From eda195c8723efc8efb44f90a269994cf07439a27 Mon Sep 17 00:00:00 2001
From: Mirko Birbaumer <mirko.birbaumer@hslu.ch>
Date: Wed, 5 Mar 2025 10:42:12 +0000
Subject: [PATCH] Leichte Aenderungen Notebooks
---
notebooks/Beta-Verteilung/BT_2_2.ipynb | 447 ++++++++++
notebooks/Beta-Verteilung/BV_4_3.ipynb | 68 ++
notebooks/Beta-Verteilung/BV_4_6.ipynb | 85 ++
.../Beta-Verteilung/BV_tongue_rolling.ipynb | 761 ++++++++++++++++++
notebooks/Beta-Verteilung/beta_commands.py | 156 ++++
5 files changed, 1517 insertions(+)
create mode 100644 notebooks/Beta-Verteilung/BT_2_2.ipynb
create mode 100644 notebooks/Beta-Verteilung/BV_4_3.ipynb
create mode 100644 notebooks/Beta-Verteilung/BV_4_6.ipynb
create mode 100644 notebooks/Beta-Verteilung/BV_tongue_rolling.ipynb
create mode 100644 notebooks/Beta-Verteilung/beta_commands.py
diff --git a/notebooks/Beta-Verteilung/BT_2_2.ipynb b/notebooks/Beta-Verteilung/BT_2_2.ipynb
new file mode 100644
index 0000000..4b360dd
--- /dev/null
+++ b/notebooks/Beta-Verteilung/BT_2_2.ipynb
@@ -0,0 +1,447 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "Matplotlib is building the font cache; this may take a moment.\n"
+ ]
+ }
+ ],
+ "source": [
+ "%matplotlib inline\n",
+ "import matplotlib.pyplot as plt\n",
+ "import numpy as np\n",
+ "\n",
+ "# Nur zur besseren Darstellung\n",
+ "plt.rcParams.update({\n",
+ " \"text.usetex\": True,\n",
+ " \"font.family\": \"sans-serif\",\n",
+ " \"font.sans-serif\": [\"Helvetica\"]})\n",
+ "## for Palatino and other serif fonts use:\n",
+ "plt.rcParams.update({\n",
+ " \"text.usetex\": True,\n",
+ " \"font.family\": \"serif\",\n",
+ " \"font.serif\": [\"Palatino\"],\n",
+ " \"font.size\": 8\n",
+ "})"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Einleitung: Prior-Posterior\n",
+ "\n",
+ "\n",
+ "Bei einer Münze sei die Wahrscheinlichkeit, Kopf $ K $ zu werfen, $ \\theta $. Die Wahrscheinlichkeit, Zahl $ Z $ zu werfen, ist dann $ 1-\\theta $. \n",
+ "\n",
+ "Nun betrachten wir einen neuen Einfränkler, der gerade von der Nationalbank in Umlauf gebracht wurde. Die Frage ist nun, wie gross ist $ \\theta $? Weil die Münze von der seriösen Nationalbank kommt, neu ist und symmetrisch aussieht, dürfen wir annehmen, dass die Münze _fair_ ist, also $ \\theta=0.5 $. \n",
+ "\n",
+ "Nun ist eine _reale_ Münze nie fair in dem Sinne, dass $ \\theta $ _exakt_ $ 0.5 $ ist. Es gilt vielleicht \n",
+ "\n",
+ "$$\n",
+ "0.48<\\theta <0.52\n",
+ "$$\n",
+ "\n",
+ "aber nie $ \\theta=0.500000000\\ldots $. Man beachte, dass es unendlich viele Werte für $ \\theta $ gibt, die zwischen $ 0 $ und $ 1 $ liegen. \n",
+ "\n",
+ "Wir möchten eine Aussage aufgrund von Daten machen, wie gross $ \\theta $ tatsächlich ist. Dazu werfen wir die Münze vorläufig einmal und erhalten $ K $, was wir mit $ y=1 $ bezeichnen (wir werden dies später verallgemeinern). Das heisst, wir haben Daten über die Münze gesammelt und wollen wissen, was wir über $ \\theta $ aussagen können. Wir suchen also die bedingte Wahrscheinlichkeit \n",
+ "\n",
+ "$$\n",
+ "P(\\theta|y=1)\n",
+ "$$\n",
+ "\n",
+ "und können die Formel von Bayes anwenden:\n",
+ "\n",
+ "$$\n",
+ "P(\\theta|y=1)=\\frac{P(y=1|\\theta)\\cdot P(\\theta)}{P(y=1)}\n",
+ "$$\n",
+ "\n",
+ "Nun haben wir auf der rechten Seite drei Grössen, die unbekannt sind:\n",
+ "\n",
+ "$$\n",
+ "P(y=1|\\theta),\\qquad P(\\theta) \\quad \\text{und}\\quad P(y=1)\n",
+ "$$\n",
+ "\n",
+ "Obwohl $ \\theta $ unendlich viele Werte annehmen kann, wollen wir $ \\theta $ vorübergehend diskretisieren. Wir nehmen an, dass $ \\theta $ nur die Werte von $ 0,0.1,0.2,\\ldots,0.9,1 $ annehmen kann. Dann gilt für die Likelihood-Funktion $ P(y=1 | \\theta) $, dass sie abhängig von $ \\theta $ ist:\n",
+ "\n",
+ "$$\n",
+ "P(y=1|\\theta)\n",
+ "=\\theta\n",
+ "$$\n",
+ "\n",
+ "das heisst, wenn die Wahrscheinlichkeit, $ K $ zu werfen, $ \\theta $ beträgt (erstes $ \\theta $), so erscheint mit einer Wahrscheinlichkeit von $ \\theta $ (zweites $ \\theta $) auch $ K $. \n",
+ "\n",
+ "Ist zum Beispiel $ \\theta=0.8 $, so ist\n",
+ "\n",
+ "$$\n",
+ "P(y=1|0.8)\n",
+ "=0.8\n",
+ "$$\n",
+ "\n",
+ "\n",
+ "die Wahrscheinlichkeit, bei einer Wurfwahrscheinlichkeit von $ 0.8 $ Kopf zu werfen, natürlich auch $ 0.8 $ ist.\n",
+ "\n",
+ "Da wir mehrere $ \\theta $'s haben, haben wir auch mehrere $ P(y=1 | \\theta) $'s"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n",
+ "[0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "theta = np.arange(11)/10\n",
+ "print(theta)\n",
+ "likeli = np.linspace(0,1,num=11)\n",
+ "print(likeli)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, '$P(y=1\\\\mid\\\\theta )$')"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.bar(theta,likeli, width=.01)\n",
+ "plt.title(\"Likelihood\")\n",
+ "plt.xlabel(r\"$\\theta$\")\n",
+ "plt.ylabel(r\"$P(y=1\\mid\\theta )$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Nun kommen wir zur Prior-Verteilung $ P(\\theta) $, und hier gibt es sehr viele Möglichkeiten. Diese müssen wir allerdings vorher festlegen. Denken wir uns die Münze als eher fair, wissen es aber nicht genau, können wir eine Wahrscheinlichkeitsverteilung wie folgt wählen.\n",
+ "\n",
+ "Die Prior-Werte für die $ \\theta $'s sind"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n",
+ "[0 1 2 3 4 5 4 3 2 1 0]\n",
+ "[0. 0.04 0.08 0.12 0.16 0.2 0.16 0.12 0.08 0.04 0. ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "theta = np.arange(11)/10\n",
+ "y = np.array([0,1,2,3,4,5,4,3,2,1,0])\n",
+ "prior = y / np.sum(y)\n",
+ "print(theta)\n",
+ "print(y)\n",
+ "print(prior)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Plausibilität für $\\\\theta$')"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.bar(theta,prior, width=.01)\n",
+ "plt.title(\"Prior\")\n",
+ "plt.xlabel(r\"$\\theta$\")\n",
+ "plt.ylabel(r\"Plausibilität für $\\theta$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Nun können wir die Posterior-Wahrscheinlichkeiten für alle $ \\theta $'s, also die Posterior-Verteilung, berechnen. So ist zum Beispiel\n",
+ "\n",
+ "$$\n",
+ "P(0.8 | y=1)\n",
+ "=\\frac{P(y=1 | 0.8)\\cdot P(0.8)}{P(y=1)}\n",
+ "=\\frac{0.8\\cdot 0.8}{0.5}\n",
+ "=0.128\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Nun updaten wir unsere Wahrscheinlichkeiten mit der Formel von Bayes für alle $\\theta$s, mit der Beobachtung, dass Kopf geworfen wurde ($y=1$):"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Zähler [0. 0.004 0.016 0.036 0.064 0.1 0.096 0.084 0.064 0.036 0. ]\n",
+ "Nenner 0.5\n",
+ "Posterior [0. 0.008 0.032 0.072 0.128 0.2 0.192 0.168 0.128 0.072 0. ]\n"
+ ]
+ }
+ ],
+ "source": [
+ "posterior = (likeli*prior) / np.sum(likeli*prior)\n",
+ "\n",
+ "print(\"Zähler\", likeli*prior)\n",
+ "print(\"Nenner\", np.sum(likeli*prior))\n",
+ "print(\"Posterior\", posterior)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, '$P(\\\\theta\\\\mid y=1)$')"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.bar(theta,posterior, width=.01)\n",
+ "plt.title(\"Posterior\")\n",
+ "plt.xlabel(r\"$\\theta$\")\n",
+ "plt.ylabel(r\"$P(\\theta\\mid y=1)$\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Wir sehen, dass die Prior-Verteilung durch eine leicht andere Gewichtung in die Posterior-Verteilung einfliesst. Die $ \\theta $'s über $ 0.5 $ werden stärker gewichtet als die unter $ 0.5 $. \n",
+ "\n",
+ "Hätten wir Zahl ($ Z $) geworfen, so hätten wir eine höhere Gewichtung für Wurfwahrscheinlichkeiten unter $ 0.5 $."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Verschiedene Priors\n",
+ "\n",
+ "Wir betrachten als erstes eine uniform verteilte Prior-Verteilung."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n",
+ "[0 1 1 1 1 1 1 1 1 1 0]\n",
+ "[0. 0.11111111 0.11111111 0.11111111 0.11111111 0.11111111\n",
+ " 0.11111111 0.11111111 0.11111111 0.11111111 0. ]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, '$P(\\\\theta)$')"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjIAAAG8CAYAAADEnk9sAAAAP3RFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMS5wb3N0MSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8kixA/AAAACXBIWXMAAA9hAAAPYQGoP6dpAAAXq0lEQVR4nO3dT09bZ/rw8Ss/VWLVYEhX1SBNHM1+asIbaGzN4rebQvIKsDXb0RSG1Wg2Q6FdPMti5g0QaHfPpnb6AsrUM/uRz1RC6i7pgUqPxKY8iwpPU/7kkAbDBZ+PZCm27wM3dyj59pwb+87R0dFRAAAk9D9XPQEAgNclZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hA1ypfr8fs7OzMTU1FZ1OJ5aXl2N2djYWFhauempAAne8si9w1brdbqytrcVwOBw9NjU1Fe12O9bW1k49ZmFhIVqtVrTb7XFNE7iG3rrqCQCcptlsRlEUZz7f6XSiXq+PcUbAdeTSEnAtFUURrVZrdL8sy5eebzabMT09/dJjg8Egut1u9Pv9Ex/v58cDN4OQAa6dbrcb9Xo92u127OzsxNTUVKyuro720hw/1u12R8d0Op0oiiIeP34cg8EgHjx4EGVZnno8cHMIGeDaKIoiut1uPHz4MLa3tyMiYn5+PprNZvT7/dje3o7Nzc3RY8f6/X784x//iPn5+ajVarG0tBS1Wi1WV1dPPR64OeyRAa6N47MwPzc9PR31en10O37sWK/XO7Ff5jhezjoeuBmckQFSuHfv3rnP/Xxj8L17916KlvOOB/ISMsC19+LFi3Mfm5+fj8FgEIPBYPRYr9eLlZWVM48HbgaXloAr1e/3Y2NjI4qiiPX19Wi321Gr1V56fjAYRFEUUa/XY35+/qXHms1mNBqN2N7ejsXFxXjy5EnUarVYXl6ORqNx6vHAzeEF8QCAtFxaAgDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKR1o19H5ocffohvv/023n777bhz585VTwcAqODo6Ci+//77ePfdd+N//uf8cy43OmS+/fbbmJmZueppAACvYW9vL371q1+dO+ZGh8zbb78dET8uxN27d694NgBAFQcHBzEzMzP6d/w8Nzpkji8n3b17V8gAQDJVtoXY7AsApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpvXXVE2B8fv3n/3visW8++t8rmEl1P5/zdZ9vRL45+74Yj2xz9n0xHhnnfN04IwMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIa+wh0+12o9vtxsLCQgwGg1PH9Pv9aLVasbOzc+FjAYDbY6whMxgMYjgcRrvdjs3NzVhcXDx1TK/Xe61jAYDbZawhs7W1FXNzcxERUavVoiiKE2MajUasra1FvV6/8LEAwO0y1pApiiJqtdro/vT0dJRl+caOPTw8jIODg5duAMDNdaM2+66ursbk5OToNjMzc9VTAgAu0VhDpl6vnziL8tOzLL/02JWVldjf3x/d9vb2Xn+yAMC1N9aQabVao428ZVlGo9EYPfeqPS/nHXtsYmIi7t69+9INALi53hrnJ2s2m7G9vR3dbjfKsozNzc2I+DFiWq1WDIfDiIjY2dmJfr8fL168iHq9Ho1G48xjAYDba6whExGxsbFx4rF6vT6KmIiI+fn5mJ+fr3QsAHB73ajNvgDA7SJkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGm9Ne5P2O12IyKi1+vFyspKNBqNymPW19ejVqvFcDiMVqsVzWZzfBMHAK6dsYbMYDCI4XAYa2tr8fjx43j06FF8/fXXlcb0+/14/vx5LC0tRVmWsbCwIGQA4JYba8hsbW3F3NxcRETUarUoiuJCY/r9fpRlGUVRRKvVOnHs4eFhHB4eju4fHBy86S8BALhGxrpHpiiKqNVqo/vT09NRlmWlMc1mMx4+fBj379+P5eXlWFpaOvHxV1dXY3JycnSbmZm5pK8EALgO0mz2PQ6eZ8+eRUTE7OzsiTErKyuxv78/uu3t7Y1zigDAmI310lK9Xj9xBuanZ1/OG9PpdKLT6USj0YherxdTU1MnPv7ExERMTEy84VkDANfVWM/ItFqt6PV6EfHjGZaf/sbS8V6Y88a8ePFi9Od6vT6OKQMA19hYz8g0m83Y3t6ObrcbZVnG5uZmRMRo8+5wODxzzNraWiwvL8dgMIjnz5/H9vb2OKcOAFxDY38dmY2NjROP1ev1GA6H546p1WqnPg4A3F5pNvsCAPyckAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIK23Xuegg4ODKIoiXrx4EdPT0/Hb3/628rHdbjciInq9XqysrESj0bjQmKIoYmdnJ5rN5qnHAgC3x4VC5tmzZ7G9vR3fffddzM3NxeTkZHzxxRfx6aefxtTUVHQ6nfj1r3995vGDwSCGw2Gsra3F48eP49GjR/H1119XHlMURaytrcXGxsbFv1IA4MapHDIff/xxPHjwID799NMzxzx79iyKooj333//1Oe3trZibm4uIiJqtVoURXGhMZ1OJ3q9XtUpAwA3XOWQ+fDDD1855tGjR7G/v3/m80VRRKvVGt2fnp6OsiyjVqu9cky/3496vR7r6+sxHA6j0+mcuLR0eHgYh4eHo/sHBwdVvjQAIKnKm30///zzePz4cczNzcUf/vCH+OSTT+Kbb745MW5ycvJNzm9kd3c3iqKIdrsds7Oz8ejRoxNjVldXY3JycnSbmZm5lLkAANdD5ZD56quvYnNzM3Z3d2NycjLu378fH330UaysrFT+ZPV6PcqyfOmxn56NOW9MWZaxsLAQtVot2u12RMSJS1MrKyuxv78/uu3t7VWeGwCQT+WQefDgQdy5cyciIt5555344IMP4tNPP43V1dX4/PPPK32MVqs12uNSluWJ30Y6b8zs7GwMh8PR+Onp6ajX6y99/ImJibh79+5LNwDg5qq8R2ZxcTE+/vjj2N3djf39/Wg0GlGv16Moitja2orf//73r/wYzWYztre3o9vtRlmWsbm5GRH/3RczHA7PHNNut6PT6US3243hcBjb29uv+SUDADfFhX79+sMPP4z//Oc/MRgM4osvvoiiKOLevXvx5z//ufLHOO1Xp+v1+ktnW8769Wq/dg0A/NSFXxDv/v37cf/+/fjggw8uYz4AAJVV3iPz5ZdfVhpXdb8MAMAvVTlkpqamYmVlJf71r3+deO7g4CCePXsWn3zySTSbzTc5PwCAM1W+tPTee+/Fe++9F5999ln87W9/i/39/ajVavHdd9/FgwcPotPpxJ/+9KfLnCsAwEsuvEfmgw8+sD8GALgWKl9a+uabb2JlZcUeGADg2qgcMu12O46OjuKrr76KJ0+eXOacAAAqqXxpqdFoxEcffRQREf/85z/jyy+/PPNdrgEAxqHyGZl33nln9OcHDx5cymQAAC6icsgsLS3Fb37zm/jd734Xy8vLURRFfPnll3FwcBB///vfL3OOAACnulDI/Pvf/46nT5+O9ss8ffo03n///eh0Opc5RwCAU1XeI3O8P2ZycnL0mjKLi4sREfHZZ59dzuwAAM5R+YzMebyuDABwFd5IyAAAXAUhAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQ19pDpdrvR7XZjYWEhBoPBa42ZnZ297GkCAAmMNWQGg0EMh8Not9uxubkZi4uLFx7T7XajKIpxTRkAuMbeGucn29rairm5uYiIqNVqpwbJeWOKooh6vX7mxz88PIzDw8PR/YODgzc1dQDgGhrrGZmiKKJWq43uT09PR1mWlcfs7OxEs9k88+Ovrq7G5OTk6DYzM/MGZw8AXDdpNvv2+/2Yn58/d8zKykrs7++Pbnt7e2OaHQBwFcZ6aaler584A/PTsy/njVlbWxvdL8syWq1WbGxsvHSpaWJiIiYmJt70tAGAa2qsZ2RarVb0er2I+DFGGo3G6LnjvTBnjen1eqNbrVaLXq937n4ZAODmG2vIHO9vOf716s3NzYj4MWJarda5YyJ+DJtutxtlWcb6+vqJMzcAwO0y1ktLEREbGxsnHqvX6zEcDs8dE/HjJaZ2ux3tdvvS5gcA5JFmsy8AwM8JGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hp7yHS73eh2u7GwsBCDwaDymLIso9PpxOzsbHQ6nSjLcoyzBgCuo7GGzGAwiOFwGO12OzY3N2NxcbHymOOw2d7ejqIoYnl5eZxTBwCuobfG+cm2trZibm4uIiJqtVoURVF5zPz8fNTr9YiI6HQ6sbGxceLYw8PDODw8HN0/ODh4418DAHB9jPWMTFEUUavVRvenp6dPXCI6a8xxxERE7O7uxsLCwomPv7q6GpOTk6PbzMzMm/4SAIBrJN1m37IsoyzLaLfbJ55bWVmJ/f390W1vb+8KZggAjMtYLy3V6/UTZ2B+evalypjV1dVTLytFRExMTMTExMQbmCkAkMFYz8i0Wq3o9XoR8eOZlUajMXrueC/MeWOWl5djZWVljDMGAK6zsYZMs9mMiP/+evXm5mZE/BgxrVbr3DGdTie63W7cv38/pqam4s6dO6duFgYAbo+xXlqKiFMvC9Xr9RgOh+eO2djYOPOSEgBwO6Xb7AsAcEzIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBIS8gAAGkJGQAgLSEDAKQlZACAtIQMAJCWkAEA0hIyAEBaQgYASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQ1thDptvtRrfbjYWFhRgMBhcaU+VYAOD2GGvIDAaDGA6H0W63Y3NzMxYXFyuPqXIsAHC7jDVktra2Ym5uLiIiarVaFEVReUyVYwGA2+WtcX6yoiii1WqN7k9PT0dZllGr1V45psqxh4eHcXh4OLq/v78fEREHBweX8NXk88Ph/zvx2HVfm5/P+brPNyLfnH1fjEe2Ofu+GI+Mcx6H43U4Ojp65dixhsxlW11djb/+9a8nHp+ZmbmC2eQw+X+uegYXk22+EeY8DtnmG2HO45BtvhE553yZvv/++5icnDx3zFhDpl6vR1mWLz320zMq542pcuzKykr88Y9/HN3/4Ycf4sWLF3Hv3r24c+fOL5z96Q4ODmJmZib29vbi7t27l/I5bjtrPB7W+fJZ48tnjS/fONb46Ogovv/++3j33XdfOXasIdNqtWJ7ezvm5+ejLMtoNBqj54qiiHq9fuaY8449NjExERMTEy899vPYuSx37971H80ls8bjYZ0vnzW+fNb48l32Gr/qTMyxsW72bTabEfHfX6Pe3NyMiJf3xZw15qzHAYDb685RlZ00nOng4CAmJydjf39f/V8Sazwe1vnyWePLZ40v33VbY6/s+wtNTEzEX/7ylxOXtHhzrPF4WOfLZ40vnzW+fNdtjZ2RAQDSckYGAEhLyAAAaQkZAOBU/X4/Wq1W7OzsnDnmqt/QWchcwC95526qedX6lWUZnU4nZmdno9PpnHiRRKq5yPfp7OzsmGZ1s1Rd46IoYn193c+L11BljdfX16Pb7cby8nL0+/0xzzC3wWAQvV7vlWOu/A2dj6jk66+/PlpaWjo6Ojo6+u67744ajcZrjeFsVdZvbW3tqNfrHQ2Hw6Nms3nUbrfHPc30LvJ9urGxcVSr1cY1tRuj6hoPh0Pfw6+pyhr3er2XxjSbzbHO8aZot9tH29vbpz63tLT00nNX8fPCGZmKfsk7d1NNlfWbn5+PZrMZ9Xo9Op2ONX4NVb9Pj19tm4urusadTic2NjbGObUbo+oa9/v9U994mDejKIqXXkH/+A2dx0nIVFTlL+s6/IVmVmX9fvoP6+7ubiwsLIxpdjdH1e/TnZ2d0StqczFV1nhnZyfq9Xqsr69Hp9NxaemCqqxxs9mMhw8fxv3792N5eTmWlpbGO0nGQsiQUlmWUZZltNvtq57KjdTv92N+fv6qp3Gj7e7uRlEU0W63Y3Z2Nh49enTVU7pxjsPm2bNnEWG/12Wo8obOl03IVPRL3rmbai6yfqurq07Jv6Yq67y2thadTidarVaUZRmtVstlvAuossZlWcbCwkLUarVRkFvj6qqs8fLycnQ6nWg0GtHr9azvG3S8lq1Wa7Qh+Kw3dL5sQqai8/6yrtNfaGZV1jjixx9OKysrY5/fTVFlnXu93uhWq9Wi1+vZL3MBVdZ4dnY2hsPh6PHp6WlrfAFVf168ePFi9Gfre3E7OzvR7/dja2trdPmzyhs9j5O3KLiA41/7Pb6kcbzBrNVqjX4gnTaG6l61xp1OJ54+fToaX5ZlDIdDP6AuqMr3clmW8fTp0+h0OrG2tub7+YIu8vNiOBzGkydP/M/PBb1qjcuyjOXl5Xjw4EE8f/48Op2OnxU3kJABANJyaQkASEvIAABpCRkAIC0hAwCkJWQAgLSEDACQlpABANISMgBAWm9d9QQAXle3243hcBhzc3Pe5BJuKSEDpLS+vj56s8XFxUUhA7eUS0tAOkVRxO7ubtRqtdH76wC3kzMyQDqDwSDKsoz19fV4/vx5PHz48KqnBFwRIQOks7u7G8vLy9FsNmNnZ8cZGbjFXFoC0imKIur1ekRE9Ho9+2PgFhMyQDrT09OjszC1Wm0UNcDtc+fo6OjoqicBcBGDwSBWV1fjyZMnzsbALSdkAIC0XFoCANISMgBAWkIGAEhLyAAAaQkZACAtIQMApCVkAIC0hAwAkJaQAQDSEjIAQFpCBgBI6/8D8RoKw8uI+j8AAAAASUVORK5CYII=",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "theta = np.arange(11)/10\n",
+ "y = np.array([0,1,1,1,1,1,1,1,1,1,0])\n",
+ "prior = y / np.sum(y)\n",
+ "print(theta)\n",
+ "print(y)\n",
+ "print(prior)\n",
+ "plt.bar(theta,prior, width=.01)\n",
+ "plt.title(\"Prior\")\n",
+ "plt.xlabel(r\"$\\theta$\")\n",
+ "plt.ylabel(r\"$P(\\theta)$\")"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "[0. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1. ]\n",
+ "[ 0. 1. 1.2 2. 5. 15. 5. 2.25 1.2 1. 0. ]\n",
+ "[0. 0.02971768 0.03566122 0.05943536 0.14858841 0.44576523\n",
+ " 0.14858841 0.06686478 0.03566122 0.02971768 0. ]\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, '$P(\\\\theta)$')"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 640x480 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "theta = np.arange(11)/10\n",
+ "y = np.array([0,1,1.2,2,5,15,5,2.25,1.2,1,0])\n",
+ "prior = y / np.sum(y)\n",
+ "print(theta)\n",
+ "print(y)\n",
+ "print(prior)\n",
+ "plt.bar(theta,prior, width=.01)\n",
+ "plt.title(\"Prior\")\n",
+ "plt.xlabel(r\"$\\theta$\")\n",
+ "plt.ylabel(r\"$P(\\theta)$\")"
+ ]
+ }
+ ],
+ "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": "3.10.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/notebooks/Beta-Verteilung/BV_4_3.ipynb b/notebooks/Beta-Verteilung/BV_4_3.ipynb
new file mode 100644
index 0000000..3b2356b
--- /dev/null
+++ b/notebooks/Beta-Verteilung/BV_4_3.ipynb
@@ -0,0 +1,68 @@
+{
+ "cells": [
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "%matplotlib inline\n",
+ "import beta_commands as bt\n",
+ "import matplotlib.pyplot as plt\n",
+ "plt.rcParams['figure.figsize'] = [12,14]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 1200x1400 with 3 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "bt.prior(a=75, b=25, z=4, N=10) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "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": "3.10.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/notebooks/Beta-Verteilung/BV_4_6.ipynb b/notebooks/Beta-Verteilung/BV_4_6.ipynb
new file mode 100644
index 0000000..89ef5f3
--- /dev/null
+++ b/notebooks/Beta-Verteilung/BV_4_6.ipynb
@@ -0,0 +1,85 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Bestimmung 95%-HDI für die Betaverteilung\n",
+ "\n",
+ "Die folgende Prozedur definiert, das HDI für die Beta-Verteilung:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [],
+ "source": [
+ "from scipy.stats import beta\n",
+ "import numpy as np\n",
+ "\n",
+ "def hdi(a,b, prob = 0.95):\n",
+ " k = 0\n",
+ " x = np.linspace(0,1,1000)\n",
+ " y = beta.pdf(x,a,b)\n",
+ " while True:\n",
+ " k = k+0.0001\n",
+ " if np.sum(y[y > k])/np.size(x) < prob:\n",
+ " break\n",
+ " return x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1] "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In `hdi(...)` müssen nur noch die Parameter $a$ und $b$ eingegeben werden. Wenn die Prozentzahl noch geändert soll, fügen Sie ein zusätzliches `prob=...` ein. prob=0.5 würde dann bedeuten, dass 50% der glaubwürdigsten Parameter im HDI enthalten sind. "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {
+ "tags": []
+ },
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "(array([0.14614615]), array([0.85385385]))"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "hdi(a=3, b=3) "
+ ]
+ }
+ ],
+ "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": "3.10.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}
diff --git a/notebooks/Beta-Verteilung/BV_tongue_rolling.ipynb b/notebooks/Beta-Verteilung/BV_tongue_rolling.ipynb
new file mode 100644
index 0000000..1b09ec4
--- /dev/null
+++ b/notebooks/Beta-Verteilung/BV_tongue_rolling.ipynb
@@ -0,0 +1,761 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "420b0ec3-843e-4124-bc1c-2cb4482fdd92",
+ "metadata": {},
+ "source": [
+ "# Tongue Rolling Examples"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9c527dfe-8d5d-498b-8598-203c19f25bc8",
+ "metadata": {},
+ "source": [
+ "Import necessary libraries and functions:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "id": "9348015e-3b76-43a3-9e44-cb9088bfdcb0",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "import numpy as np\n",
+ "import pandas as pd\n",
+ "import matplotlib.pyplot as plt\n",
+ "from scipy import stats\n",
+ "plt.style.use('ggplot')"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ba908c7a-8963-4bd9-8c0c-1b23a441bc9b",
+ "metadata": {},
+ "source": [
+ "## Discrete Bayesian Inference"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "52b3eb36-5601-4ccf-adae-caea3afced83",
+ "metadata": {},
+ "source": [
+ "Selected values for $\\pi$:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "id": "2432d501-8bec-42ac-8bb0-4141dbbeeb0a",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pi_values = np.array([0.2, 0.5, 0.8])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8987ee85-0ba9-4ca8-b81d-3570e5f29347",
+ "metadata": {},
+ "source": [
+ "Measured data:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "id": "0b52c574-837e-4a24-868a-ed28db698fa8",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "n = 4 # to be updated in class\n",
+ "k = 3 # to be updated in class"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c1e572ba-6968-4b1a-a605-8f745878fc50",
+ "metadata": {},
+ "source": [
+ "### Prior probabilities"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "id": "6f3fd5bb-3f52-42ea-a6c3-fcb1f18081b3",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "uninformed_prior = np.ones(3) / 3\n",
+ "geneticist_prior = np.array([1, 3, 8]) / 12"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "id": "376c356f-5b56-439d-8215-66d2e6c2e0a2",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 1500x300 with 2 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1, 2, sharey=True, figsize=(15,3) )\n",
+ "ax[0].bar( [\"$\\pi={}$\".format(pi) for pi in pi_values], uninformed_prior )\n",
+ "ax[0].set_title(\"uninformed prior\")\n",
+ "ax[1].bar( [\"$\\pi={}$\".format(pi) for pi in pi_values], geneticist_prior )\n",
+ "ax[1].set_title(\"informed geneticist prior\");"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "52314c0d-7c80-4ebf-b67a-b50f1e44823f",
+ "metadata": {},
+ "source": [
+ "### Likelihood"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "42ac22e8-45c6-4e3e-9e84-97e4f47fd9c2",
+ "metadata": {},
+ "source": [
+ "Computes \n",
+ "$$P(X=k|\\pi=0.2) = \\begin{pmatrix} n \\\\ k \\end{pmatrix} \\; 0.2^k \\; 0.8^{(n-k)}$$"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 6,
+ "id": "85dc72ec-c1ae-4a3c-b575-2a2ba247ae0a",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "0.0256"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "stats.binom.pmf(k=k, n=n, p=pi_values[0])"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "abf9626e-043b-4d1a-be5f-ab4596c03b1a",
+ "metadata": {},
+ "source": [
+ "Evaluate likelihood for all values of $\\pi$:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 7,
+ "id": "a7ed2023-9166-4f3e-871f-5030ab02bbde",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "[0.0256, 0.25000000000000006, 0.4096000000000001]"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "likelihood = [stats.binom.pmf(k=k, n=n, p=pi) for pi in pi_values]\n",
+ "likelihood"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 8,
+ "id": "bb925eea-cc36-4eb1-8f9b-67f72844f0a0",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 1.0, 'likelihood (n=4, k=3)')"
+ ]
+ },
+ "execution_count": 8,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 600x300 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure( figsize=(6,3) )\n",
+ "plt.bar( [\"$\\pi={}$\".format(pi) for pi in pi_values], likelihood )\n",
+ "plt.title(\"likelihood (n={}, k={})\".format(n, k))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "d0f4719b-8814-40cc-8a94-508c7be5629c",
+ "metadata": {},
+ "source": [
+ "### Bayesian inference"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "290f16b2-e511-4d9c-92f9-ec30067a92fc",
+ "metadata": {},
+ "source": [
+ "$$P(\\pi = \\pi_i | Y=k ) = \\frac{P(Y=k | \\pi = \\pi_i ) \\; P( \\pi = \\pi_i )}{P(Y=k)}$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a3c83fae-a380-452e-9f57-e0391085de7e",
+ "metadata": {},
+ "source": [
+ "Let's put it together and ignore the evidence for the moment:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 9,
+ "id": "b7af0641-421b-48ff-8a32-8a51feb7f153",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([0.00853333, 0.08333333, 0.13653333])"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "posterior = likelihood * uninformed_prior\n",
+ "posterior"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "e0c2ed0c-384a-40e4-805e-6b625b6e888c",
+ "metadata": {},
+ "source": [
+ "The evidence just normalizes the posterior such that it's a PMF - for this we don't have to compute the evidence!"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 10,
+ "id": "7a74faaf-5da8-40e2-bbd8-b10f7071c38f",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([0.03736135, 0.36485698, 0.59778167])"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "posterior = posterior / np.sum( posterior )\n",
+ "posterior"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 11,
+ "id": "a098bd40-2e5e-44bc-83ad-2cd7b278fbaa",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0.5, 1.0, 'uninformed prior')"
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 600x300 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.figure( figsize=(6,3) )\n",
+ "plt.bar( [\"$\\pi={}$\".format(pi) for pi in pi_values], posterior )\n",
+ "plt.title(\"uninformed prior\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c2b4e28c-0e97-4db5-8939-56cf3d8736ec",
+ "metadata": {},
+ "source": [
+ "This reflects our posterior belief in the different specified values for $\\pi$!"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5d0bf39f-3b2c-49ca-9321-d4c7b27b2e4f",
+ "metadata": {},
+ "source": [
+ "### What's the impact of the chosen prior?"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "98752661-db93-4813-8a5d-a2c3f7ad335b",
+ "metadata": {},
+ "source": [
+ "Compute posteriors:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 12,
+ "id": "e4a3f652-1dc0-4b51-9169-a7bfd2fad7bf",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "uninformed_posterior = likelihood * uninformed_prior\n",
+ "geneticist_posterior = likelihood * geneticist_prior\n",
+ "uninformed_posterior /= np.sum( uninformed_posterior )\n",
+ "geneticist_posterior /= np.sum( geneticist_posterior )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "ec647a3c-882e-485d-ae26-857574075e3d",
+ "metadata": {},
+ "source": [
+ "Plot:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 13,
+ "id": "02179c21-f742-4178-9801-4e16cbf52624",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 1500x300 with 2 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1, 2, sharey=True, figsize=(15,3) )\n",
+ "ax[0].bar( [\"$\\pi={}$\".format(pi) for pi in pi_values], uninformed_posterior )\n",
+ "ax[0].set_title(\"using uninformed prior\")\n",
+ "ax[1].bar( [\"$\\pi={}$\".format(pi) for pi in pi_values], geneticist_posterior )\n",
+ "ax[1].set_title(\"using informed geneticist prior\");"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "abd85b76-ec3e-4bc5-828b-1782d9d790f5",
+ "metadata": {},
+ "source": [
+ "## Continuous Bayesian inference"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "b4b18655-babf-46d9-8ec5-f979899f69ad",
+ "metadata": {},
+ "source": [
+ "### Prior distributions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 14,
+ "id": "20928cbb-a27b-40a3-a7cb-5c0d3f499cad",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "alpha_uninformed = 1\n",
+ "beta_uninformed = 1\n",
+ "\n",
+ "alpha_geneticist = 75\n",
+ "beta_geneticist = 25"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "1b93462f-d6a2-47d5-b9ea-8fe44150ef7e",
+ "metadata": {},
+ "source": [
+ "Set evaluation range for pi:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 15,
+ "id": "348af1cb-2498-488c-a7da-d9c902c206af",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "pi_range = np.linspace(0, 1, 100)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fc75f5b6-5f6d-47b1-befa-5794b64b1f6e",
+ "metadata": {},
+ "source": [
+ "Plot:"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "id": "950fd0ac-afec-44f5-a52b-e6e467108139",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "iVBORw0KGgoAAAANSUhEUgAABLEAAAEqCAYAAADqJsJzAAAAP3RFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjkuMS5wb3N0MSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8kixA/AAAACXBIWXMAAA9hAAAPYQGoP6dpAABMrklEQVR4nO3deXxU9b3/8feZTJbJRggQwh5AFrUqGJeKWAEruO9VKm6Xal1qbbXVn9Ja91q8rdKrbW1tr7gUlAsVhXpFsLiAXkURWwsKAgGULSGZ7Mss398fw4yEJJAJSb6zvJ6PRx6QM2fO+cxnJplvPvP9fo5jjDECAAAAAAAAYpjLdgAAAAAAAADAwVDEAgAAAAAAQMyjiAUAAAAAAICYRxELAAAAAAAAMY8iFgAAAAAAAGIeRSwAAAAAAADEPIpYAAAAAAAAiHkUsQAAAAAAABDzKGIBAAAAAAAg5lHEAuLENddcI8dxVFJScsjHqqqq0i233KKioiK53W45jqM1a9Yc8nHjzYQJE+Q4TtLHAACATSUlJXIcR9dcc02nHO/111/XuHHjlJeXJ8dxdMEFF3TKcePJm2++KcdxdO+999oOJaZ0Rl4Saex27733ynEcvfnmm7ZDAdrNbTsAAN3vjjvu0B//+Eedc845uvLKK5WSkqLCwkLbYQEAABySkpISnX/++crLy9P06dOVm5ur0aNH2w4L3aSkpERDhw7V1VdfrdmzZ9sOp1VFRUWS1CkfTAPJiCIWECcefvhh3XnnnRowYMAhH2vx4sUaOXKkFi1a1AmR4VA8++yzqqursx0GAADWDBgwQOvWrVOPHj0O+VjLli1TQ0ODfvOb3+jyyy/vhOiQSE444QStW7dOvXv37vAxEmnsdvPNN2vq1KkaPHiw7VCAdqOIBcSJfv36qV+/fp1yrO3bt+tb3/pWpxwLh4ZBAwAg2aWmpnbabKnt27dLkvr3798px0NiyczMPOTXWiKN3Xr37n1IBT3ABnpiAYfoYGvri4qKItOGw2bPni3HcTR79mwtX75cEyZMUE5OjnJzc3X22Wdr3bp1LY7TWk+sfXtIlJSUaOrUqerdu7cyMjJ03HHHafHixc2OEV7Db4zRW2+9Jcdx5DiOJkyYENknGAzqySef1PHHH6/s7GxlZWXp+OOP1x/+8AcFg8EWcYXvv3PnTl177bUaMGCAUlJSIlO4w7fv2rVL06dPV9++fZWVlaVx48bpnXfekSTV1tbq9ttv15AhQ5Senq4jjzxS//M//9NmzufOnauJEycqLy9PGRkZOvzww/Xggw+qsbGx1f1feOEFFRcXy+PxqKCgQFdeeWVkkBuN8HNZWVmpm2++WQMGDFBGRoaOOOII/dd//ZeMMc323/f5Wb9+vS677DIVFBTI5XJFeg+01Vehs58HAABiVVs9sfYd+/zxj3/UUUcdpYyMDPXt21ff//73VVlZGdk3PB675557JEkTJ06MjHP27fezYcMGXXXVVRowYIDS0tLUv39/XXXVVdqwYUOLuPbtFzRnzhydeOKJys7Ojozr9r197ty5Ki4uVmZmpvr376/bbrstMi75xz/+oQkTJig3N1c9e/bUlVdeqT179rSaiy+//FI333yzhg0bpvT0dPXq1UvnnXeeVq1a1er+u3bt0ve+9z317dtXHo9HY8aM0TPPPNPe1DdTWVmpH//4xxo4cKAyMjI0evRoPfroo9q0aVObPcvq6ur08MMPa8yYMcrKylJ2drZOOukkzZ07t8W++46Z16xZo7PPPlt5eXnKzMzUqaeeqnfffbfVuPx+v37/+9/rm9/8pnJzc5WZmamxY8fqiSeeaDYmuvfeezV06FBJ0jPPPBN5/sNj7v1j2F95ebl+9rOf6Rvf+IYyMzPVo0cPHXPMMbrzzjtVW1sb2a+1sZsxRs8884zGjRunPn36KCMjQ4MGDdKUKVP04osvNjv3li1btGXLlmbxtacfXPjnYdOmTXr00Uc1evRoZWRkaODAgbr11ltVVVXV4j7hsWtVVZVuu+02FRUVKTU1NfL4D9QT64033tAZZ5yh/Px8paena+TIkbrzzjub/dztn5Ompibdf//9GjVqlNLT0zutzx2wL2ZiARYtXrxYL7/8ss4880zdcMMNWrt2rV599VWtWrVKa9eubfcnI1u2bNEJJ5ygYcOG6corr1R5eblefPFFnX/++Vq2bJkmTpwoKfTmN2HCBN13330aMmRI5I1l3yLblVdeqTlz5mjQoEG69tpr5TiOXnrpJd10001asWKF/vrXv7Y4f3l5ub75zW8qOztbF110kVwul/r27Ru53ev16uSTT1ZOTo6++93vqry8XC+88IKmTJmi9957T9dff73Ky8t1zjnnyOfzae7cubrssss0aNAgffOb32x2runTp+vpp5/WwIEDdfHFFysvL0//93//p7vvvltvvPGGli5dKrf7619tjz32mG677Tbl5eXpqquuUl5enpYsWaJx48Z1aNlCU1OTvv3tb8vr9Wrq1KlqamrSggUL9KMf/Uiff/65fve737W4z8aNG3XiiSdq5MiRmjZtmurr65Wbm3vA83TF8wAAQDy64447tGTJEp177rmaPHmyli9frqeeekpffPGF/vGPf0gKjWXuuecevfnmm3rrrbd09dVXR8Y34X9XrVqlb3/726qurtZ5552nI444Qp999pmef/55vfzyy1q2bJmOP/74Fuf/zW9+o6VLl+rcc8/VxIkTW/wR//jjj+t///d/dcEFF2jChAl6/fXX9dhjj6m8vFznn3++pk6dqrPPPlvf//739e677+r5559XWVmZ/vd//7fZcVavXq3JkyervLxcU6ZM0UUXXaSysjItXLhQ48eP10svvaSzzjorsn9ZWZnGjRunTZs2afz48Ro/frx27NihG264QZMnT44qxw0NDZo0aZJWr16tsWPHatq0aaqsrNRDDz0U+dBxf16vV5MmTdLHH3+sY489VtOnT1cwGNSSJUt0+eWX69///rcefPDBFvf78MMP9cgjj+ikk07Stddeq61bt2rBggU67bTTtGbNGo0aNSqyr8/n07nnnqslS5Zo1KhRuvzyy5WRkaHly5frhz/8od5//30999xzkkKFFK/Xq9/+9rc65phjmjX0HzNmzAEf/+bNmzVx4kRt2bJFxcXFuvHGGxUMBrV+/Xo99thjuuGGG5SVldXm/X/2s5/p4Ycf1tChQ3XppZeqR48e2rFjh1atWqX/+Z//0WWXXRZ5jc6aNUuS9OMf/7jd8e3r1ltv1dtvv61LL71U559/vpYsWaJZs2bpnXfe0YoVK5SRkdFs/6amJk2aNEnl5eWaPHmycnNzI8W+tvzxj3/UjTfeqKysLH3nO99RQUGB3nzzTc2cOVOLFi3SypUrlZeX1+J+F198sVatWqUzzzxTF1xwgQoKCtr9uIB2MwAOyfLly40kc88997R6+5AhQ8yQIUOabXv66aeNJJOSkmKWLVvW7LY777zTSDIzZ85stv3qq682kszmzZsj2zZv3mwkGUnm3nvvbbb/a6+9ZiSZM888s0VMksypp57aYvucOXOMJDN27FhTXV0d2V5TU2OKi4uNJPPXv/61xbEkmSuvvNL4fL5WzyXJXH/99SYQCES2P/vss0aS6dmzpznnnHNMfX195La3337bSDIXXHBBs2OF83bhhReaurq6Zrfdc889RpKZNWtWs/ykpqaanj17NstbIBAwF110USS29hoyZIiRZE4++WTT0NAQ2b5nzx4zbNgwI8m89dZbzc4fPsddd93V6jFPPfXUFjF0xfMAAECsCr9fXn311c22h8c+gwYNMlu2bIls9/l85pRTTjGSzPvvv9/sPuHxwPLly5ttDwaDZvTo0UaSef7555vd9sILLxhJZtSoUc3GKuFjZWZmmtWrV7eIO3x7bm6uWbt2bWR7Q0ODOeKII4zL5TL5+fnmzTffjNwWCATMt7/9bSPJfPzxx80e0/Dhw016enqz/Y0x5quvvjL9+/c3hYWFzcYf1113nZFkfvzjHzfbf9WqVcbtdh9wfLq/+++/30gyU6dONcFgMLJ969atpnfv3gd8fvYfs9bX15spU6YYx3GaPcbwmFmSefrpp5vd58knnzSSzI033thsezjHN998s/H7/ZHtfr/fTJ8+3UgyCxcujGxv67W0fwz75+Wkk04ykswvf/nLFvcpLS1tNk5tbeyWn59vBgwYYGpra1u9/75a+9ugPcL57tWrlykpKYls33dce//997c4lyRz2mmnmZqamhbHbO3npaSkxKSlpZmcnByzbt26ZvvfeOONRpK57rrrmm0P5+Soo45q8XiBzkYRCzhEh1LEmjZtWov9N23aZCSZiy++uNn2AxWxhgwZ0uyNPWzw4MGmV69eLba3VcQKD6qWLFnS4rZly5YZSWbixIktjpWWlmZ27drV4j7h2zMzM01VVVWz7X6/PzLA2rhxY4v7FRUVmaKiombbxowZY9xut6moqGixv9/vN7169TLHH398ZNuDDz5oJJlf/OIXLfbfuHGjcblcHSpivf322y1uCz+n11xzTWRb+Pnp27dvs0HnvlobCHXF8wAAQKw6WBHrqaeeanGf//7v/zaSzOOPP95se1tFrBUrVhhJ5qSTTmo1hvHjx7f4MCp8rP2LRPvf/vOf/7zFbffdd1/kw6X9zZ4920gys2fPjmxbuHChkWR++tOftnquWbNmGUnm73//uzHGmKamJpOZmWlycnKM1+ttsX84d+0tYg0fPty4XK5m48yw8Hhq3+enrKzMpKSkmOOOO67V461Zs8ZIMrfffntkW3jMfPLJJ7fYv6mpybjdblNcXBzZFggETH5+viksLGz1A7qKigrjOI75zne+E9nWkSLWhx9+aCSZMWPGNCtitqWtIlZRUVGb4719HWoRa/9ClTFfj2v3HzuHx65r1qxp9Zit/byEn+/WPoAtLy83OTk5JiMjo9ljDedk34Ii0FVYTghYdNxxx7XYNmjQIElSRUVFu48zZswYpaSktHqs9957r93HWb16tVwuV7MeWWGnnnqqUlJS9PHHH7e4raio6IDThUeOHKmcnJxm21JSUtS3b1/V1tZq2LBhLe4zYMAAvf/++5Hv6+rq9Mknn6h3796Radj7S09Pb9ZPbPXq1ZHY9zds2DANGjRIW7ZsaTPu1rjdbo0bN67F9nDOWsvPMccco/T09Hafo6ueBwAA4lFnjJfCY4JJkya1evukSZO0YsUKffzxxy0ufnPCCSdEHV+4sXxxcXGL28JXmv7yyy8j28LjtS1btrTaryncs2vdunU666yz9Nlnn6murk6nnHJKq+0RJkyY0O7eWFVVVdq4caMGDRrUoo+rJI0fP77FtlWrVikQCLTZX8rn80Xi3V9r+UpNTVXfvn2bPZ/r169XeXm5RowY0eqyREnyeDytniMa//d//ydJmjJlilyujrWMnjZtmh5//HEdccQRuvTSS3XqqafqpJNO6pQrbu7vQOPakpISeb3eZkv9MjIydPTRR7f7+Af6WenZs6fGjh2rt99+W5999pmOOeaYZrcf7GcF6AwUsQCLWltLHu7nFAgEDuk44WO11gS8LZWVlcrPz1daWlqrx+rdu7d2797d4rbCwsIDHretN3C3233A2/x+f+T7iooKGWNUWlqq++6774DnCwv3rGirL1RhYWHURazevXu3WjAM56C1ZpcHy8/+uup5AAAgHnXGeCn8/tzWlZ7D271eb4vbOjLOCcd3oNvChR5JkUbvB7qwjSTV1NRIat8Yp73CDcHbOlZr28Pxrlq1qs2m8/vGu68DjVv3fT7D59iwYcMBx36tnSMa4ec8XFzsiMcee0zDhg3T008/rV/96lf61a9+JbfbrbPOOku/+c1vdNhhhx1SjPs62Li2srKyWY4LCgpavYhQW7ryZwXoDFydEDhE4U9s9i247Ku1X/CxqkePHiovL282qArz+/0qKytrtSF5NG+MhxKbJI0dO1YmtBS6za/977Nr165Wj7lz586o4ygrK2t1wBw+VmuD1WjzE8vPAwAA8Sj8/tzWe/+OHTua7bev7hznvPzyywcc44SvvtiZY5zwmKKtY7W2PXz+W2+99YDxLl++vN1xtHWOCy+88IDn2Lx5c4fPIX1dVPvqq686fIyUlBT9+Mc/1ieffKJdu3ZpwYIFuvDCC/XKK6/ojDPOaPMK2h1xsOd8/9dwR8ah+x5vf7Z/VgCKWMAh6tmzpyRp27ZtLW774osvWp2ZE6vGjh2rYDCot99+u8Vtb7/9tgKBgI499lgLkUnZ2dk68sgj9e9//1vl5eXtuk841rfeeqvFbZs2bWr1OTsYv9/f6iWgw5cmHjt2bNTH3F8sPw8AAMSj8Ptz+P16f+Fii6331/DVmNu6EuD+Ro8erczMTK1Zs6bVsWZbj7M1ubm5GjZsmL766iuVlJS0uH3FihUttp1wwglyuVztjrcjRo8eHbkKdWsf7LUmPFs+mhUN4dwvWbIkqhUMbSkoKNBFF12kefPmadKkSdq4caM+/fTTZjFGE9/+DjSuLSoqanOmW3sd6GfF6/VqzZo1ysjI0OGHH35I5wE6iiIWcIhGjx6t3Nxcvfzyy82WeNXX1+uWW26xGFn0pk+fLkm66667VFdXF9leV1enO++8U5L0ve99z0psknTbbbepqalJ06dPb3WGW0VFRWQdvxTqT5CamqrHH3+82aAsGAzq9ttv7/BA5a677mr2iVp5eXmkV8N//Md/dOiY+4r15wEAgHhz8skna9SoUVqxYoXmz5/f7Lb58+frnXfe0ciRI1vt/9Qdzj//fA0fPly/+93v9Oqrr7a6z3vvvRcZF6SmpmratGmqrq5u0ZPqww8/1F//+teozn/VVVcpGAzqrrvuajarfdu2ba32Ii0oKNC0adP04Ycf6oEHHmi1KLNx48ZDmiXldrv1wx/+UDt27NAtt9yi+vr6Fvvs2LFDa9eujXzfs2dPOY6jrVu3tvs8xcXFGjdunNasWaOZM2e2uH3Pnj1qaGho8/6NjY1auXJli+0+ny/ywWtmZmZke69evVRaWtrq42mP3/72t83aYew7ru2McegVV1wRGT9/8cUXzW67++67VVVVpSuuuCKqfq9AZ6InFnCIUlNT9aMf/UgPPPCAxo4dqwsvvFB+v19Lly5V//79I40948Hll1+ul19+WfPmzdORRx6pCy64QI7jaOHChdq8ebMuu+wyTZs2zVp806dP10cffaTf//73Gj58uKZMmaLBgwervLxcmzdv1ttvv63/+I//0JNPPikp1Oj8V7/6lX7yk59o7Nixuuyyy9SjRw8tWbJEXq9XRx99tP75z39GFUO/fv3U2Niob3zjGzrvvPPk8/k0f/587dixQzfddFOLZrAdEevPAwAA8cZxHD3zzDM6/fTTddlll+n888/X6NGj9fnnn2vhwoXKycnRs88+2+HG3ocqNTVVf/vb3zRlyhSdffbZGjdunMaMGaPMzExt27ZNq1at0qZNm7Rjx45IQeSXv/yl3njjDc2aNUsffvihxo8frx07dujFF1/UWWedpVdeeaXd57/jjju0cOFCvfDCC/r88881efJkVVZWat68efrWt76lhQsXtsjNE088oQ0bNugXv/iFnnvuOY0fP159+/bV9u3btW7dOq1atUpz587V0KFDO5yXu+++W5988omefPJJLVq0SJMmTdKAAQO0e/dubdiwQStXrtRDDz2kI444QlJo5v6JJ56od955R9OmTdPIkSOVkpKi884774DNzZ9//nlNmDBBM2bM0IIFCzRhwgQZY7Rhwwa9/vrr+uyzz1ptei+FPrgeP368DjvsMBUXF2vIkCFqaGjQ0qVLtW7dOp133nnNZi2ddtppWrVqlc444wx961vfUnp6uo455hide+657crJySefrDFjxjQb137yyScqLi7WHXfc0f7ktqGoqEizZs3SD37wAx177LG69NJL1adPH7311lt67733NHr06FaLfUB3oYgFdIL77rtPmZmZeuqpp/SnP/1JhYWFmjp1qu69997Im2q8mDt3rk499VT993//t/74xz9Kkg4//HD95Cc/0Y033mg5Oul3v/udzjzzTD355JNatmyZvF6v8vPzNXjwYN1+++264oormu1/2223qV+/fvrP//xPzZ49Wzk5OZoyZYoeeeQRXX755VGfPy0tTcuWLdOMGTP0wgsvqKysTMOGDdOdd96pH/7wh531MGP+eQAAIN6ceOKJWrVqlR588EEtW7ZMixYtUu/evfXd735Xd999t0aNGmU1vqOPPlqffPKJHn30US1evFhPP/20XC6X+vXrp7Fjx+q+++5T7969I/v37t1bK1eu1IwZM7Ro0SJ9+OGHGjVqlP7whz+oqKgoqiKWx+PR8uXL9Ytf/ELz58/XY489pqFDh2rGjBk65ZRTtHDhwhb9OHNzc/XWW2/pT3/6k+bMmaMFCxaooaFBffv21YgRI/TYY4/p9NNPP6ScpKamauHChXr++ec1e/ZsLV68WDU1NerTp4+GDh2qBx54oMUHe88995xuvfVWvfbaa5o7d66MMRo4cOABi1hDhw7V6tWr9cgjj2jhwoV64oknlJGRoaKiIv3kJz854NWfs7KyNHPmTC1fvlzvvvtupCg6fPhw/eEPf4jMsA/7+c9/Lq/Xq0WLFmnlypUKBAK6+uqr213Eeuyxx/TSSy/pqaeeUklJiXr16qUf/ehHuv/++5WRkdGuYxzMTTfdpMMOO0y//vWvtWDBAtXV1WnQoEG6/fbbNWPGjENesggcCsfsO18UANCm8CdwrfWLAAAASERPPfWUvv/97+vJJ5/U9ddfbzucpHXNNdfomWee0ebNm9ucFQYkA3piAQAAAECS2759e4ttW7du1QMPPCC3293umUIA0JVYTggAAAAASe7iiy+Wz+dTcXGx8vLyVFJSosWLF6uurk4PP/xwXPV5BZC4KGIBAAAAQJK78sor9dxzz2nBggWqrKyMNEm/+eabddFFF9kODwAk0RMLAAAAAAAAcYCeWAAAAAAAAIh5FLEAAAAAAAAQ8yhiAQAAAAAAIOZRxAIAAAAAAEDMs3Z1woqKCvn9/i45dp8+fVRaWtolx8bBkX+7yL9d5N8u8m9XV+bf7XarZ8+eXXJsdD7GeYmL/NtF/u0i/3aRf7tiZZxnrYjl9/vl8/k6/biO40SOz4UXux/5t4v820X+7SL/dpF/7ItxXmIi/3aRf7vIv13k365Yyj/LCQEAAAAAABDzKGIBAAAAAAAg5lHEAgAAAAAAQMyjiAUAAAAAAICYRxELAAAAAAAAMY8iFgAAAAAAAGIeRSwAAAAAANApjDEyVV6ZYNB2KEhAbtsBAAAAAACA+Ge8e2T+9ZHMnt1yDR4mHTvOdkhIMBSxAAAAAABAh5nGBmndJzIlX8jUVEkNdQoayTXkMDm9CmyHhwRCEQsAAAAAAHSI2bxeZt0nMlVeqaZKTn4fyZMpU1Ml8+lq6ZTJclx0MkLn4JUEAAAAAACiZnZtV/Dj92V2fiUnEJAz+mg5w0dLQ4bLaWqUKdslfbnZdphIIBSxAAAAAABA1MzWTVJdjZyevaQjx8rJ6SFJclLTpAGDpepKmXX/lPH5LEeKREERCwAAAAAARMU0NUo7t0kN9VLfAXIcp/kOfQfIcblkKsulL9baCRIJhyIWAAAAAACIzvatMg31cjI8crKyW9zsuFzS4GFSdZXMF+tkamssBIlEQxELAAAAAABExWzbLNXXSb37tr1TXi852TkyNZXSujXdFhsSF0UsAAAAAADQbqa6SmbPbjlNjVKvgjb3cxxHGjxMTm2NgttKZPaUdmOUSEQUsQAAAAAAQPt9uTnUCys3T05a2gF3dTKzQ4Wuuhpp28ZuChCJiiIWAAAAAABoF2OMzJclB19KuK/8PlJTo0zZ7i6NDYmPIhYAAAAAAGifsl0y1ZVyTFDK69W+++TkyvH7ZWqqZOpo8I6Oo4gFAAAAAADaJzwLK7+PnJSUdt3FSXFLWdmSr0liNhYOAUUsAAAAAABwUMbvk9m+VWqIYilhWG4PqbFRKtvVNcEhKVDEAgAAAAAAB7fjS5n6WjmpaVJ2bnT3zc2TfI0ye3bLGNMl4SHxUcQCAAAAAAAHZbZtjjR0dxwnujtn95ATCMjUVoeuVAh0AEUsAAAAAABwQKahXirdKTU0SL0Kor6/k5IiZeVITfTFQsdRxAIAAAAAAAdWXirT1CjHkyknw9OxY+TmSU30xULHUcQCAAAAAAAHVl4WurpgTpS9sPaV20NqapTZs4u+WOgQilgAAAAAAOCATHlpqIgVbUP3fWX3kBMMyNTVSjXVnRcckgZFLAAAAAAA0Cbj90uV5XtnYvXo8HEclytUBGtqlPawpBDRo4gFAAAAAADa5t0j09Qkx50qpaUf2rHoi4VDQBELAAAAAAC0bZ9+WI7jHNqxcsJ9sXbTFwtRo4gFAAAAAADa1Cn9sMKyc+UYE+qLVV156MdDUnFHs3MwGNS8efP0zjvvyOv1Kj8/X6eeeqouvvjiQ6/GAgAAAACAmGKMkSrKpKbOKWI5LpdMdm7oeHt2h5YXAu0UVRFr4cKFWrp0qX7wgx9o4MCB2rRpk37/+98rMzNTZ511VlfFCAAAAAAAbKiulGmolyMjZWZ3zjFz86Sy3TJlu+QMHdk5x0RSiKqItX79eh133HE69thjJUkFBQVasWKFvvjiiy4JDgAAAAAAWFSxtx9WVk7o6oKdIaeHtH1bqJBlDCu70G5RvQJHjhypTz/9VNu3b5cklZSU6PPPP9fYsWO7JDgAAAAAAGDRntLQ0r+cTuiHFZaVI0dGpqFOqvJ23nGR8KKaiXXBBReovr5et956q1wul4LBoKZOnapTTjmlzfv4fD75fL7I947jyOPxRP7f2cLHpJJrB/m3i/zbRf7tIv92kf/kxDgvuZB/u8i/Xcmcf1NRJsfXJGX3kNQ5j99xpcjk9JDja5JTUSYnL//A+ydx/mNBLOXfMVFc03LlypV6/vnndcUVV2jQoEEqKSnR7NmzddVVV2nChAmt3mfevHmaP39+5PuhQ4dq5syZhxw4AAAA7GKcBwCJLVhfp6r5zyqwY5s8J0+S407ttGM3bVqvQMUeeY4bJ88JbU+MAfYVVRHrxhtv1Pnnn68zzjgjsm3BggV65513NGvWrFbv09YndKWlpfL7/R2PvA2O46iwsFA7d+5UFA8NnYT820X+7SL/dpF/u7o6/263W3369On04+LQMM5LLuTfLvJvV7Lm32zfpuDKZVJDvZyjjuvcY5ftkr7cLGf4aLlOmXzAfZM1/7EilsZ5US0nbGxslGu/Rm4ul+uADyI1NVWpqa1Xa7vyxWeM4cVtEfm3i/zbRf7tIv92kf/kwjgvOZF/u8i/XcmWf7Nnt0xTo5zsXEmd/Lgzs2T8PqnKq2Aw2K6lasmW/1gTC/mPqohVXFysv/3tb+rdu7cGDhyokpISLV68WBMnTuyq+AAAAAAAgAUmfGXCzmzqHpbhkWNMqEhWXytlZnf+OZBwoipiTZ8+XS+++KL+/Oc/q7KyUvn5+Tr99NN1ySWXdFV8AAAAAACgmxm/X/KWh4pY2Z1fxHJcLpmMTGnvbCyKWGiPqIpYHo9H11xzja655pouCgcAAAAAAFhXWS7ja5ST4pbSM7rmHJlZUmNDqIhVOLBrzoGE4jr4LgAAAAAAIKnsKZWamqScHu3qV9UhmVmS3x8qYgHtQBELAAAAAAA0E+mH1QVLCSM8WZLfJ1Nd2XXnQEKhiAUAAAAAACKMMVJ52d6ZWF1YxMoMFbFUXSUTCHTdeZAwKGIBAAAAAICv1dfKNNbLMcGubbiemiYnxR1qIs9sLLQDRSwAAAAAAPC1Sm9ohpQnU46r68oGjuN8PRuLvlhoB4pYAAAAAADga1UVks/XtbOwwihiIQoUsQAAAAAAQISprAgVljKzuv5k4ebuFLHQDhSxAAAAAADA17p7JpbPR08stAtFLAAAAAAAIEkyviaZ2hop4O+2mVhOMCDTUCfTUN/150Nco4gFAAAAAABCKiskv19OWrocd2qXn85JSZHSM0LLF5mNhYOgiAUAAAAAAEIi/bC6YSlhWGaW5PPT3B0HRRELAAAAAACEVHn39sPqhqWEYR6uUIj2oYgFAAAAAAAk7XNlwqzunImVzRUK0S4UsQAAAAAAgEwwINVUdv9yQk9mpCeWCQa777yIOxSxAAAAAACAVF0l0+ST43JJaendd94MjxzHkfH5pNqa7jsv4g5FLAAAAAAA0Kypu+M43XZax3G+no3FkkIcAEUsAAAAAAAgVVVI/qbuXUoYtrcvlqoquv/ciBsUsQAAAAAAgEylV/L5u/fKhGF7r1BIc3ccCEUsAAAAAACSnDHG8kysTMkXau4OtIUiFgAAAAAAya6+VqaxQY4xof5U3c2TLQX8MrU1oQbvQCsoYgEAAAAAkOwqvaGeVJ7M0NUJu5mTmionNU0K+KRqb7efH/GBIhYAAAAAAMmuqiK0nM/GUsKwDI/k90s1VfZiQEyjiAUAAAAAQJIzlRWhmVg2mrqHeTL3FrGq7cWAmEYRCwAAAACAZBcTM7EyQ32xmImFNlDEAgAAAAAgiRlfk0xtjRTw252JFV5OWMtMLLSOIhYAAAAAAMmsskLy++Wkpctxp9qLwxOaiaXaaplg0F4ciFkUsQAAAAAASGaRflgWlxJKUlq6HEnG55fqauzGgphEEQsAAAAAgGRW5d3bD8viUkJJjuNE+mLR3B2toYgFAAAAAEASM7EyE0uSPHv7YtHcHa2giAUAAAAAQJIywWCoYOS3PxNLUqi5e8BHc3e0iiIWAAAAAADJqrZaxtcUWsqXnmE7mtByQr9fhplYaAVFLAAAAAAAklVVZWgWliczVMiybW8Ri+WEaA1FLAAAAAAAklVVRahoFAv9sKRQT6xAQKahXsbXZDsaxBiKWAAAAAAAJClTHZ6JFQP9sCQ5KW45aWlSICBVMxsLzVHEAgAAAAAgWVV5JZ9Pysy0HcnXMvZeoZDm7tiPO9o7lJeX6/nnn9eaNWvU2NiowsJC3XTTTRo+fHhXxAcAAAAAALqA8flkamukgF/yxMhyQinUF6u+hr5YaCGqIlZNTY3uvvtuHXnkkZoxY4Zyc3O1Y8cOZWXFxrRDAAAAAADQTtWVUsAvx50qJzXVdjRf83ikaq9MTbVioNU8YkhURayXX35ZvXr10k033RTZVlBQ0OlBAQAAAACALlbtDfXDyoyxiSlcoRBtiKqI9eGHH+qYY47Ro48+qrVr1yo/P1+TJ0/Wt7/97Tbv4/P55PP5It87jiOPxxP5f2cLHzMmLg2ahMi/XeTfLvJvF/m3i/wnJ8Z5yYX820X+7UrU/JvqSjl+n5SdJ8XSnKeMzNAMsboayRg5rlA770TLf7yIpde/Y4wx7d152rRpkqSzzz5bJ510kjZu3Kinn35a1113nSZMmNDqfebNm6f58+dHvh86dKhmzpx5aFEDAADAOsZ5ABDfapcuUsO6T5Q2ZLjchQNshxNhTFD177yhlL79lXvhNLlycm2HhBgR1UysYDCo4cOH6/LLL5cUGqhs3bpVS5cubbOIdeGFF+qcc86JfB+u3JWWlsrv93cw7LY5jqPCwkLt3LlTUdTn0EnIv13k3y7ybxf5t6ur8+92u9WnT59OPy4ODeO85EL+7SL/diVi/o0xMtu2KFhVqfqmgJzyCtshNWOMJG+F6jZukKtwQMLlP57E0jgvqiJWz549NXDgwGbbBg4cqPfff7/N+6Smpiq1jQZxXfniM8bw4raI/NtF/u0i/3aRf7vIf3JhnJecyL9d5N+uRMq/aahTsKFeTiAQaqSuGHtcGR4Zv1+mulKmb39JiZX/eBQL+XdFs/OoUaO0ffv2Ztu2b9/OJ6MAAAAAAMSTqspQU/d0j5yUFNvRtJThkQI+qabadiSIIVEVsc4++2xt2LBBf/vb37Rz506tWLFCb7zxhqZMmdJV8QEAAAAAgM5W5Q1dATDWrkwY5smU/AEZrlCIfUS1nPCwww7TT3/6U82ZM0cLFixQQUGBrr76ap1yyildFR8AAAAAAOhs1XtnYuX2sB1J68IzsWopYuFrURWxJKm4uFjFxcVdEQsAAAAAAOgGpsobKmJ5YnQmVsbemVj1dTI+n+1oECOiWk4IAAAAAADimwkGv56JFaPLCR23W05qqhQIMBsLERSxAAAAAABIJrU1Mr4mOY4jpWfYjqZtGZ5Q365qilgIoYgFAAAAAEAyqfaGikOezFAhK1Z5MqWAn+buiKCIBQAAAABAMon1flhhGZmhYlttte1IECMoYgEAAAAAkEQiTd1jtB9WRPgKhSwnxF4UsQAAAAAASCbhpu6xPhPL8/VMLGOM7WgQAyhiAQAAAACQJIzfJ9XWhIpDsT4TKz1DjiTja5KprbEdDWIARSwAAAAAAJJFdZWM3yfHnSonNc12NAcUunqiRwoEFKyutB0OYgBFLAAAAAAAkkW89MMKy/BIfp8ClV7bkSAGUMQCAAAAACBZVHvjox9WmMcj+f0KVnttR4IYQBELAAAAAIAkYaq8ki8O+mGFZWRKAT/LCSGJIhYAAAAAAEnBGPP1csJ4mYmV4ZHx+xVkOSFEEQsAAAAAgOTQUC/T0CAnGIi7mViB2hoZv992NLCMIhYAAAAAAMkgPAsrI1OOKz7KAU5qqpwUtxTwS7XVtsOBZfHxqgUAAAAAAIemsiK+rkwY5smU8fukmirbkcAyilgAAAAAACSD8JUJ462IleGRfD5mYoEiFgAAAAAAycBUVoSKQZnZtkOJTkamTMAvU81MrGRHEQsAAAAAgARn/H6ppjpuZ2IZZmJBFLEAAAAAAEh8NZUyfp8ct1tKTbMdTXQyMkPFt5oqGWNsRwOLKGIBAAAAAJDoKr17Z2Fly3Ec29FEJ8MjBYMyTY1SY4PtaGARRSwAAAAAABJdlTfUD8sTZ0sJJTkul5wMj+T3s6QwyVHEAgAAAAAgwZmqivjsh7WX48mUAn6phubuyYwiFgAAAAAACcwYE5qJ5Y/DKxPu5crMCs3EqmEmVjKjiAUAAAAAQCKrr5NpbJATDEqeTNvRdIjjyZICfhlmYiU1ilgAAAAAACSy8FJCT5YcV3yWAZiJBYkiFgAAAAAAiS3c1D1O+2FJkpOZJRPwS3U1MsGA7XBgCUUsAAAAAAASmKn0hmYxxXMRKy1djuOS8fuk2lrb4cASilgAAAAAACSySFP3OC5iOY6U4QkV42rpi5WsKGIBAAAAAJCgQjOXqvf2xIrPKxNGZHikgF+iuXvSoogFAAAAAECiqqqU8fvkuFPlpKXZjubQZGTS3D3JUcQCAAAAACBRVXvjfilhxN6ZWKaWIlayoogFAAAAAECiqqzYe2XCOF9KKO0zE4vlhMmKIhYAAAAAAAnKJEBT9wiPRwoEZBrqZXxNtqOBBRSxAAAAAABIQMaYhLgyYZiT4g719QoEpGpmYyWjQypiLVy4UJdeeqlmz57dSeEAAAAAAIBOUVcr09Qox5jQUrxEkOEJLSmkL1ZS6nAR64svvtDSpUs1ZMiQzowHAAAAAAB0hipvqB+WJ1OOK0EWYmVkSgEffbGSVIdexQ0NDXr88cd1/fXXKysr/qckAgAAAACQcKoq9i4lTICm7mF7Z2KZGmZiJaMOFbH+/Oc/a+zYsTr66KM7Ox4AAAAAANAJjLc8YfphRWR4pIBfqmUmVjJyR3uHlStXavPmzXr44Yfbtb/P55PP54t87ziOPB5P5P+dLXzMrjg2Do7820X+7SL/dpF/u8h/cmKcl1zIv13k3654zL8xRk5luYzPJ2XlSoqf2PcXTrvjSMaTJfkDcmprJGMSZ5lkDIul139URayysjLNnj1bP//5z5WWltau+7z00kuaP39+5PuhQ4dq5syZ6tOnT3SRRqmwsLBLj48DI/92kX+7yL9d5N8u8p9cGOclJ/JvF/m3K57yH6yrUVWKS4G0VHkGDpKTkmI7pEPWs2dPmbweqv/Co5T0NOXkZCklN892WEkjFl7/jjHGtHfnDz74QL/+9a/l2qfSGQwG5TiOHMfRnDlzmt0mtf0JXWlpqfx+fyc8hOYcx1FhYaF27typKB4aOgn5t4v820X+7SL/dnV1/t1ud5cXRhA9xnnJhfzbRf7tisf8mx3bFFyxTGqol3PUcbbDOSSOEypgVVRUyBjJfPqRlJ4u1/jT5fQbZDu8hBdL47yoZmIdddRR+vWvf91s2x/+8Af1799f559/fosCliSlpqYqNTW11eN15Q+/MSZufrkkIvJvF/m3i/zbRf7tIv/JhXFeciL/dpF/u+Ip/6Zij4yvSU52jqT4iLktxjh7/5UkI3kyZRobZKq8UuFAm6EllVh4/UdVxPJ4PBo8eHCzbenp6crJyWmxHQAAAAAA2GG85ZKvSepVYDuUzufJlOpqpOpK25Ggm9EBDQAAAACABGKMkbzlks8nZeXYDqfzebIkv0+GIlbSifrqhPu79957OyEMAAAAAADQKepqZRrr5ZiglJllO5rO58mU/H6ppkomGOQKhUmEZxoAAAAAgETi3ROahZWZlZgFnvQMOY4j4/NJtTW2o0E3SsBXMwAAAAAASSzcDysRlxIqdLU8ZeydjVXttR0OuhFFLAAAAAAAEohJ5H5YYZmhvliqrrIdCboRRSwAAAAAABKECQZDywn9TVJWtu1wuo6HmVjJiCIWAAAAAACJorZapqlRjhS6il+iilyhkJlYyYQiFgAAAAAAicJbHlpml5kd6h2VqMIzsWqrZIIB29Ggm1DEAgAAAAAgUSR4U/eItHQ5LhdXKEwyFLEAAAAAAEgQxrsn8Zu6a+8VCsOzsaoqbYeDbkIRCwAAAACABGCCAamyYu9MrARu6h7mydx7hUKv7UjQTShiAQAAAACQCKqrZJqa5LhcUobHdjRdj+buSYciFgAAAAAAicBbLvmbEr+pe1h4OSEzsZIGRSwAAAAAABJBuB9WdmL3w4rIzNp7hcIamQBXKEwGFLEAAAAAAEgAJlmuTBiWmha6QqHfJ9WypDAZUMQCAAAAACDOmUBAqqpIiisThjmOI2WGm7tTxEoGFLEAAAAAAIh3VV4Zn0+O2y2lpduOpvt49i4prPLajgTdgCIWAAAAAADxrqJs71LCJGnqHuYJzcQyNczESgYUsQAAAAAAiHNmz26pqUnK6WE7lO4VmYlVaTsSdAOKWAAAAAAAxDFjjLRnt9TUmIRFrL09sWqruUJhEqCIBQAAAABAPKuulKmvkyOTNE3dI1LT5KS4Zfx+iSWFCY8iFgAAAAAA8WxPaWgpYXauHFdy/ZnvOE5oNlbAJ1V7bYeDLpZcr24AAAAAABLNnl2SLwmXEoZ5skJLCquZiZXoKGIBAAAAABCnjDEye0qTsx9WWGam5PfLVHltR4IuRhELAAAAAIB4VVMtU1crJxiUsnNtR2OHJ0vy+SSKWAmPIhYAAAAAAPGqfHdoKWES9sOKyMqWE/DL1NXINNTbjgZdKElf4QAAAAAAJICy3aGm7sm6lFCSk+IONXf3+STvHtvhoAtRxAIAAAAAIA6F+mHtCvXDyk3eIpYkKStH8jVJ3nLbkaALUcQCAAAAACAe1dXs7YcVkLKStB9WWFaO5PPJMBMroVHEAgAAAAAgHoWXEmblyElJsR2NXeGZWBXlMsbYjgZdhCIWAAAAAADxaM9ulhKGZWbJMUGZxnqprtZ2NOgiFLEAAAAAAIhDZs/eKxMmcVP3MMflkjKzaO6e4ChiAQAAAAAQZ0xdjUxttRy/X8qmiCUp1BfM1yRVUMRKVBSxAAAAAACIN2W7QwUb+mF9LStb8jXR3D2BUcQCAAAAACDelNMPq4Xs0BUKVVkhEwzajgZdgCIWAAAAAABxxoSvTJiTZzuU2JGRKcdxZJoapZpK29GgC1DEAgAAAAAgjpj6Opmaajl+n5STazucmOE4TmRJoSrKbYeDLuCOZueXXnpJH3zwgb766iulpaVp5MiRuuKKK9S/f/+uig8AAAAAAOxr9/bQUsKsbDkpUf1Zn/iycqQqr+Qtl4YMtx0NOllUM7HWrl2rKVOm6KGHHtLPf/5zBQIBPfjgg2poaOiq+AAAAAAAwD7Mji+lxnqpZ2/bocSe7ByauyewqEq2P/vZz5p9/4Mf/EDXXnutNm3apCOOOKJTAwMAAAAAAM0Zn08q3Sk1Nkg9e9kOJ/Zk7W3uXlUhEwhw5cYEc0jzDuvq6iRJ2dnZbe7j8/nk8/ki3zuOI4/HE/l/ZwsfsyuOjYMj/3aRf7vIv13k3y7yn5wY5yUX8m8X+bcrpvJfukOmsUFOWoaUkSUpBmLqYuG0O45kzEEeb1qGHLdb8vnkVHnl5DNb7VDF0uvfMcaYjtwxGAzqkUceUW1trR544IE295s3b57mz58f+X7o0KGaOXNmR04JAACAGMI4DwC6X93KN9SwZpVSevZS2vBRtsOJSQ3/+kgyRpmnTFb66G/YDgedqMNFrKeeekpr1qzR/fffr1692p7C2NYndKWlpfL7/R059QE5jqPCwkLt3LlTHXxoOATk3y7ybxf5t4v829XV+Xe73erTp0+nHxeHhnFeciH/dpF/u2Il/yYYkHntbwru2CZn5FFycnpYi6U7OY7Us2dPVVRUqD3pN19tkSpK5Rw+Rq7icV0fYIKLpXFeh5YT/uUvf9Hq1at13333HbCAJUmpqalKTU1t9bau/OE3xvDL3SLybxf5t4v820X+7SL/yYVxXnIi/3aRf7ts59+U7lKwrlaO4wo1MFdyvBbCSwhDqW/HY87Kltn1lVSxh5+XTmT79S9FeXVCY4z+8pe/6IMPPtAvfvELFRQUdFVcAAAAAABgXzu/3NvQvXdM9CeKWVk5kt8nU1Mp42uyHQ06UVRFrL/85S9655139KMf/Ugej0der1der1dNTbwoAAAAAADoKsYYmZ1fSg31XJXwIJzUVDnpGZLfL3nLbYeDThTVcsLXX39dknTvvfc2237TTTdpwoQJnRUTAAAAAADYV8UemZoaOcZIuXm2o4l9WTmSr0mq2CP1KbQdDTpJVEWsefPmdVUcAAAAAACgLTu/lBrrpbx8Oa6oFlUlp6wcqXSHTPluOTrSdjToJLzyAQAAAACIcSbSD4ulhO3So6fU2CiV7Zbpgivmwg6KWAAAAAAAxDBTXSVT5ZXj90l5+bbDiQ+eTDmpqTKN9dKe3bajQSehiAUAAAAAQCwLz8LKzZOTElVXoKTlOI7UIz80G2v3dtvhoJNQxAIAAAAAIIaFrkrYIOWxlDAqeflSY4PMru0yxtiOBp2AIhYAAAAAADHK1NbI7CmVmuiHFbXcPDkBv0xNlVRTbTsadAKKWAAAAAAAxKotG6SGOjm5eXLS0m1HE1eclBQppwdLChMIRSwAAAAAAGKQ8ftltmyS6mqlvgNshxOfeuxdUrh7h+1I0AkoYgEAAAAAEIu2b5WprQrNKOKqhB2Tlx9ailm2S8bvsx0NDhFFLAAAAAAAYowxRmbz+tAsrIJ+oavtIXoZHjlp6TKNoUIW4htFLAAAAAAAYk3FHpnyUjlNTVKffrajiVuO44SWFDY1SLtYUhjvKGIBAAAAABBrStZL9bVSrz5yUlNtRxPf8vKlxkaZ3dtljLEdDQ4BRSwAAAAAAGKIaWyQ+WqLVFcnFfS3HU78y+khJ+CXqamWqittR4NDQBELAAAAAIBYsmWjTF2dnMxMOdk5tqOJe05KipSbF1pSuHu77XBwCChiAQAAAAAQI0wwKFOyQaqvkfoOsB1O4uiRLzU2yOymL1Y8c9sOoDMZY6SAX8bnk/H7WOtqg+OQf5vIv13k3y7yb1c4/+QeAIBDs+srmepKOcZI+X1sR5M48vKlbZukPbtlfD76jMWphCpiKeBX8NX5qsrJVrC6RhID6e5m5JB/i8i/XeTfLvJvVzj/+taZUkpiDS8AAOhOZtN6qa5W6tNPjovFU53FyfBIaRkyjY1ySndI/QfbDgkdkJCjTN+XW2TqG8QfMTY48lVmkH9ryL9d5N8u8m+XI+WMsh0EAABxzez8Smb3djmN9VJBP9vhJJ68fKnKK7N1kxyKWHEpsYpYKW65zv6OMrd9oYZyr/gjxgZHmfl55N8a8m8X+beL/NvlKHfKuaotLbUdCAAAcckEAjL/Xh26el7f/nLSM2yHlHj69peze7vMzi9DSzZzetiOCFFKqCKW4zhy3KlyUtyhqw/wR4wFDvm3ivzbRf7tIv92OXJSU+U4Dn2xAADoiI2fyZSXyQkEpAFDbEeTkJwMj0yPfKm+Ttq0XjrmeNshIUossAUAAAAAwCJTXyez/lOp2isNHiaH/pJdp3CAVFcjs22TTGOj7WgQJYpYAAAAAADYtPbj0PI2T5bUq8B2NIktp0doRlZdjbRlg+1oECWKWAAAAAAAWGLKdim4dbOc2mppyHA5jmM7pITmOI5UOFCqrZHZvEEmELAdEqJAEQsAAAAAAAtMMCjzr4+kmkqpT6GcrBzbISWH/D6hPp7VldJXW2xHgyhQxAIAAAAAwIbN62X27Jbj80kDimxHkzQcl0vq2z/UG2vT51yUJo5QxAIAAAAAoJuZsl0yaz+WqrzSwCI5qam2Q0ouBf3k+Jpkysuksl22o0E7UcQCAAAAAKAbmepKmQ/elikvk5ObJxX0sx1S0nHcqVLvwshsLMQHilgAAAAAAHQT01Av8/6bMuWlctLSpGGjaOZuS9/+chrqZHZsk6mqsB0N2oEiFgAAAAAA3cD4fTIfvCVTuktOMCiN+IaclBTbYSUtx5Mp5eVLNdUyH70r4/fZDgkHQRELAAAAAIAuZoLBUKFk51dyGuqkUUfRBysWDBkhx++TKd0pfbKKJu8xjiIWAAAAAABdyPiaZD5aKbNts5zqSmnEkXIyPLbDghRa0nnY4XKqKhXc8oVUssF2SDgAt+0AAAAAAABIVKZiT6iAtWe3nJoqadhoOTk9bIeFfTg5PWQGFknbt8r86yOpR76c/N62w0IrmIkFAAAAAEAnM8bIbPxM5p3XZXZsk9NQL40+muJIrCocICc3T8ZbHio6NjbajgitoIgFAAAAAEAnMnW1Mh+8reCa92XKdoYaiH+jWE52ru3Q0AbHcaRhI+VIMnt2hwpZNHqPOSwnBAAAAACgE5iqCumLz2S+3CxTWyOntloaPEwq6B8qkiCmOSlumRGHy1m7RubLzVJdjXTMCXL6FNoODXt1qIj12muvadGiRfJ6vRoyZIimT5+uww47rLNjAwAAAAAgpplgUNqzO7R0cOeXUl2tVFcTmnV1xBg5WTm2Q0QUnMxsmZHfkLPpc5ntW2Wqq+QaNir0XHI1SeuiLmK9++67evbZZ3XddddpxIgR+vvf/66HHnpIs2bNUo8eNKcDAAAAACQ2U1crle6USnfIlO6Sqa+V6mrlNNRJPXtJQw6Tk03xKl45uXkyRxXL2bZZpnSngk2NcnZvl44YI/XtL8dNMcuWqItYixcv1mmnnaaJEydKkq677jqtXr1ay5cv1wUXXNDZ8QEAAAAA0O1MMCg1NYZmVtVWqWHnFgW3lMhUV8pUV4Vua2qQGhvlOJJ6FUgjjpCT4bEdOjqBk+KWikZI+X2kzetltm+TqayQk54h07uvnIJ+oYIWfc66VVRFLL/fr02bNjUrVrlcLh111FFav359Z8cGAAAASJJMQ71UUyW/AjKlpTLG2A4p+TgO+bcpGfPf4nGa1r+N7Gf2bjOhbeEvGSloJBOUgvt+BaSAX/KHvkzAL/mapMavi1PGBKWAX44/oLr0NJmqShm/T47fL2XnSD17S3n5UlYOPa8SlJObJ/ONYjnbt4aWjXr3SBV7ZLZuktLT5aRnSBkeKSNTjscjpXuk1FQpxS25UqSUvV9yJEeS4wr9Gzp6KyeMwddR+PeP3+x9LPZEVcSqqqpSMBhUXl5es+15eXnavn17q/fx+Xzy+b7u6O84jjweT+T/nS18TMeRjInBJz/BhZ9S8m8H+beL/NtF/u36Ov/kPpl06zivvFTmo5Wqzc6Wqalp+bctup4j8m9TUub/IA+0xc2mlf/uu818XfBqUeDaW+QyJlTc2lvocoyR0tKkzGy5+xTKyS8IXWkwK4f+SN3JceTKzpXT5GuluNkNp5ek3KNkjJFTXydVlMlUlEmVFaFBUEqK5EqR2fuvXK5I3KFBktOycOW0OEPs2vv7xznpNMmdZTWULr864UsvvaT58+dHvh86dKhmzpypPn36dN1JCwvFBE67yL9d5N8u8m8X+bersJCr9yST7hzn+YxfjbuGSJJ65PXq9OOj/ci/XUmX/7b+to8Uyvf5FGvf4rnjyHFcoW2uUBHB2afA4LhcUkpKqLeR2y3H7ZbcqXJS0+TK8MgJf6VnhPbdi4VjdvW3HcB+jN+vYG21TF2tgnW1CtbXytTVyfh9UsAvEwh8/e/+swNbK8bFeIG6b2E/uTLjqIiVm5srl8slr9fbbLvX620xOyvswgsv1DnnnBP5PvypXGlpqfx+f3TRtoPjOCosLNTOnTuTZ5ptDCH/dpF/u8i/XeTfrq7Ov9vt7toPwNAh3TrOc9xyisfzc24Rv2ftIv/drKEp9KVKSeTfttjPf4qUmRv6SsA6c7P8V1Z1+vGjGedFVcRyu90aNmyYPv30U51wwgmSpGAwqE8//VRnnHFGq/dJTU1VahvTLLvyxWeMidEXd3Ig/3aRf7vIv13k3y7yn1wY5yUn8m8X+beL/NtF/u2KhfxHvZzwnHPO0e9+9zsNGzZMhx12mF599VU1NjZqwoQJXRAeAAAAAAAA0IEi1rhx41RVVaV58+bJ6/WqqKhIM2bMaHM5IQAAAAAAAHCoOtTY/Ywzzmhz+SAAAAAAAADQ2VwH3wUAAAAAAACwiyIWAAAAAAAAYh5FLAAAAAAAAMS8DvXE6pQTu7v21F19fBwY+beL/NtF/u0i/3Z1Vf55XuML47zERv7tIv92kX+7yL9dsTDOc4wxpkuiAAAAAAAAADpJwi0nrK+v1//7f/9P9fX1tkNJSuTfLvJvF/m3i/zbRf7RHXid2UX+7SL/dpF/u8i/XbGU/4QrYhljtHnzZjHBzA7ybxf5t4v820X+7SL/6A68zuwi/3aRf7vIv13k365Yyn/CFbEAAAAAAACQeChiAQAAAAAAIOYlXBErNTVVl1xyiVJTU22HkpTIv13k3y7ybxf5t4v8ozvwOrOL/NtF/u0i/3aRf7tiKf9cnRAAAAAAAAAxL+FmYgEAAAAAACDxUMQCAAAAAABAzKOIBQAAAAAAgJhHEQsAAAAAAAAxz207gI547bXXtGjRInm9Xg0ZMkTTp0/XYYcd1ub+7733nl588UWVlpaqsLBQ06ZN07HHHtuNESeWaPK/bNkyvf3229q2bZskadiwYfrud797wOcLBxbt6z9s5cqV+u1vf6vjjjtOd9xxRzdEmpiizX9tba3mzp2rDz74QDU1NerTp4+uvvpqfgd1ULT5//vf/67XX39dZWVlys3N1YknnqjLL79caWlp3Rh1Yli7dq1eeeUVbd68WRUVFfrpT3+qE0444YD3+fe//61nn31W27ZtU69evXTxxRdrwoQJ3RMw4hbjPLsY59nFOM8uxnl2Mc6zJ57GeXE3E+vdd9/Vs88+q0suuUQzZ87UkCFD9NBDD6mysrLV/T///HP99re/1aRJkzRz5kwdf/zx+s///E9t3bq1myNPDNHmf+3atTr55JN1zz336MEHH1SvXr304IMPqry8vJsjTwzR5j9s9+7deu6553T44Yd3U6SJKdr8+/1+PfjggyotLdVtt92mWbNm6frrr1d+fn43R54Yos3/ihUrNGfOHH3nO9/RY489phtuuEHvvfee5s6d282RJ4bGxkYVFRXpe9/7Xrv23717t371q1/pyCOP1COPPKKzzz5bTz75pNasWdO1gSKuMc6zi3GeXYzz7GKcZxfjPLviaZwXd0WsxYsX67TTTtPEiRM1cOBAXXfddUpLS9Py5ctb3f/VV1/VmDFjdN5552ngwIGaOnWqhg0bptdee62bI08M0eb/lltu0ZQpU1RUVKQBAwbohhtukDFG//rXv7o58sQQbf4lKRgM6vHHH9ell16qgoKCbow28USb/3/84x+qqanR7bffrtGjR6ugoEBHHHGEioqKujfwBBFt/j///HONGjVK48ePV0FBgY455hidfPLJ+uKLL7o58sQwduxYTZ069aCfyoW9/vrrKigo0FVXXaWBAwfqjDPO0De/+U39/e9/7+JIEc8Y59nFOM8uxnl2Mc6zi3GeXfE0zourIpbf79emTZt01FFHRba5XC4dddRRWr9+fav3Wb9+fbP9JemYY47Rhg0bujTWRNSR/O+vsbFRfr9f2dnZXRVmwupo/ufPn6/c3FxNmjSpO8JMWB3J/0cffaQRI0boL3/5i6677jr95Cc/0d/+9jcFg8HuCjthdCT/o0aN0qZNmyKDmV27dunjjz/W2LFjuyXmZLdhw4ZW33/b+36B5MM4zy7GeXYxzrOLcZ5djPPij81xXlz1xKqqqlIwGFReXl6z7Xl5edq+fXur9/F6verRo0ezbT169JDX6+2iKBNXR/K/v7/+9a/Kz89v8YLHwXUk/5999pn+8Y9/6JFHHumGCBNbR/K/a9culZaWavz48brrrru0c+dO/fnPf1YgENB3vvOdbog6cXQk/+PHj1dVVZXuvvtuSVIgENDpp5+uiy66qKvDhdp+/62vr1dTUxP9KtAC4zy7GOfZxTjPLsZ5djHOiz82x3lxVcRCfFu4cKFWrlype++9lz9eukF9fb0ef/xxXX/99crNzbUdTlIyxig3N1fXX3+9XC6Xhg0bpvLycr3yyisMbrrBv//9b7300ku69tprNWLECO3cuVNPP/205s+fr0suucR2eACQUBjndS/GefYxzrOLcV7yiqsiVm5urlwuV4tP17xeb4uqbVheXl6LZnCVlZVt7o+2dST/Ya+88ooWLlyou+++W0OGDOm6IBNYtPkPfzo0c+bMyDZjjCRp6tSpmjVrlgoLC7sy5ITS0d8/brdbLtfXK7cHDBggr9crv98vtzuufgVb1ZH8v/jii/rWt76l0047TZI0ePBgNTQ06E9/+pMuuuiiZs8LOl9b778ej4c/cNEqxnl2Mc6zi3GeXYzz7GKcF39sjvPi6pl1u90aNmyYPv3008i2YDCoTz/9VCNHjmz1PiNHjmzRXPKf//ynRowY0aWxJqKO5F+SXn75ZS1YsEAzZszQ8OHDuyPUhBRt/vv3769f//rXeuSRRyJfxcXFkStI9O7duzvDj3sdef2PGjVKO3fubNYbYceOHerZsycDmyh1JP+NjY1yHKfZNgY03WfEiBGtvv8e6P0CyY1xnl2M8+xinGcX4zy7GOfFH5vjvLh7ls855xy98cYbevPNN/Xll1/qz3/+sxobGzVhwgRJ0hNPPKE5c+ZE9j/rrLP0ySefaNGiRfrqq680b948bdy4UWeccYalRxDfos3/woUL9eKLL+rGG29UQUGBvF6vvF6vGhoaLD2C+BZN/tPS0jR48OBmX1lZWcrIyNDgwYN5c+2AaF//kydPVk1NjWbPnq3t27dr9erVeumllzRlyhRLjyC+RZv/4uJiLV26VCtXrtTu3bv1z3/+Uy+++KKKi4sZ5HRAQ0ODSkpKVFJSIil0aeWSkhKVlZVJkubMmaMnnngisv/kyZO1e/duPf/88/rqq6+0ZMkSvffeezr77LNthI84wTjPLsZ5djHOs4txnl2M8+yKp3Fe3P12GzdunKqqqjRv3jx5vV4VFRVpxowZkWmGZWVlzSqyo0aN0i233KIXXnhBc+fOVb9+/XT77bdr8ODBlh5BfIs2/0uXLpXf79ejjz7a7DiXXHKJLr300u4MPSFEm390rmjz37t3b/3sZz/TM888o9tvv135+fk688wzdcEFF9h5AHEu2vxffPHFchxHL7zwgsrLy5Wbm6vi4mJ997vftfQI4tvGjRt13333Rb5/9tlnJUmnnnqqfvCDH6iioiIy0JGkgoIC3XnnnXrmmWf06quvqlevXrrhhhs0ZsyY7g4dcYRxnl2M8+xinGcX4zy7GOfZFU/jPMeEF08DAAAAAAAAMYp5dgAAAAAAAIh5FLEAAAAAAAAQ8yhiAQAAAAAAIOZRxAIAAAAAAEDMo4gFAAAAAACAmEcRCwAAAAAAADGPIhYAAAAAAABiHkUsAAAAAAAAxDyKWAAAAAAAAIh5FLEAAAAAAAAQ8yhiAQAAAAAAIOZRxAIAAAAAAEDM+/8dsh6yrC/MAAAAAABJRU5ErkJggg==",
+ "text/plain": [
+ "<Figure size 1500x300 with 2 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1, 2, sharey=True, figsize=(15,3) )\n",
+ "uninformed_prior = [stats.beta.pdf(pi, a=alpha_uninformed, b=beta_uninformed) for pi in pi_range]\n",
+ "ax[0].plot( pi_range, uninformed_prior, alpha=0.5 )\n",
+ "ax[0].fill_between( pi_range, uninformed_prior, alpha=0.3 )\n",
+ "ax[0].set_title(\"uninformed prior\")\n",
+ "geneticist_prior = [stats.beta.pdf(pi, a=alpha_geneticist, b=beta_geneticist) for pi in pi_range]\n",
+ "ax[1].plot( pi_range, geneticist_prior, alpha=0.5 )\n",
+ "ax[1].fill_between( pi_range, geneticist_prior, alpha=0.3 )\n",
+ "ax[1].set_title(\"informed geneticist prior\");"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "078c7bff-3384-4c3b-b80a-decb9d21534a",
+ "metadata": {},
+ "source": [
+ "### Likelihood"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "id": "1052f26e-4985-440c-ae32-28af44b8d536",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 1000x300 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "pi_range = np.linspace(0, 1, 100)\n",
+ "likelihood = [stats.binom.pmf(k=k, n=n, p=pi) for pi in pi_range]\n",
+ "\n",
+ "plt.figure( figsize=(10,3) )\n",
+ "plt.plot( pi_range, likelihood )\n",
+ "plt.fill_between( pi_range, likelihood, alpha=0.3 )\n",
+ "plt.title( \"n={}, k={}\".format(n, k) );"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "fafcaa76-291b-4c3c-bf9a-561f964fc174",
+ "metadata": {},
+ "source": [
+ "The likelihood is not a probability distribution! (hence the different name)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "326b2f98-3812-4899-b6dc-2f27715e9733",
+ "metadata": {},
+ "source": [
+ "### Posterior distributions"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "id": "2c654812-b1eb-4651-87b4-ef7fbc756e54",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 1500x300 with 2 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "fig, ax = plt.subplots(1, 2, sharey=True, figsize=(15,3) )\n",
+ "uninformed_posterior = [stats.beta.pdf(pi, a=alpha_uninformed+k, b=beta_uninformed+n-k) for pi in pi_range]\n",
+ "ax[0].plot( pi_range, uninformed_posterior, alpha=0.5 )\n",
+ "ax[0].fill_between( pi_range, uninformed_posterior, alpha=0.3 )\n",
+ "ax[0].set_title(\"using uninformed prior\")\n",
+ "geneticist_posterior = [stats.beta.pdf(pi, a=alpha_geneticist+k, b=beta_geneticist+n-k) for pi in pi_range]\n",
+ "ax[1].plot( pi_range, geneticist_posterior, alpha=0.5 )\n",
+ "ax[1].fill_between( pi_range, geneticist_posterior, alpha=0.3 )\n",
+ "ax[1].set_title(\"using informed geneticist prior\");"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7793a52f-a031-4785-a996-c62084c573b9",
+ "metadata": {},
+ "source": [
+ "### Plotting everything all at once"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "id": "b229b3ee-73da-44c9-905a-6eb78a0f0f79",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": "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",
+ "text/plain": [
+ "<Figure size 1300x300 with 1 Axes>"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "from scipy import stats\n",
+ "\n",
+ "def plot_beta_binomial( alpha, beta, n, k, figsize=(13,3) ):\n",
+ " # create figure\n",
+ " plt.figure( figsize=figsize )\n",
+ " \n",
+ " # numeric evaluation range for pi\n",
+ " pi_range = np.linspace(0, 1, 1000)\n",
+ " \n",
+ " # prior\n",
+ " prior = [stats.beta.pdf(pi, a=alpha, b=beta) for pi in pi_range]\n",
+ " plt.plot( pi_range, prior, alpha=0.5, label=\"prior\", c=\"orange\" )\n",
+ " plt.fill_between( pi_range, prior, alpha=0.3, color=\"orange\" )\n",
+ "\n",
+ " # scaled likelihood\n",
+ " likelihood = [stats.binom.pmf(n=n, k=k, p=pi) for pi in pi_range]\n",
+ " likelihood /= np.sum( likelihood ) * (pi_range[1]-pi_range[0])\n",
+ " plt.plot( pi_range, likelihood, alpha=0.5, label=\"(scaled) likelihood\", c=\"blue\" )\n",
+ " plt.fill_between( pi_range, likelihood, alpha=0.3, color=\"blue\" )\n",
+ "\n",
+ " # posterior\n",
+ " posterior = [stats.beta.pdf(pi, a=alpha+k, b=beta+n-k) for pi in pi_range]\n",
+ " plt.plot( pi_range, posterior, alpha=0.5, label=\"posterior\", color=\"darkgreen\" )\n",
+ " plt.fill_between( pi_range, posterior, alpha=0.3, color=\"darkgreen\" )\n",
+ " \n",
+ " # enable legend and set descriptive title\n",
+ " plt.legend( fontsize=14 )\n",
+ " plt.title( \"$\\\\alpha = {}, \\; \\\\beta={}, \\; n={}, \\; k={}$\".format(alpha, beta, n, k) )\n",
+ "\n",
+ "plot_beta_binomial( 1, 1, n, k )"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "9a07e4aa-7477-4d04-b4df-07a681694e82",
+ "metadata": {},
+ "source": [
+ "## Summaries"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "id": "766e56d7-f869-4873-a5c5-0ee3892d3515",
+ "metadata": {},
+ "outputs": [
+ {
+ "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>model</th>\n",
+ " <th>alpha</th>\n",
+ " <th>beta</th>\n",
+ " <th>mean</th>\n",
+ " <th>mode</th>\n",
+ " <th>var</th>\n",
+ " <th>std</th>\n",
+ " </tr>\n",
+ " </thead>\n",
+ " <tbody>\n",
+ " <tr>\n",
+ " <th>0</th>\n",
+ " <td>prior</td>\n",
+ " <td>1</td>\n",
+ " <td>1</td>\n",
+ " <td>0.500000</td>\n",
+ " <td>0.000</td>\n",
+ " <td>0.083333</td>\n",
+ " <td>0.288675</td>\n",
+ " </tr>\n",
+ " <tr>\n",
+ " <th>1</th>\n",
+ " <td>posterior</td>\n",
+ " <td>4</td>\n",
+ " <td>2</td>\n",
+ " <td>0.666667</td>\n",
+ " <td>0.375</td>\n",
+ " <td>0.031746</td>\n",
+ " <td>0.178174</td>\n",
+ " </tr>\n",
+ " </tbody>\n",
+ "</table>\n",
+ "</div>"
+ ],
+ "text/plain": [
+ " model alpha beta mean mode var std\n",
+ "0 prior 1 1 0.500000 0.000 0.083333 0.288675\n",
+ "1 posterior 4 2 0.666667 0.375 0.031746 0.178174"
+ ]
+ },
+ "execution_count": 20,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "def summarize_beta_binomial( alpha, beta, n, k, figsize=(13,3) ):\n",
+ " alpha_prime = alpha + k\n",
+ " beta_prime = beta + n - k\n",
+ "\n",
+ " # computing functions\n",
+ " def expectation(alpha, beta):\n",
+ " return alpha/(alpha+beta)\n",
+ "\n",
+ " def mode(alpha, beta):\n",
+ " return (alpha-1)/(alpha+beta+2)\n",
+ "\n",
+ " def var(alpha, beta):\n",
+ " return alpha * beta / ((alpha+beta)**2 * (alpha + beta + 1))\n",
+ "\n",
+ " def std(alpha, beta):\n",
+ " return np.sqrt( var(alpha, beta) )\n",
+ " \n",
+ " \n",
+ " #model alpha beta mean mode var sd\n",
+ " \n",
+ " return pd.DataFrame({\n",
+ " 'model': ['prior', 'posterior'],\n",
+ " 'alpha': [alpha, alpha_prime],\n",
+ " 'beta': [beta, beta_prime],\n",
+ " 'mean': [expectation(alpha, beta), expectation(alpha_prime, beta_prime)],\n",
+ " 'mode': [mode(alpha, beta), mode(alpha_prime, beta_prime)],\n",
+ " 'var': [var(alpha, beta), var(alpha_prime, beta_prime)],\n",
+ " 'std': [std(alpha, beta), std(alpha_prime, beta_prime)]\n",
+ " })\n",
+ "\n",
+ "summarize_beta_binomial( 1, 1, n, k )"
+ ]
+ }
+ ],
+ "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": "3.10.11"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/notebooks/Beta-Verteilung/beta_commands.py b/notebooks/Beta-Verteilung/beta_commands.py
new file mode 100644
index 0000000..0d1072b
--- /dev/null
+++ b/notebooks/Beta-Verteilung/beta_commands.py
@@ -0,0 +1,156 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+"""
+Created on Fri Jan 22 13:14:42 2021
+
+@author: bl
+"""
+
+from scipy.stats import beta
+
+import matplotlib.pyplot as plt
+import numpy as np
+import arviz as av
+
+
+
+
+def hdi(a,b, prob):
+ k = 0
+ x = np.linspace(0,1,1000)
+ y = beta.pdf(x,a,b)
+ while True:
+ k = k+0.001
+ if np.sum(y[y > k])/np.size(x) < prob:
+ break
+ return np.array([x[np.argwhere(y > k)][0] ,x[np.argwhere(y > k)][np.argwhere(y > k).size-1]])
+
+x = np.linspace(0,1,1000)
+
+
+
+def prior(a,b,z,N, prob=.95):
+ plt.subplots(3, 1)
+ plt.subplot(311)
+ y = beta.pdf(x,a,b)
+ omega = np.round((z+a-1)/(z+a+N-z+b-2),3)
+ pr = int(prob*100)
+ plt.plot(x,y,color="seagreen")
+ plt.title("Prior (beta)")
+ plt.xlabel("θ")
+ plt.ylabel(r"beta$(θ\mid$"+str(a)+" ," +str(b)+")")
+ if a>1 and b > 1:
+ omega_prior = np.round((a-1)/(a+b-2),3)
+ xl = np.round(hdi(a,b,prob)[0][0],3)
+ xr = np.round(hdi(a,b,prob)[1][0],3)
+ yl = beta.pdf(xl,a,b)
+ plt.plot([xl,xl],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xr,xr],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xl,xr],[yl,yl],color="orange")
+ plt.text(xl-.01,yl, str(xl),ha="right",va="bottom")
+ plt.text(xr+.01,yl, str(xr),ha="left",va="bottom")
+ plt.text((xr+xl)/2,yl+.1*beta.pdf(0.5,a,b),str(pr)+"% HDI",ha="center")
+ plt.text(0,beta.pdf(omega,z+a,N-z+b)*.75,"Modus: "+str(omega_prior),ha="left")
+
+ elif a==1 and b==1:
+ plt.text(0,beta.pdf(omega,z+a,N-z+b)*.75,"Modus: 0.5",ha="left")
+ plt.ylim(0,beta.pdf(omega,z+a,N-z+b))
+ plt.fill_between(x,y,facecolor="mediumaquamarine")
+
+
+ plt.subplot(312)
+
+ y = x**z*(1-x)**(N-z)
+ plt.ylim(0, np.max(y)*1.1)
+ plt.plot(x,y,color="seagreen")
+ plt.title("Likelihood (Bernoulli)")
+ plt.xlabel(r"$θ$")
+ plt.ylabel(r"$p(D\mid θ)$")
+ plt.fill_between(x,y,facecolor="mediumaquamarine")
+ plt.text(0, np.max(y)*.75, "Daten: $z=\ $"+str(z)+", $N =\ $"+str(N),ha="left")
+ plt.text(0, np.max(y)*.4, "Max bei 0.85",ha="left")
+
+
+
+
+
+ plt.subplot(313)
+ a, b = z+a, N-z+b
+ y = beta.pdf(x,a,b)
+ plt.plot(x,y,color="seagreen")
+ plt.title("Posterior (beta)")
+ plt.xlabel(r"$θ$")
+ plt.ylabel(r"beta$(θ\mid$"+str(a)+" ," +str(b)+")")
+ plt.fill_between(x,y,facecolor="mediumaquamarine")
+ xl = np.round(hdi(a,b,prob)[0][0],3)
+ xr = np.round(hdi(a,b,prob)[1][0],3)
+ yl = beta.pdf(xl,a,b)
+ plt.plot([xl,xl],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xr,xr],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xl,xr],[yl,yl],color="orange")
+ plt.text(xl-.01,yl, str(xl),ha="right",va="bottom")
+ plt.text(xr+.01,yl, str(xr),ha="left",va="bottom")
+
+ plt.text((xr+xl)/2,yl+.1*beta.pdf(omega, a,b),str(pr)+"% HDI",ha="center")
+
+ plt.text(0,beta.pdf(omega, a,b)*.75,"Modus: "+str(omega),ha="left")
+ plt.fill_between(x,y,facecolor="mediumaquamarine")
+ plt.ylim(0,beta.pdf(omega, a,b))
+ plt.tight_layout(w_pad=3, h_pad=3)
+
+
+def beta_hist(a,b,N):
+ x = np.linspace(0,1,1000)
+
+ plt.subplots(1, 2, sharey=True,figsize=(10,5))
+
+ plt.subplot(121)
+ y = beta.pdf(x,a,b)
+ plt.plot(x,y,color="seagreen")
+ plt.title("Exakte Verteilung")
+ plt.xlabel("θ")
+ plt.ylabel("p(θ)")
+ xl = np.round(hdi(a,b)[0][0],3)
+ xr = np.round(hdi(a,b)[1][0],3)
+
+ yl = beta.pdf(xl,a,b)
+ plt.plot([xl,xl],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xr,xr],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xl,xr],[yl,yl],color="orange")
+ plt.text(xl-.01,yl, str(xl),ha="right",va="bottom")
+ plt.text(xr+.01,yl, str(xr),ha="left",va="bottom")
+ omega = np.round((a-1)/(a+b-2),3)
+ plt.text(0,3.5,"Modus: "+str(omega),ha="left")
+ plt.text((xr+xl)/2,yl+.075*beta.pdf(omega, a,b),r"95$\%$ HDI",ha="center")
+ plt.fill_between(x,y,facecolor="mediumaquamarine")
+ plt.ylim(0,4)
+
+ plt.subplot(122)
+
+ y = beta.rvs(a,b,size=N)
+ bin = np.linspace(0,1,51)
+
+ plt.title("N="+str(N))
+ plt.xlabel("θ")
+ plt.ylabel("p(θ)")
+ n, b = np.histogram(y,bins=bin,density=True)
+ bin_max = np.where(n == n.max())
+ omega = np.round(b[bin_max][0],2)
+ xl = np.round(av.hdi(y,hdi_prob=0.95)[0],3)
+ xr = np.round(av.hdi(y,hdi_prob=0.95)[1],3)
+ yl = .5
+ plt.hist(y,bins=bin,edgecolor="black",density=True, color="mediumaquamarine",zorder=1)
+ plt.plot([xl,xl],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xr,xr],[0,yl], linestyle="dashed",color="black")
+ plt.plot([xl,xr],[yl,yl],color="orange")
+ plt.text(xl-.01,yl, str(xl),ha="right",va="bottom")
+ plt.text(xr+.01,yl, str(xr),ha="left",va="bottom")
+ plt.text(0,3.5,"Modus: "+str(omega),ha="left")
+ plt.text((xr+xl)/2,yl+.075,"95% HDI",ha="center")
+ plt.ylim(0,4)
+
+
+
+
+
+
--
GitLab