": "8bf58a8a-ac10-4d66-9e7e-e04f2787183e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x12e579b80>]"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(grid, trials_for_p)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91d94214-0a2c-4712-86f7-6405d85a27a0",
   "metadata": {},
   "source": [
    "# Hard section"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "08f6b5ca-3154-40de-8219-180e525fd70b",
   "metadata": {},
   "outputs": [],
   "source": [
    "birth1 = np.array([1, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 0,\n",
    "                   1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1])\n",
    "birth2 = np.array([0, 1, 0, 1, 0, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 1, 0,\n",
    "                   1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
    "                   1, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1,\n",
    "                   0, 0, 0, 1, 1, 1, 0, 0, 0, 0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "id": "cbaabd66-3c1a-474a-9f05-aff34a581b15",
   "metadata": {},
   "outputs": [],
   "source": [
    "boys = sum(birth1)+sum(birth2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 152,
   "id": "117bb770-1399-4f93-976e-df26808ba8e2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "111"
      ]
     },
     "execution_count": 152,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "id": "44582352-3995-4c81-b593-9a214371423c",
   "metadata": {},
   "outputs": [],
   "source": [
    "births = len(birth1)+len(birth2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "id": "9c90fc62-c448-4b5f-9f6b-b5d50f5b9d15",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "200"
      ]
     },
     "execution_count": 156,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "births"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "472f1cda-ae5e-42fd-a9e7-9ca6a6986862",
   "metadata": {},
   "source": [
    "# 3H1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "id": "2a4fffbc-c2cf-4128-807e-409f27c58783",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314312605)>"
      ]
     },
     "execution_count": 157,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior = posterior_grid_approx(100, boys, births)\n",
    "plot_posterior(posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "id": "7d7b25d6-1e7b-43e2-ad26-520798283fb4",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.choice(posterior.param_value, p=posterior.p, size=int(1e5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 167,
   "id": "31c87fd9-c991-4ca8-8147-e28c9af73c87",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0.54545455, 0.58585859]),\n",
       " array([0.50505051, 0.60606061]),\n",
       " array([0.48484848, 0.62626263])]"
      ]
     },
     "execution_count": 167,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[az.hdi(samples, density) for density in [0.5, 0.89, 0.97]]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c2fe722c-1d1a-4ac7-a637-f63b645564f0",
   "metadata": {},
   "source": [
    "# 3H3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "id": "3be7dd53-f39d-4994-a561-ac022d72fff3",
   "metadata": {},
   "outputs": [],
   "source": [
    "replicates = stats.binom(p=samples, n=200).rvs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "id": "43cc5888-d530-41bf-b1b4-f857d162d2c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([4.3000e+01, 6.9400e+02, 4.2210e+03, 1.7483e+04, 2.9594e+04,\n",
       "        3.1243e+04, 1.3831e+04, 2.5860e+03, 2.9400e+02, 1.1000e+01]),\n",
       " array([ 69. ,  77.6,  86.2,  94.8, 103.4, 112. , 120.6, 129.2, 137.8,\n",
       "        146.4, 155. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 174,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAD4CAYAAAAO9oqkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAR+UlEQVR4nO3df6xfdX3H8efLVhB/jQLXDtu6NtJsKWRWbKCL+8PBhILLigkzZYt0rrEmlkw3k1lcMpxKAtmUhAxYamgoi1IIamikWhtGYkzkxwURKMi4KyBtCq2UHxozsOS9P76fbl/L9/Z+e2/v/V64z0dy8j3nfT7nnM85fOF1z4/vIVWFJGlme9OgOyBJGjzDQJJkGEiSDANJEoaBJAmYPegOjNdJJ51UCxcuHHQ3JOl15b777vtFVQ0dWn/dhsHChQsZHh4edDck6XUlyVO96l4mkiQZBpIkw0CShGEgScIwkCRhGEiSMAwkSRgGkiQMA0kSr+NfIEvT1cL1tw9s209e8ZGBbVuvb54ZSJIMA0mSYSBJwjCQJNFHGCR5S5J7kvw0yY4k/9zqi5LcnWQkyc1Jjmn1Y9v0SJu/sGtdl7b6Y0nO7aqvaLWRJOsnYT8lSYfRz5nBy8BZVfU+YCmwIsly4Ergqqo6BXgeWNParwGeb/WrWjuSLAFWAacCK4Brk8xKMgu4BjgPWAJc1NpKkqbImGFQHb9qk29uQwFnAbe2+ibggja+sk3T5p+dJK2+uaperqongBHgjDaMVNXOqnoF2NzaSpKmSF/3DNpf8A8Ae4HtwH8DL1TVgdZkFzCvjc8DngZo818ETuyuH7LMaPVe/VibZDjJ8L59+/rpuiSpD32FQVW9WlVLgfl0/pL/g8ns1GH6saGqllXVsqGh1/wvPCVJ43RETxNV1QvAncAfAccnOfgL5vnA7ja+G1gA0Ob/DvBcd/2QZUarS5KmyJivo0gyBPymql5IchzwYTo3he8ELqRzjX81cFtbZEub/nGb/59VVUm2AN9M8jXg3cBi4B4gwOIki+iEwCrgL4/eLmqmGuRrIaTXm37eTXQysKk99fMm4Jaq+m6SR4DNSb4C/AS4vrW/HviPJCPAfjr/caeqdiS5BXgEOACsq6pXAZJcAmwDZgEbq2rHUdtDSdKYxgyDqnoQeH+P+k469w8Orf8P8BejrOty4PIe9a3A1j76K0maBP4CWZJkGEiSDANJEoaBJAnDQJKEYSBJwjCQJGEYSJIwDCRJGAaSJAwDSRKGgSQJw0CShGEgScIwkCRhGEiSMAwkSRgGkiQMA0kShoEkCcNAkoRhIEnCMJAkYRhIkugjDJIsSHJnkkeS7EjymVb/YpLdSR5ow/ldy1yaZCTJY0nO7aqvaLWRJOu76ouS3N3qNyc55mjvqCRpdP2cGRwAPldVS4DlwLokS9q8q6pqaRu2ArR5q4BTgRXAtUlmJZkFXAOcBywBLupaz5VtXacAzwNrjtL+SZL6MGYYVNWeqrq/jf8SeBSYd5hFVgKbq+rlqnoCGAHOaMNIVe2sqleAzcDKJAHOAm5ty28CLhjn/kiSxuGI7hkkWQi8H7i7lS5J8mCSjUnmtNo84OmuxXa12mj1E4EXqurAIfVe21+bZDjJ8L59+46k65Kkw+g7DJK8HfgW8Nmqegm4DngvsBTYA3x1MjrYrao2VNWyqlo2NDQ02ZuTpBljdj+NkryZThB8o6q+DVBVz3bN/zrw3Ta5G1jQtfj8VmOU+nPA8Ulmt7OD7vaSpCnQz9NEAa4HHq2qr3XVT+5q9lHg4Ta+BViV5Ngki4DFwD3AvcDi9uTQMXRuMm+pqgLuBC5sy68GbpvYbkmSjkQ/ZwYfBD4OPJTkgVb7Ap2ngZYCBTwJfAqgqnYkuQV4hM6TSOuq6lWAJJcA24BZwMaq2tHW93lgc5KvAD+hEz6SpCkyZhhU1Y+A9Ji19TDLXA5c3qO+tddyVbWTztNGkqQB8BfIkiTDQJJkGEiSMAwkSRgGkiQMA0kShoEkCcNAkoRhIEnCMJAkYRhIkjAMJEkYBpIkDANJEoaBJAnDQJKEYSBJwjCQJGEYSJIwDCRJGAaSJAwDSRKGgSQJw0CSRB9hkGRBkjuTPJJkR5LPtPoJSbYnebx9zmn1JLk6yUiSB5Oc3rWu1a3940lWd9U/kOShtszVSTIZOytJ6q2fM4MDwOeqagmwHFiXZAmwHrijqhYDd7RpgPOAxW1YC1wHnfAALgPOBM4ALjsYIK3NJ7uWWzHxXZMk9WvMMKiqPVV1fxv/JfAoMA9YCWxqzTYBF7TxlcCN1XEXcHySk4Fzge1Vtb+qnge2AyvavHdW1V1VVcCNXeuSJE2BI7pnkGQh8H7gbmBuVe1ps54B5rbxecDTXYvtarXD1Xf1qPfa/tokw0mG9+3bdyRdlyQdRt9hkOTtwLeAz1bVS93z2l/0dZT79hpVtaGqllXVsqGhocnenCTNGH2FQZI30wmCb1TVt1v52XaJh/a5t9V3Awu6Fp/faoerz+9RlyRNkX6eJgpwPfBoVX2ta9YW4OATQauB27rqF7enipYDL7bLSduAc5LMaTeOzwG2tXkvJVnetnVx17okSVNgdh9tPgh8HHgoyQOt9gXgCuCWJGuAp4CPtXlbgfOBEeDXwCcAqmp/ki8D97Z2X6qq/W3808ANwHHA99ogSZoiY4ZBVf0IGO25/7N7tC9g3Sjr2ghs7FEfBk4bqy+SpMnhL5AlSYaBJMkwkCRhGEiSMAwkSRgGkiQMA0kShoEkCcNAkoRhIEnCMJAk0d+L6qRxW7j+9kF3QVIfPDOQJBkGkiTDQJKEYSBJwjCQJGEYSJIwDCRJGAaSJAwDSRKGgSQJw0CShGEgSaKPMEiyMcneJA931b6YZHeSB9pwfte8S5OMJHksybld9RWtNpJkfVd9UZK7W/3mJMcczR2UJI2tnzODG4AVPepXVdXSNmwFSLIEWAWc2pa5NsmsJLOAa4DzgCXARa0twJVtXacAzwNrJrJDkqQjN2YYVNUPgf19rm8lsLmqXq6qJ4AR4Iw2jFTVzqp6BdgMrEwS4Czg1rb8JuCCI9sFSdJETeSewSVJHmyXkea02jzg6a42u1pttPqJwAtVdeCQek9J1iYZTjK8b9++CXRdktRtvGFwHfBeYCmwB/jq0erQ4VTVhqpaVlXLhoaGpmKTkjQjjOv/dFZVzx4cT/J14LttcjewoKvp/FZjlPpzwPFJZrezg+72kqQpMq4zgyQnd01+FDj4pNEWYFWSY5MsAhYD9wD3Aovbk0PH0LnJvKWqCrgTuLAtvxq4bTx9kiSN35hnBkluAj4EnJRkF3AZ8KEkS4ECngQ+BVBVO5LcAjwCHADWVdWrbT2XANuAWcDGqtrRNvF5YHOSrwA/Aa4/WjsnSerPmGFQVRf1KI/6H+yquhy4vEd9K7C1R30nnaeNJEkD4i+QJUmGgSRpnE8TSZqeFq6/fSDbffKKjwxkuzp6PDOQJBkGkiTDQJKEYSBJwjCQJGEYSJIwDCRJGAaSJAwDSRKGgSQJw0CShGEgScIwkCRhGEiSMAwkSRgGkiQMA0kShoEkCcNAkoRhIEnCMJAk0UcYJNmYZG+Sh7tqJyTZnuTx9jmn1ZPk6iQjSR5McnrXMqtb+8eTrO6qfyDJQ22Zq5PkaO+kJOnw+jkzuAFYcUhtPXBHVS0G7mjTAOcBi9uwFrgOOuEBXAacCZwBXHYwQFqbT3Ytd+i2JEmTbMwwqKofAvsPKa8ENrXxTcAFXfUbq+Mu4PgkJwPnAturan9VPQ9sB1a0ee+sqruqqoAbu9YlSZoi471nMLeq9rTxZ4C5bXwe8HRXu12tdrj6rh51SdIUmvAN5PYXfR2Fvowpydokw0mG9+3bNxWblKQZYbxh8Gy7xEP73Nvqu4EFXe3mt9rh6vN71Huqqg1Vtayqlg0NDY2z65KkQ403DLYAB58IWg3c1lW/uD1VtBx4sV1O2gack2ROu3F8DrCtzXspyfL2FNHFXeuSJE2R2WM1SHIT8CHgpCS76DwVdAVwS5I1wFPAx1rzrcD5wAjwa+ATAFW1P8mXgXtbuy9V1cGb0p+m88TSccD32iBJmkJjhkFVXTTKrLN7tC1g3Sjr2Qhs7FEfBk4bqx+SpMnjL5AlSYaBJMkwkCRhGEiSMAwkSRgGkiQMA0kShoEkCcNAkoRhIEnCMJAkYRhIkjAMJEkYBpIkDANJEoaBJAnDQJKEYSBJwjCQJGEYSJIwDCRJGAaSJAwDSRKGgSSJCYZBkieTPJTkgSTDrXZCku1JHm+fc1o9Sa5OMpLkwSSnd61ndWv/eJLVE9slSdKROhpnBn9SVUuralmbXg/cUVWLgTvaNMB5wOI2rAWug054AJcBZwJnAJcdDBBJ0tSYjMtEK4FNbXwTcEFX/cbquAs4PsnJwLnA9qraX1XPA9uBFZPQL0nSKCYaBgX8IMl9Sda22tyq2tPGnwHmtvF5wNNdy+5qtdHqkqQpMnuCy/9xVe1O8i5ge5Kfdc+sqkpSE9zG/2mBsxbgPe95z9FarSTNeBM6M6iq3e1zL/AdOtf8n22Xf2ife1vz3cCCrsXnt9po9V7b21BVy6pq2dDQ0ES6LknqMu4wSPK2JO84OA6cAzwMbAEOPhG0GritjW8BLm5PFS0HXmyXk7YB5ySZ024cn9NqkqQpMpHLRHOB7yQ5uJ5vVtX3k9wL3JJkDfAU8LHWfitwPjAC/Br4BEBV7U/yZeDe1u5LVbV/Av2SJB2hcYdBVe0E3tej/hxwdo96AetGWddGYON4+yJJmpiJ3kDW68TC9bcPuguSpjFfRyFJMgwkSYaBJAnDQJKEYSBJwjCQJGEYSJIwDCRJGAaSJAwDSRK+jkLSUTCo1508ecVHBrLdNyLPDCRJhoEkyTCQJGEYSJIwDCRJGAaSJAwDSRKGgSQJw0CShGEgScIwkCThu4mm1KDe3yJJY/HMQJI0fcIgyYokjyUZSbJ+0P2RpJlkWlwmSjILuAb4MLALuDfJlqp6ZLA9kzSdDfLS6xvt9dnT5czgDGCkqnZW1SvAZmDlgPskSTPGtDgzAOYBT3dN7wLOPLRRkrXA2jb5qySPTUHfptpJwC8G3YlpymPTm8dldJN2bHLlZKx1Svxer+J0CYO+VNUGYMOg+zGZkgxX1bJB92M68tj05nEZncemf9PlMtFuYEHX9PxWkyRNgekSBvcCi5MsSnIMsArYMuA+SdKMMS0uE1XVgSSXANuAWcDGqtox4G4Nyhv6MtgEeWx687iMzmPTp1TVoPsgSRqw6XKZSJI0QIaBJMkwGKQkf5dkR5KHk9yU5C3tJvrd7bUcN7cb6m94STYm2Zvk4a7aCUm2J3m8fc5p9SS5uh2jB5OcPrieT75Rjs2/JPlZ2//vJDm+a96l7dg8luTcgXR6ivQ6Nl3zPpekkpzUpmfU9+ZIGQYDkmQe8LfAsqo6jc6N81XAlcBVVXUK8DywZnC9nFI3ACsOqa0H7qiqxcAdbRrgPGBxG9YC101RHwflBl57bLYDp1XVHwL/BVwKkGQJne/RqW2Za9vrXt6obuC1x4YkC4BzgJ93lWfa9+aIGAaDNRs4Lsls4K3AHuAs4NY2fxNwwWC6NrWq6ofA/kPKK+kcA/jtY7ESuLE67gKOT3LylHR0AHodm6r6QVUdaJN30fltDnSOzeaqermqngBG6Lzu5Q1plO8NwFXAPwDdT8jMqO/NkTIMBqSqdgP/Sucvlz3Ai8B9wAtd/5LvovOqjplqblXtaePPAHPbeK/Xl8zk4/Q3wPfa+Iw/NklWArur6qeHzJrxx+ZwDIMBade/VwKLgHcDb6PH6a46qvMMtM9BHyLJPwIHgG8Mui/TQZK3Al8A/mnQfXm9MQwG50+BJ6pqX1X9Bvg28EE6p64Hfww401/L8ezB0/j2ubfVfX0JkOSvgT8D/qr+/wdDM/3YvJfOH1g/TfIknf2/P8nv4rE5LMNgcH4OLE/y1iQBzgYeAe4ELmxtVgO3Dah/08EWOscAfvtYbAEubk+HLAde7LqcNCMkWUHnmvifV9Wvu2ZtAVYlOTbJIjo3S+8ZRB8Hoaoeqqp3VdXCqlpI51LQ6VX1DH5vDsswGJCqupvOjeL7gYfo/LPYAHwe+PskI8CJwPUD6+QUSnIT8GPg95PsSrIGuAL4cJLH6ZxJXdGabwV20rk5+nXg0wPo8pQZ5dj8G/AOYHuSB5L8O0B7jcstdP6w+D6wrqpeHVDXJ90ox2Y0M+p7c6R8HYUkyTMDSZJhIEnCMJAkYRhIkjAMJEkYBpIkDANJEvC/8RxgVRZ9pj0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(replicates)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db563379-dab1-4247-af32-9246befade08",
   "metadata": {},
   "source": [
    "Consistent with observations"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9779b323-27d9-4581-bfe2-b9907c708403",
   "metadata": {},
   "source": [
    "# 3H4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b7993d19-cd59-4456-a147-fa4580dcd796",
   "metadata": {},
   "outputs": [],
   "source": [
    "I do not interpret the problem as the Pymc solution, may need to further check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 177,
   "id": "f5ae8508-cb55-4724-b7b3-6ee43bece342",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "51"
      ]
     },
     "execution_count": 177,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(birth1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "id": "a18f1cd1-618d-4bb4-8a1f-38c02d8700eb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100"
      ]
     },
     "execution_count": 185,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(birth1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "id": "90800c26-76d5-4079-bce2-0e3a723b03e7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<ggplot: (314533756)>"
      ]
     },
     "execution_count": 180,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior = posterior_grid_approx(100, sum(birth1), len(birth1))\n",
    "plot_posterior(posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 181,
   "id": "da38e4fe-a92d-43ee-858d-8e61d62757a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "samples = np.random.choice(posterior.param_value, p=posterior.p, size=int(1e5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "a434e41d-277c-46f5-a001-8a2646eb2c94",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0.47474747, 0.53535354]),\n",
       " array([0.43434343, 0.58585859]),\n",
       " array([0.39393939, 0.60606061])]"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[az.hdi(samples, density) for density in [0.5, 0.89, 0.97]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "id": "94c59238-27a2-4f3e-b382-df94aaad36a5",
   "metadata": {},
   "outputs": [],
   "source": [
    "replicates = stats.binom(p=samples, n=200).rvs()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 184,
   "id": "65dd54c0-566b-45a0-b9d2-25dd1ff73ec7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([3.0000e+00, 1.5100e+02, 1.9600e+03, 9.6340e+03, 2.6941e+04,\n",
       "        3.4561e+04, 1.9392e+04, 6.4720e+03, 8.4000e+02, 4.6000e+01]),\n",
       " array([ 45. ,  55.7,  66.4,  77.1,  87.8,  98.5, 109.2, 119.9, 130.6,\n",
       "        141.3, 152. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 184,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(replicates)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6961f1f8-01a3-4dda-8e0b-280fd07ff032",
   "metadata": {},
   "source": [
    "# 3H5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97b4a103-f817-465d-a882-710b3a014dbf",
   "metadata": {},
   "source": [
    "Girl + Boy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "id": "ef512cc8-8497-4720-be84-e5b379f8f119",
   "metadata": {},
   "outputs": [],
   "source": [
    "first_females = sum(abs(birth1-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "id": "f991e4fb-05bd-4b15-be1e-2e6ec36fc48a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "49"
      ]
     },
     "execution_count": 189,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "first_females"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "id": "51831738-21e0-46a1-9e70-c350cf3cdf2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "boys_followed_girls = sum(abs(birth1-1)*birth2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "id": "ed2b289f-2dda-4ccb-b58c-c6e3b7821c56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "39"
      ]
     },
     "execution_count": 195,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "boys_followed_girls"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "186ffead-82b9-4265-aa1a-9d0eb7f89a12",
   "metadata": {},
   "source": [
    "Given my model's posterior distribution, I simulate 49 births, and the chance of getting 39 boys is too low. After having a girl, it seems that there's greater chance of a boy, but the model doesn't account for that."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "id": "cf744a6f-780d-4d14-85a6-7ddd21578451",
   "metadata": {},
   "outputs": [],
   "source": [
    "posterior_predictive_samples = np.random.binomial(n=49, p=samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "id": "4a2bac42-8c08-40f1-bea4-e635f4d01781",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([8.0000e+00, 2.7000e+02, 3.6190e+03, 1.6953e+04, 3.3950e+04,\n",
       "        3.0877e+04, 1.2168e+04, 2.0300e+03, 1.2200e+02, 3.0000e+00]),\n",
       " array([ 6. ,  9.9, 13.8, 17.7, 21.6, 25.5, 29.4, 33.3, 37.2, 41.1, 45. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 201,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(posterior_predictive_samples)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e299083f-cb60-4240-b53e-449d850c642a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}