From 9284c01ca92de62221422ccfa13e3aec42f95e87 Mon Sep 17 00:00:00 2001
From: Balaji Alwar <balajialwar@berkeley.edu>
Date: Fri, 10 May 2024 17:02:01 -0700
Subject: [PATCH] Testing the workflow now!

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "3e6fb570",
+   "metadata": {},
+   "source": [
+    "# Probabilistic Programming using PyMC, and Graphical Models\n",
+    "\n",
+    "Today, we shall discuss the following two topics:\n",
+    "\n",
+    "1. Probabilistic Programming using PyMC\n",
+    "2. Graphical Models "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7efab4fa",
+   "metadata": {},
+   "source": [
+    "Practical Bayesian Inference is often carried out through specialized probabilistic programming libraries such as PyMC. In these libraries, one inputs the probability model (prior and likelihood) and obtains an output of the posterior distributions in the form of Monte Carlo samples. The outputted Monte Carlo samples provide an approximation of the posterior distributions."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "28cdb539",
+   "metadata": {},
+   "source": [
+    "To illustrate probabilistic programming with PyMC, consider the following simple probability model. We have four binary random variables: overweight, smoking, heart disease and cough. Suppose we specify a probability model for these random variables as:\n",
+    "\\begin{align*}\n",
+    "   & \\text{overweight} \\sim \\text{Bernoulli}(0.1) \\\\\n",
+    "   & \\text{smoking} \\sim \\text{Bernoulli}(0.1) \\\\\n",
+    "   & \\text{heart disease} \\mid \\text{overweight} = 1, \\text{smoking} = 1 \\sim \\text{Bernoulli}(0.75) \\\\\n",
+    "   & \\text{heart disease} \\mid \\text{overweight} = 1, \\text{smoking} = 0 \\sim \\text{Bernoulli}(0.5) \\\\\n",
+    "   & \\text{heart disease} \\mid \\text{overweight} = 0, \\text{smoking} = 1 \\sim \\text{Bernoulli}(0.4) \\\\\n",
+    "   & \\text{heart disease} \\mid \\text{overweight} = 0, \\text{smoking} = 0 \\sim \\text{Bernoulli}(0.1) \\\\\n",
+    "   & \\text{cough} \\mid \\text{smoking} = 1 \\sim \\text{Bernoulli}(0.6) \\\\\n",
+    "   & \\text{cough} \\mid \\text{smoking} = 0 \\sim \\text{Bernoulli}(0.05)\n",
+    "\\end{align*}\n",
+    "The above model starts by specifying the marginal distribution of overweight and smoking. Then it specifies the conditional distribution of heart disease conditional on overweight and smoking. Finally, it specifies the conditional distribution of cough conditional on smoking. Based on this model, we might be interested in several probability questions such as:\n",
+    "1. What is the marginal distribution of heart disease i.e., $\\mathbb{P}(\\text{heart disease} = 1)$?\n",
+    "2. What is the conditional distribution of overweight conditional on heart disease i.e., $\\mathbb{P}(\\text{overweight} = 1 \\mid \\text{heart disease} = 1)$?\n",
+    "3. What is conditional distribution of smoking conditional on cough i.e., $\\mathbb{P}(\\text{smoking} = 1 \\mid \\text{cough} = 1)$?\n",
+    "\n",
+    "All these probabilities can be calculated exactly using the model specification. One way of doing this is to note that for every binary $b_o, b_s, b_h, b_c \\in \\{0, 1\\}$, we can write\n",
+    "\\begin{align*}\n",
+    "  &\\mathbb{P}\\left(\\text{overweight} = b_o, \\text{smoking} = b_s, \\text{heart} = b_h, \\text{cough} = b_c \\right) \\\\\n",
+    "  &= \\mathbb{P}\\left(\\text{overweight} = b_o \\right) \\mathbb{P}\\left(\\text{smoking} = b_s \\right) \\mathbb{P} \\left(\\text{heart} = b_h \\mid \\text{overweight} = b_o, \\text{smoking} = b_s \\right) \\mathbb{P} \\left(\\text{cough} = b_c \\mid \\text{smoking} = b_s \\right)\n",
+    "\\end{align*}\n",
+    "and these probabilities can then be read off from the model specification. For example, with $b_o = b_s = b_h = b_c = 1$, we get\n",
+    "\\begin{align*}\n",
+    "    &\\mathbb{P}\\left(\\text{overweight} = 1, \\text{smoking} = 1, \\text{heart} = 1, \\text{cough} = 1 \\right) \\\\\n",
+    "    &= \\mathbb{P}\\left(\\text{overweight} = 1 \\right) \\mathbb{P}\\left(\\text{smoking} = 1 \\right) \\mathbb{P} \\left(\\text{heart} = 1 \\mid \\text{overweight} = 1, \\text{smoking} = 1 \\right) \\mathbb{P} \\left(\\text{cough} = 1 \\mid \\text{smoking} = 1 \\right) \\\\\n",
+    "    &= 0.1 \\times 0.1 \\times 0.75 \\times 0.6\n",
+    "\\end{align*}\n",
+    "From the full joint distribution of the four variables, all the probabilities asked in the questions can be calculated. \n",
+    "\n",
+    "It is clear that this approach will be quite tedious especially if we are dealing with more than four random variables. Probabilistic Programming Libraries (such as PyMC) automate the calculation of these probabilities. However, instead of calculating probabilities exactly, they output \"samples\" from which probabilities can be approximated. Here is how this works for this simple health probability model."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "0ffe418b",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'pymc3'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[1], line 6\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mmatplotlib\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mpyplot\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mplt\u001b[39;00m\n\u001b[1;32m      5\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mnumpy\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mnp\u001b[39;00m\n\u001b[0;32m----> 6\u001b[0m \u001b[38;5;28;01mimport\u001b[39;00m \u001b[38;5;21;01mpymc3\u001b[39;00m \u001b[38;5;28;01mas\u001b[39;00m \u001b[38;5;21;01mpm\u001b[39;00m \u001b[38;5;66;03m#pymc3 is the previous version of pymc. We shall switch to pymc as soon as it gets installed in datahub\u001b[39;00m\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'pymc3'"
+     ]
+    }
+   ],
+   "source": [
+    "#Import the necessary libraries:\n",
+    "import arviz as az\n",
+    "import pandas as pd\n",
+    "import matplotlib.pyplot as plt\n",
+    "import numpy as np\n",
+    "import pymc3 as pm #pymc3 is the previous version of pymc. We shall switch to pymc as soon as it gets installed in datahub"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "f02500bd-0e06-45ef-a8b1-32243b2819a2",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'graphviz'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[4], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mgraphviz\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Digraph\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'graphviz'"
+     ]
+    }
+   ],
+   "source": [
+    "from graphviz import Digraph"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "d9ab026e",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "BinaryGibbsMetropolis: [overweight, smoking, heart, cough]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='24000' class='' max='24000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [24000/24000 00:03&lt;00:00 Sampling 4 chains, 0 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 5 seconds.\n",
+      "/opt/conda/lib/python3.9/site-packages/arviz/utils.py:187: NumbaDeprecationWarning: \u001b[1mThe 'nopython' keyword argument was not supplied to the 'numba.jit' decorator. The implicit default value for this argument is currently False, but it will be changed to True in Numba 0.59.0. See https://numba.readthedocs.io/en/stable/reference/deprecation.html#deprecation-of-object-mode-fall-back-behaviour-when-using-jit for details.\u001b[0m\n",
+      "  numba_fn = numba.jit(**self.kwargs)(self.function)\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Specify the Model in PyMC: \n",
+    "health_model = pm.Model()\n",
+    "with health_model:\n",
+    "    \n",
+    "    overweight = pm.Bernoulli('overweight', 0.1)\n",
+    "    smoking = pm.Bernoulli('smoking', 0.1)\n",
+    "    # Deterministic probabilities for 'heart' based on conditions\n",
+    "    p_heart = pm.Deterministic('p_heart', pm.math.switch(overweight, \n",
+    "                                      pm.math.switch(smoking, 0.75, 0.5), \n",
+    "                                      pm.math.switch(smoking, 0.4, 0.1)))\n",
+    "\n",
+    "    # 'heart' random variable\n",
+    "    heart = pm.Bernoulli('heart', p_heart)\n",
+    "    # Deterministic probability for 'cough' based on 'smoking'\n",
+    "    p_cough = pm.Deterministic('p_cough', pm.math.switch(smoking, 0.6, 0.05))\n",
+    "    # 'cough' random variable\n",
+    "    cough = pm.Bernoulli('cough', p_cough)\n",
+    "    #This ends the specification of the model. \n",
+    "    #To obtain samples from PyMC, run the following:\n",
+    "    idata = pm.sample(5000, chains = 4, return_inferencedata = True)\n",
+    "    #This will generate 5000*4 = 20000 posterior samples from (overweight, smoking, heart, cough)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "7e9c600d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<xarray.Dataset>\n",
+      "Dimensions:     (chain: 4, draw: 5000)\n",
+      "Coordinates:\n",
+      "  * chain       (chain) int64 0 1 2 3\n",
+      "  * draw        (draw) int64 0 1 2 3 4 5 6 ... 4994 4995 4996 4997 4998 4999\n",
+      "Data variables:\n",
+      "    overweight  (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 0 0 0 0 0 0 0 0 0 0\n",
+      "    smoking     (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 0 1 1 0 0 0 0 0 0 0\n",
+      "    heart       (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 0 1 0 1 0 0 0 0 0 0\n",
+      "    cough       (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 0 0 1 0 0 0 0 0 0 0\n",
+      "    p_heart     (chain, draw) float64 0.1 0.1 0.1 0.1 0.1 ... 0.1 0.1 0.1 0.1\n",
+      "    p_cough     (chain, draw) float64 0.05 0.05 0.05 0.05 ... 0.05 0.05 0.05\n",
+      "Attributes:\n",
+      "    created_at:                 2023-09-19T23:03:00.075509\n",
+      "    arviz_version:              0.12.1\n",
+      "    inference_library:          pymc3\n",
+      "    inference_library_version:  3.11.2\n",
+      "    sampling_time:              5.032527685165405\n",
+      "    tuning_steps:               1000\n",
+      "[[0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [1 0 0 0]\n",
+      " [1 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 1]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [1 0 1 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 1 0]\n",
+      " [1 0 0 0]\n",
+      " [0 0 1 0]\n",
+      " [0 1 0 0]\n",
+      " [0 0 0 1]\n",
+      " [0 0 0 1]\n",
+      " [0 0 0 0]\n",
+      " [1 0 1 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [1 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [1 0 1 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [1 0 1 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 1]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 0 0]\n",
+      " [0 0 1 0]\n",
+      " [0 0 0 0]\n",
+      " [1 0 0 0]\n",
+      " [0 0 0 0]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(idata.posterior)\n",
+    "overweight_samples = idata.posterior['overweight'].values.flatten()\n",
+    "smoking_samples = idata.posterior['smoking'].values.flatten()\n",
+    "heart_samples = idata.posterior['heart'].values.flatten()\n",
+    "cough_samples = idata.posterior['cough'].values.flatten()\n",
+    "all_samples = np.column_stack((overweight_samples, smoking_samples, heart_samples, cough_samples))\n",
+    "print(all_samples[:80])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8cc8f9e2",
+   "metadata": {},
+   "source": [
+    "With these samples, the questions we posed previously can be answered. For example, the marginal distribution of heart disease can be calculated as:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "cf819534",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.1631\n",
+      "0.16950000000000004\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Marginal probability that heart = 1:\n",
+    "print(np.sum(heart_samples)/len(heart_samples))\n",
+    "\n",
+    "#This should be compared to the actual value of the probability which can be calculated (more tediously) as:\n",
+    "p_overweight = 0.1\n",
+    "p_smoking = 0.1\n",
+    "# Conditional probabilities for heart\n",
+    "p_heart_given_overweight_and_smoking = 0.75\n",
+    "p_heart_given_overweight_and_not_smoking = 0.5\n",
+    "p_heart_given_not_overweight_and_smoking = 0.4\n",
+    "p_heart_given_not_overweight_and_not_smoking = 0.1\n",
+    "# Calculate the marginal probability of heart being 1\n",
+    "p_heart = (\n",
+    "    p_overweight * p_smoking * p_heart_given_overweight_and_smoking +\n",
+    "    p_overweight * (1 - p_smoking) * p_heart_given_overweight_and_not_smoking +\n",
+    "    (1 - p_overweight) * p_smoking * p_heart_given_not_overweight_and_smoking +\n",
+    "    (1 - p_overweight) * (1 - p_smoking) * p_heart_given_not_overweight_and_not_smoking\n",
+    ")\n",
+    "print(p_heart)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "d5cd2b15",
+   "metadata": {},
+   "source": [
+    "The second question asked to calculate the conditional distribution of overweight conditional on heart disease i.e., $\\mathbb{P}(\\text{overweight} = 1 \\mid \\text{heart disease} = 1)$? We can again calculate this using the previous samples in the following. We only consider those samples for which heart = 1. Then we calculate the proportion of these samples where overweight also equals 1. This can be done as follows:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "985cbae3",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "3262\n",
+      "0.30257510729613735\n",
+      "0.30973451327433627\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Calculating the conditional probability of overweight = 1 given heart = 1 from the posterior samples.\n",
+    "mask = (heart_samples == 1)\n",
+    "print(sum(mask)) #this means that many of the original samples are discarded for this calculation.\n",
+    "count_overweight_given_heart = sum(overweight_samples[mask] == 1)\n",
+    "required_probability = count_overweight_given_heart/sum(mask)\n",
+    "print(required_probability)\n",
+    "\n",
+    "#Exact calculation\n",
+    "print((p_overweight * p_smoking * p_heart_given_overweight_and_smoking + p_overweight * (1 - p_smoking) * p_heart_given_overweight_and_not_smoking) / p_heart)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c674fd36",
+   "metadata": {},
+   "source": [
+    "Thus even though we had 20000 posterior samples to begin with, only about 3200 of them have heart disease equal to 1. This means that this probability is approximated based on only 3200 samples (as opposed to 20000). In PyMC, if you want to generate samples conditional on certain values (such as $\\text{heart disease} = 1$ in the above example), one plugs this information into the model at the specification stage. This prevents the wastage of samples as above. This is illustrated below."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "92c7e49b",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "BinaryGibbsMetropolis: [overweight, smoking, cough]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='24000' class='' max='24000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [24000/24000 00:03&lt;00:00 Sampling 4 chains, 0 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 4 seconds.\n"
+     ]
+    }
+   ],
+   "source": [
+    "#PyMC model when heart is pre-specified as 1. \n",
+    "health_model_1 = pm.Model()\n",
+    "with health_model_1:\n",
+    "    overweight = pm.Bernoulli('overweight', 0.1)\n",
+    "    smoking = pm.Bernoulli('smoking', 0.1)\n",
+    "    # Deterministic probabilities for 'heart' based on conditions\n",
+    "    p_heart = pm.Deterministic('p_heart', pm.math.switch(overweight, \n",
+    "                                      pm.math.switch(smoking, 0.75, 0.5), \n",
+    "                                      pm.math.switch(smoking, 0.4, 0.1)))\n",
+    "\n",
+    "    # 'heart' random variable\n",
+    "    heart = pm.Bernoulli('heart', p_heart, observed = 1) \n",
+    "    #observed = 1 means we want heart to be fixed at the observed value of 1.\n",
+    "    #If we want heart to be fixed at 0, we would say observed = 0.\n",
+    "    # Deterministic probability for 'cough' based on 'smoking'\n",
+    "    p_cough = pm.Deterministic('p_cough', pm.math.switch(smoking, 0.6, 0.05))\n",
+    "    # 'cough' random variable\n",
+    "    cough = pm.Bernoulli('cough', p_cough)\n",
+    "    #This ends the specification of the model. \n",
+    "    #To obtain samples from PyMC, run the following:\n",
+    "    idata = pm.sample(5000, chains = 4, return_inferencedata = True)\n",
+    "    #This will generate 5000*4 = 20000 posterior samples from (overweight, smoking, heart, cough)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "900d32ee",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<xarray.Dataset>\n",
+      "Dimensions:     (chain: 4, draw: 5000)\n",
+      "Coordinates:\n",
+      "  * chain       (chain) int64 0 1 2 3\n",
+      "  * draw        (draw) int64 0 1 2 3 4 5 6 ... 4994 4995 4996 4997 4998 4999\n",
+      "Data variables:\n",
+      "    overweight  (chain, draw) int64 1 0 1 0 1 0 0 0 0 1 ... 0 0 0 0 0 0 0 1 1 0\n",
+      "    smoking     (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 1 1 0 0 0 0 0 0 0 0\n",
+      "    cough       (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 1 0 0 0 0 0 0 0 0 0\n",
+      "    p_heart     (chain, draw) float64 0.5 0.1 0.5 0.1 0.5 ... 0.1 0.5 0.5 0.1\n",
+      "    p_cough     (chain, draw) float64 0.05 0.05 0.05 0.05 ... 0.05 0.05 0.05\n",
+      "Attributes:\n",
+      "    created_at:                 2023-09-19T23:11:52.450208\n",
+      "    arviz_version:              0.12.1\n",
+      "    inference_library:          pymc3\n",
+      "    inference_library_version:  3.11.2\n",
+      "    sampling_time:              4.087341785430908\n",
+      "    tuning_steps:               1000\n",
+      "[[1 0 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
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+      " [1 0 0]\n",
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+      " [0 1 1]\n",
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+      " [0 0 1]\n",
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+      " [1 0 0]\n",
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+      " [0 0 0]\n",
+      " [0 0 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
+      " [1 0 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
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+      " [0 0 0]\n",
+      " [1 0 0]\n",
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+      " [0 0 0]\n",
+      " [1 0 0]\n",
+      " [1 1 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
+      " [0 1 1]\n",
+      " [0 1 1]\n",
+      " [0 1 0]\n",
+      " [0 1 1]\n",
+      " [0 1 0]\n",
+      " [1 0 0]\n",
+      " [0 1 0]\n",
+      " [0 1 1]\n",
+      " [1 0 0]\n",
+      " [1 1 0]\n",
+      " [0 1 1]\n",
+      " [0 1 1]\n",
+      " [0 1 0]\n",
+      " [0 1 1]\n",
+      " [0 1 0]\n",
+      " [0 1 1]\n",
+      " [0 1 1]\n",
+      " [0 1 0]\n",
+      " [1 0 0]\n",
+      " [0 0 0]\n",
+      " [0 0 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
+      " [0 0 0]\n",
+      " [1 0 0]\n",
+      " [0 0 0]]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(idata.posterior)\n",
+    "overweight_samples = idata.posterior['overweight'].values.flatten()\n",
+    "smoking_samples = idata.posterior['smoking'].values.flatten()\n",
+    "cough_samples = idata.posterior['cough'].values.flatten()\n",
+    "all_samples = np.column_stack((overweight_samples, smoking_samples, cough_samples))\n",
+    "print(all_samples[:80])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a5a187d3",
+   "metadata": {},
+   "source": [
+    "With these samples (conditioned on $\\text{heart} = 1$), we can calculate the conditional probability of overweight given heart disease as:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "29851dbc",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.31235\n"
+     ]
+    }
+   ],
+   "source": [
+    "#Marginal probability that heart = 1:\n",
+    "print(np.sum(overweight_samples)/len(overweight_samples))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "e483fdb6",
+   "metadata": {},
+   "source": [
+    "For the third question, we need to calculate the conditional distribution of smoking conditional on cough i.e.,  $\\mathbb{P}(\\text{smoking}=1∣\\text{cough}=1)$. This can be again be done by insisting on $\\text{cough} = 1$ in the PyMC model specification as follows."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "5cba3e40",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "BinaryGibbsMetropolis: [overweight, smoking, heart]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='24000' class='' max='24000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [24000/24000 00:03&lt;00:00 Sampling 4 chains, 0 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 4 seconds.\n"
+     ]
+    }
+   ],
+   "source": [
+    "#PyMC model when cough is pre-specified as 1. \n",
+    "health_model_2 = pm.Model()\n",
+    "with health_model_2:\n",
+    "    overweight = pm.Bernoulli('overweight', 0.1)\n",
+    "    smoking = pm.Bernoulli('smoking', 0.1)\n",
+    "    # Deterministic probabilities for 'heart' based on conditions\n",
+    "    p_heart = pm.Deterministic('p_heart', pm.math.switch(overweight, \n",
+    "                                      pm.math.switch(smoking, 0.75, 0.5), \n",
+    "                                      pm.math.switch(smoking, 0.4, 0.1)))\n",
+    "\n",
+    "    # 'heart' random variable\n",
+    "    heart = pm.Bernoulli('heart', p_heart) \n",
+    "    #observed = 1 means we want heart to be fixed at the observed value of 1.\n",
+    "    #If we want heart to be fixed at 0, we would say observed = 0.\n",
+    "    # Deterministic probability for 'cough' based on 'smoking'\n",
+    "    p_cough = pm.Deterministic('p_cough', pm.math.switch(smoking, 0.6, 0.05))\n",
+    "    # 'cough' random variable\n",
+    "    cough = pm.Bernoulli('cough', p_cough, observed = 1)\n",
+    "    #This ends the specification of the model. \n",
+    "    #To obtain samples from PyMC, run the following:\n",
+    "    idata = pm.sample(5000, chains = 4, return_inferencedata = True)\n",
+    "    #This will generate 5000*4 = 20000 posterior samples from (overweight, smoking, heart, cough)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "38d245ee",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<xarray.Dataset>\n",
+      "Dimensions:     (chain: 4, draw: 5000)\n",
+      "Coordinates:\n",
+      "  * chain       (chain) int64 0 1 2 3\n",
+      "  * draw        (draw) int64 0 1 2 3 4 5 6 ... 4994 4995 4996 4997 4998 4999\n",
+      "Data variables:\n",
+      "    overweight  (chain, draw) int64 0 0 0 0 0 0 0 0 0 0 ... 0 1 1 1 0 0 0 0 0 0\n",
+      "    smoking     (chain, draw) int64 1 0 0 1 0 1 1 1 1 0 ... 1 1 1 0 1 0 1 0 1 0\n",
+      "    heart       (chain, draw) int64 0 0 1 0 0 0 1 0 1 0 ... 0 1 0 1 1 0 0 0 0 0\n",
+      "    p_heart     (chain, draw) float64 0.4 0.1 0.1 0.4 0.1 ... 0.4 0.1 0.4 0.1\n",
+      "    p_cough     (chain, draw) float64 0.6 0.05 0.05 0.6 ... 0.6 0.05 0.6 0.05\n",
+      "Attributes:\n",
+      "    created_at:                 2023-09-19T23:13:30.935572\n",
+      "    arviz_version:              0.12.1\n",
+      "    inference_library:          pymc3\n",
+      "    inference_library_version:  3.11.2\n",
+      "    sampling_time:              4.06363320350647\n",
+      "    tuning_steps:               1000\n",
+      "0.56815\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(idata.posterior)\n",
+    "overweight_samples = idata.posterior['overweight'].values.flatten()\n",
+    "smoking_samples = idata.posterior['smoking'].values.flatten()\n",
+    "heart_samples = idata.posterior['heart'].values.flatten()\n",
+    "all_samples = np.column_stack((overweight_samples, smoking_samples, heart_samples))\n",
+    "#Required conditional probability:\n",
+    "print(np.sum(smoking_samples)/len(smoking_samples))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3512f57c",
+   "metadata": {},
+   "source": [
+    "## Graphical Models\n",
+    "\n",
+    "It is often convenient to represent Bayesian probability models in the form of **Graphical Models**. Graphical Models are graphical representations of probability models. Each random variable in the model is represented by a circle (sometimes random variables whose values are observed are shaded). A directed edge is put from edge $w$ to edge $v$ if the distribution of $v$ in the model is described in terms of $w$. \n",
+    "\n",
+    "Graphical models should be constructed sequentially in the same order as the variables appear in the PyMC specification. For example, in this health model, the following steps should be followed in sequence to form the graphical model:\n",
+    "1. The first random variable in the PyMC model specification is \"overweight\". So we first draw a node (circle) for this random variable. At this stage, the graphical model only consists of a single node (overweight) \n",
+    "2. The second variable is \"smoking\" so we draw a node (circle) for smoking. The probability specification for smoking does not involve the first variable overweight so we do not place any edge from overweight to smoking. At this stage, the graphical model only consists of two nodes (overweight and smoking) without any edge between them. \n",
+    "3. The third variable is \"heart disease\" so we draw a node (circle) for heart disease. The probability specification for heart disease clearly uses both overweight and smoking so we place two directed edges: one from overweight to heart, and the other from smoking to heart. \n",
+    "4. The fourth variable is \"cough\" so we draw a node for cough. The probability specification for cough clearly uses smoking (and not overweight or heart disease) so we play one directed edge from smoking to heart. \n",
+    "\n",
+    "This graphical model can be drawn in Python as follows:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "37505bec",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<!-- Generated by graphviz version 2.43.0 (0)\n",
+       " -->\n",
+       "<!-- Title: %3 Pages: 1 -->\n",
+       "<svg width=\"270pt\" height=\"116pt\"\n",
+       " viewBox=\"0.00 0.00 270.04 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
+       "<title>%3</title>\n",
+       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 266.04,-112 266.04,4 -4,4\"/>\n",
+       "<!-- overweight -->\n",
+       "<g id=\"node1\" class=\"node\">\n",
+       "<title>overweight</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"76.69\" cy=\"-90\" rx=\"64.99\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"76.69\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">Overweight</text>\n",
+       "</g>\n",
+       "<!-- heart_disease -->\n",
+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>heart_disease</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"76.69\" cy=\"-18\" rx=\"76.89\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"76.69\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Heart Disease</text>\n",
+       "</g>\n",
+       "<!-- overweight&#45;&gt;heart_disease -->\n",
+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>overweight&#45;&gt;heart_disease</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M76.69,-71.7C76.69,-63.98 76.69,-54.71 76.69,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"80.19,-46.1 76.69,-36.1 73.19,-46.1 80.19,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- smoking -->\n",
+       "<g id=\"node2\" class=\"node\">\n",
+       "<title>smoking</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"210.69\" cy=\"-90\" rx=\"51.19\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"210.69\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">Smoking</text>\n",
+       "</g>\n",
+       "<!-- smoking&#45;&gt;heart_disease -->\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>smoking&#45;&gt;heart_disease</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M183.25,-74.67C163.82,-64.52 137.48,-50.75 115.85,-39.45\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"117.38,-36.31 106.9,-34.78 114.14,-42.51 117.38,-36.31\"/>\n",
+       "</g>\n",
+       "<!-- cough -->\n",
+       "<g id=\"node4\" class=\"node\">\n",
+       "<title>cough</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"211.69\" cy=\"-18\" rx=\"40.09\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"211.69\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Cough</text>\n",
+       "</g>\n",
+       "<!-- smoking&#45;&gt;cough -->\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>smoking&#45;&gt;cough</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M210.94,-71.7C211.05,-63.98 211.18,-54.71 211.31,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"214.81,-46.15 211.45,-36.1 207.81,-46.05 214.81,-46.15\"/>\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<graphviz.dot.Digraph at 0x7f3f979c2970>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from graphviz import Digraph\n",
+    "def create_graphical_model():\n",
+    "    # Create a new directed graph\n",
+    "    dot = Digraph()\n",
+    "\n",
+    "    # Add nodes\n",
+    "    dot.node('overweight', 'Overweight')\n",
+    "    dot.node('smoking', 'Smoking')\n",
+    "    dot.node('heart_disease', 'Heart Disease')\n",
+    "    dot.node('cough', 'Cough')\n",
+    "    \n",
+    "    # Add edges\n",
+    "    dot.edge('overweight', 'heart_disease')\n",
+    "    dot.edge('smoking', 'heart_disease')\n",
+    "    dot.edge('smoking', 'cough')\n",
+    "\n",
+    "    return dot\n",
+    "\n",
+    "# Display the graph\n",
+    "display(create_graphical_model())"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "8757a962",
+   "metadata": {},
+   "source": [
+    "Graphical models are useful because interesting (conditional) independence facts can be simply read off from them. The language of familial relationships is extremely useful when discussing graphical models. For example, in the above graphical model, we can use the following terminology: \n",
+    "1. Overweight and Smoking variables can be seen as \"founders\" of this family of variables. \n",
+    "2. Heart disease is child born to parents overweight and smoking.\n",
+    "3. Cough is a child born to Smoking. \n",
+    "\n",
+    "The conditional independence relationships induced by graphical models exactly match those found in simple Mendelian genetics. For example, in the above graphical model: \n",
+    "1. Overweight and Smoking are marginally independent\n",
+    "2. Conditional on the parents (overweight and smoking), the children (heart disease and cough) are independent. \n",
+    "3. Without conditioning on parents, heart disease and cough are **not** independent. Knowing something about heart disease will change what we think about cough. \n",
+    "4. Conditional on smoking, the two children heart disease and cough are independent. \n",
+    "5. Cough and Overweight are marginally independent. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "56249a5c",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
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+       "<!-- D&#45;&gt;F -->\n",
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+       "<title>D&#45;&gt;F</title>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<graphviz.dot.Digraph at 0x7f3f96fb5c10>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Another Graphical Model:\n",
+    "from graphviz import Digraph\n",
+    "\n",
+    "# Create a directed graph\n",
+    "dot = Digraph()\n",
+    "\n",
+    "# Add nodes to the graph\n",
+    "for node in ['A', 'B', 'C', 'D', 'E', 'F']:\n",
+    "    dot.node(node)\n",
+    "\n",
+    "# Add directed edges\n",
+    "edges = [('A', 'C'), ('B', 'C'), ('C', 'E'), ('D', 'E'), ('C', 'F'), ('D', 'F')]\n",
+    "for edge in edges:\n",
+    "    dot.edge(edge[0], edge[1])\n",
+    "\n",
+    "# Display the graph in the Jupyter notebook\n",
+    "display(dot)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "9e0f3b66-34d9-4151-ae38-7e9421ffea32",
+   "metadata": {},
+   "outputs": [
+    {
+     "ename": "ModuleNotFoundError",
+     "evalue": "No module named 'graphviz'",
+     "output_type": "error",
+     "traceback": [
+      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
+      "Cell \u001b[0;32mIn[2], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mgraphviz\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m Digraph\n",
+      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'graphviz'"
+     ]
+    }
+   ],
+   "source": [
+    "from graphviz import Digraph"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "3e0975b1",
+   "metadata": {},
+   "source": [
+    "Here are some conditional independence relationships induced by this graphical model:\n",
+    "1. A, B, D are marginally independent. \n",
+    "2. E and F are conditionally independent given C and D. \n",
+    "3. C and D are marginally independent. \n",
+    "4. C and D are **not** conditionally independent given E.\n",
+    "5. A and B are **not** conditionally independent given E."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "242340a5",
+   "metadata": {},
+   "source": [
+    "# Bayesian Statistics using PyMC\n",
+    "\n",
+    "Next we revisit the simple examples that we studied in the previous two lectures. We shall use PyMC to answer questions based on these models. We shall also draw the graphical models associated with these models. \n",
+    "\n",
+    "## Microwave Example using PyMC\n",
+    "\n",
+    "In the Microwave Example, there are two parameters: $\\theta_A$ and $\\theta_B$ representing the qualities of the two microwaves. The data for Microwave A is given by 3 out of 3 positive reviews: $\\text{pos}_A = 3, n_A = 3$ ($n_A$ is the total number of reviews for A). The data for Microwave B is given by 19 out of 20 positive reviews: $\\text{pos}_B = 19$, $n_B = 20$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "df91a1ab",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "#Data\n",
+    "pos_A_obs = 3\n",
+    "neg_A_obs = 0\n",
+    "n_A_obs = 3\n",
+    "pos_B_obs = 19\n",
+    "neg_B_obs = 1\n",
+    "n_B_obs = 20"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a2cfc7d7",
+   "metadata": {},
+   "source": [
+    "The prior is given by $\\theta_A, \\theta_B \\overset{\\text{i.i.d}}{\\sim} \\text{uniform}[0, 1]$ and the likelihood is $\\text{pos}_A \\mid \\theta_A \\sim \\text{Bin}(n_A, \\theta_A)$ and $\\text{pos}_B \\mid \\theta_B \\sim \\text{Bin}(n_B, \\theta_B)$. We can input this Bayesian model in PyMC as follows:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "9b4c235d",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (4 chains in 4 jobs)\n",
+      "NUTS: [theta_B, theta_A]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
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+       "</style>\n"
+      ],
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+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='24000' class='' max='24000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [24000/24000 00:08&lt;00:00 Sampling 4 chains, 0 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 4 chains for 1_000 tune and 5_000 draw iterations (4_000 + 20_000 draws total) took 8 seconds.\n"
+     ]
+    }
+   ],
+   "source": [
+    "#PyMC Model:\n",
+    "microwave_model = pm.Model()\n",
+    "with microwave_model:\n",
+    "    #Priors\n",
+    "    theta_A = pm.Beta(\"theta_A\", alpha=1, beta=1)\n",
+    "    theta_B = pm.Beta(\"theta_B\", alpha=1, beta=1)\n",
+    "    #Likelihoods\n",
+    "    pos_A = pm.Binomial(\"pos_A\", n=n_A_obs, p=theta_A, observed = pos_A_obs)\n",
+    "    pos_B = pm.Binomial(\"pos_B\", n=n_B_obs, p=theta_B, observed = pos_B_obs)\n",
+    "    #Sample from posterior:\n",
+    "    idata = pm.sample(5000, chains = 4, return_inferencedata = True) \n",
+    "    #The above step is asking for 5000*4 = 20000 posterior samples of theta_A and theta_B"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "a51861c6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "20000"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([0.75401301, 0.9005176 , 0.79450101, ..., 0.89130518, 0.90965358,\n",
+       "       0.83777861])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "20000"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "array([0.98174034, 0.94598862, 0.9778023 , ..., 0.951163  , 0.95447991,\n",
+       "       0.78704502])"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#We can access the posterior samples in the following way:\n",
+    "theta_A_samples = idata.posterior['theta_A'].values.flatten()\n",
+    "display(len(theta_A_samples))\n",
+    "display(theta_A_samples)\n",
+    "theta_B_samples = idata.posterior['theta_B'].values.flatten()\n",
+    "display(len(theta_B_samples))\n",
+    "display(theta_B_samples)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "55873f98",
+   "metadata": {},
+   "source": [
+    "We saw in Lecture Six that the correct posterior for $\\theta_A$ is $\\text{Beta}(4, 1)$\n",
+    "Also the correct posterior for $\\theta_B$ is $\\text{Beta}(20, 2)$. We can check if the\n",
+    "samples generated above correctly approximate the correct posteriors as follows. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "d07e9131",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from scipy.stats import beta\n",
+    "plt.hist(theta_A_samples, bins = 100, density = True, alpha = 0.6, label = 'Posterior Samples for theta_A') #alpha controls the opacity of the plotted histogram bars \n",
+    "#alpha = 1 is completely opaque and alpha = 0 is completely transparent\n",
+    "x = np.linspace(0, 1, 1000)\n",
+    "pdf_values = beta.pdf(x, pos_A_obs + 1, neg_A_obs + 1)\n",
+    "plt.plot(x, pdf_values, 'r-', label = 'Beta(4, 1) Density')\n",
+    "plt.xlabel('Theta_A_value')\n",
+    "plt.ylabel('Density')\n",
+    "plt.legend()\n",
+    "plt.title('Histogram of theta_A_samples and Beta(4, 1) density')\n",
+    "plt.show()\n",
+    "\n",
+    "plt.hist(theta_B_samples, bins = 100, density = True, alpha = 0.6, label = 'Posterior Samples for theta_B') #alpha controls the opacity of the plotted histogram bars \n",
+    "#alpha = 1 is completely opaque and alpha = 0 is completely transparent\n",
+    "x = np.linspace(0, 1, 1000)\n",
+    "pdf_values = beta.pdf(x, pos_B_obs + 1, neg_B_obs + 1)\n",
+    "plt.plot(x, pdf_values, 'r-', label = 'Beta(20, 2) Density')\n",
+    "plt.xlabel('Theta_B_value')\n",
+    "plt.ylabel('Density')\n",
+    "plt.legend()\n",
+    "plt.title('Histogram of theta_B_samples and Beta(20, 2) density')\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2e87a756",
+   "metadata": {},
+   "source": [
+    "These samples can be used to approximate the probability that $\\theta_A$ is strictly smaller than $\\theta_B$ as follows (recall from Lecture Six that the exact value of this probability equals 0.7). "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "f82ebcff",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.70435\n"
+     ]
+    }
+   ],
+   "source": [
+    "N = len(theta_A_samples)\n",
+    "proportion_AleqB = np.sum(theta_A_samples < theta_B_samples)/N\n",
+    "print(proportion_AleqB) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "72b482a2",
+   "metadata": {},
+   "source": [
+    "Here is the Graphical Model for the Microwave Model: there are four random variables: $\\theta_A, \\text{pos}_A$ and $\\theta_B, \\text{pos}_B$. The distribution of $\\text{pos}_A$ is described through $\\theta_A$ as $\\text{Bin}(n_A, \\theta_A)$ so we put a directed edge going from $\\theta_A$ to $\\text{pos}_A$. Similarly there will be a directed edge going from $\\theta_B$ to $\\text{pos}_B$. This is a very simple graphical model and it should be clear that $\\theta_A$ and $\\theta_B$ are conditionally independent given $\\text{pos}_A$ and $\\text{pos}_B$.  "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "303794b8",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<!-- Generated by graphviz version 2.43.0 (0)\n",
+       " -->\n",
+       "<!-- Title: %3 Pages: 1 -->\n",
+       "<svg width=\"178pt\" height=\"116pt\"\n",
+       " viewBox=\"0.00 0.00 178.04 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
+       "<title>%3</title>\n",
+       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 174.04,-112 174.04,4 -4,4\"/>\n",
+       "<!-- theta_A -->\n",
+       "<g id=\"node1\" class=\"node\">\n",
+       "<title>theta_A</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"37.7\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"37.7\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ_A</text>\n",
+       "</g>\n",
+       "<!-- pos_A -->\n",
+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>pos_A</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"37.7\" cy=\"-18\" rx=\"37.89\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"37.7\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">pos_A</text>\n",
+       "</g>\n",
+       "<!-- theta_A&#45;&gt;pos_A -->\n",
+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>theta_A&#45;&gt;pos_A</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M37.7,-71.7C37.7,-63.98 37.7,-54.71 37.7,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"41.2,-46.1 37.7,-36.1 34.2,-46.1 41.2,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_B -->\n",
+       "<g id=\"node2\" class=\"node\">\n",
+       "<title>theta_B</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"131.7\" cy=\"-90\" rx=\"27.1\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"131.7\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ_B</text>\n",
+       "</g>\n",
+       "<!-- pos_B -->\n",
+       "<g id=\"node4\" class=\"node\">\n",
+       "<title>pos_B</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"131.7\" cy=\"-18\" rx=\"38.19\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"131.7\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">pos_B</text>\n",
+       "</g>\n",
+       "<!-- theta_B&#45;&gt;pos_B -->\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>theta_B&#45;&gt;pos_B</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M131.7,-71.7C131.7,-63.98 131.7,-54.71 131.7,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"135.2,-46.1 131.7,-36.1 128.2,-46.1 135.2,-46.1\"/>\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<graphviz.dot.Digraph at 0x7f044c590580>"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import graphviz\n",
+    "def create_graph():\n",
+    "    dot = graphviz.Digraph(format='png')\n",
+    "    # Define nodes\n",
+    "    dot.node('theta_A', 'θ_A')\n",
+    "    dot.node('theta_B', 'θ_B')\n",
+    "    dot.node('pos_A', 'pos_A')\n",
+    "    dot.node('pos_B', 'pos_B')\n",
+    "    # Define edges\n",
+    "    dot.edge('theta_A', 'pos_A')\n",
+    "    dot.edge('theta_B', 'pos_B')\n",
+    "    return dot\n",
+    "# Display the graph\n",
+    "create_graph()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f6f36002",
+   "metadata": {},
+   "source": [
+    "## Kidney Cancer Data Analysis using PyMC\n",
+    "\n",
+    "We analyzed the kidney cancer dataset in Lecture Seven where we did a Bayesian analysis with a Beta prior that was learned from the naive proportions of large counties."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "768c2550",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "      state                   Location  fips  dc     pop  dc.2   pop.2  dct  \\\n",
+      "0   ALABAMA    Autauga County, Alabama  1001   2   61921     1   64915    3   \n",
+      "1   ALABAMA    Baldwin County, Alabama  1003   7  170945    15  195253   22   \n",
+      "2   ALABAMA    Barbour County, Alabama  1005   0   33316     1   33987    1   \n",
+      "3   ALABAMA       Bibb County, Alabama  1007   0   30152     1   31175    1   \n",
+      "4   ALABAMA     Blount County, Alabama  1009   3   88342     5   91547    8   \n",
+      "5   ALABAMA    Bullock County, Alabama  1011   0    8313     0    8197    0   \n",
+      "6   ALABAMA     Butler County, Alabama  1013   0   31963     1   31722    1   \n",
+      "7   ALABAMA    Calhoun County, Alabama  1015   9  243105    12  233021   21   \n",
+      "8   ALABAMA   Chambers County, Alabama  1017   7   59985     0   57813    7   \n",
+      "9   ALABAMA   Cherokee County, Alabama  1019   0   43401     0   43828    0   \n",
+      "10  ALABAMA    Chilton County, Alabama  1021   2   65792     3   68837    5   \n",
+      "11  ALABAMA    Choctaw County, Alabama  1023   1   22741     3   22441    4   \n",
+      "12  ALABAMA     Clarke County, Alabama  1025   1   38611     3   37772    4   \n",
+      "13  ALABAMA       Clay County, Alabama  1027   3   27846     3   26954    6   \n",
+      "14  ALABAMA   Cleburne County, Alabama  1029   2   29718     1   29735    3   \n",
+      "15  ALABAMA     Coffee County, Alabama  1031   3   80334     4   81882    7   \n",
+      "16  ALABAMA    Colbert County, Alabama  1033   3  108797     6  104971    9   \n",
+      "17  ALABAMA    Conecuh County, Alabama  1035   2   22009     2   20687    4   \n",
+      "18  ALABAMA      Coosa County, Alabama  1037   2   18003     1   17828    3   \n",
+      "19  ALABAMA  Covington County, Alabama  1039   4   76229     3   75990    7   \n",
+      "\n",
+      "        popm  \n",
+      "0    63418.0  \n",
+      "1   183099.0  \n",
+      "2    33651.5  \n",
+      "3    30663.5  \n",
+      "4    89944.5  \n",
+      "5     8255.0  \n",
+      "6    31842.5  \n",
+      "7   238063.0  \n",
+      "8    58899.0  \n",
+      "9    43614.5  \n",
+      "10   67314.5  \n",
+      "11   22591.0  \n",
+      "12   38191.5  \n",
+      "13   27400.0  \n",
+      "14   29726.5  \n",
+      "15   81108.0  \n",
+      "16  106884.0  \n",
+      "17   21348.0  \n",
+      "18   17915.5  \n",
+      "19   76109.5  \n"
+     ]
+    }
+   ],
+   "source": [
+    "#Read the kidney cancer dataset\n",
+    "import pandas as pd\n",
+    "d_full = pd.read_csv(\"KidneyCancerClean.csv\", skiprows=4)\n",
+    "d = d_full[['state', 'Location', 'fips', 'dc', 'pop', 'dc.2', 'pop.2']].copy()\n",
+    "#Combine the death and population counts for the two periods 80-84 and 85-89\n",
+    "d['dct'] = d['dc'] + d['dc.2'] #dct stands for death count total\n",
+    "d['popm'] = (d['pop'] + d['pop.2']) / 2\n",
+    "print(d.head(20))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 18,
+   "id": "05726627",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "11.781889938777496"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "120049.39668603124"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Our specific procedure for obtaining the prior was:\n",
+    "d['naiveproportion'] = d['dct'] / d['popm']\n",
+    "proportions_largecounties = d['naiveproportion'][d['popm'] >= 300000] #filter out the high population counties\n",
+    "m = np.mean(proportions_largecounties)\n",
+    "V = np.var(proportions_largecounties)\n",
+    "a = ((m*m*(1-m))/V) - m\n",
+    "b = (((1-m)*(1-m)*m)/V) - (1-m)\n",
+    "aes = a\n",
+    "bes = b\n",
+    "display(a, b)\n",
+    "d['bayesestimate'] = (d['dct'] + a)/(d['popm'] + a + b)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4175f7c0",
+   "metadata": {},
+   "source": [
+    "After obtaining the prior, we did a standard Bayesian analysis with Binomial likelihood and Beta prior. This part can also be done via PyMC. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "c4b287d1",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (2 chains in 4 jobs)\n",
+      "NUTS: [theta]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [4000/4000 00:25&lt;00:00 Sampling 2 chains, 0 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 26 seconds.\n",
+      "The acceptance probability does not match the target. It is 0.7170667963818471, but should be close to 0.8. Try to increase the number of tuning steps.\n"
+     ]
+    }
+   ],
+   "source": [
+    "N = d.shape[0] #this is the number of counties\n",
+    "n = np.round(d['popm'].values)\n",
+    "y_obs = d['dct'].values\n",
+    "\n",
+    "kidney_model = pm.Model()\n",
+    "with kidney_model:\n",
+    "    theta = pm.Beta(\"theta\", alpha=a, beta=b, shape = N)\n",
+    "    Y = pm.Binomial(\"Y\", n=n, p=theta, observed=y_obs)\n",
+    "    #Sample from posterior:\n",
+    "    idata = pm.sample(1000, chains = 2, return_inferencedata = True) "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 20,
+   "id": "dc99c035",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "<xarray.Dataset>\n",
+      "Dimensions:      (chain: 2, draw: 1000, theta_dim_0: 3110)\n",
+      "Coordinates:\n",
+      "  * chain        (chain) int64 0 1\n",
+      "  * draw         (draw) int64 0 1 2 3 4 5 6 7 ... 993 994 995 996 997 998 999\n",
+      "  * theta_dim_0  (theta_dim_0) int64 0 1 2 3 4 5 ... 3105 3106 3107 3108 3109\n",
+      "Data variables:\n",
+      "    theta        (chain, draw, theta_dim_0) float64 4.044e-05 ... 7.283e-05\n",
+      "Attributes:\n",
+      "    created_at:                 2023-09-20T01:41:37.825315\n",
+      "    arviz_version:              0.12.1\n",
+      "    inference_library:          pymc3\n",
+      "    inference_library_version:  3.11.2\n",
+      "    sampling_time:              25.946101188659668\n",
+      "    tuning_steps:               1000\n",
+      "0.0002029461144040448\n",
+      "2000\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(idata.posterior)\n",
+    "#Let us now focus on one of the theta variables (say theta corresponding to the county\n",
+    "#in row 346) and then check if the histogram of posterior samples closely approximate\n",
+    "#the correct posterior Beta density. \n",
+    "#Posterior samples for theta_346 can be accessed as follows.\n",
+    "theta_346_samples = idata.posterior['theta'][:, :, 346].values.flatten()\n",
+    "print(np.mean(theta_346_samples))\n",
+    "print(len(theta_346_samples))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 21,
+   "id": "f350f974",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "state                               FLORIDA\n",
+      "Location           Sarasota County, Florida\n",
+      "fips                                  12115\n",
+      "dc                                       55\n",
+      "pop                                  485595\n",
+      "dc.2                                     65\n",
+      "pop.2                                573711\n",
+      "dct                                     120\n",
+      "popm                               529653.0\n",
+      "naiveproportion                    0.000227\n",
+      "bayesestimate                      0.000203\n",
+      "Name: 346, dtype: object\n",
+      "0.00020283055885838032\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Let us plot this histogram along with the exact posterior Beta(a + Pos, b + Neg) density:\n",
+    "print(d.iloc[346])\n",
+    "Tot = round(d.loc[346, 'popm'])\n",
+    "Pos = d.loc[346, 'dct']\n",
+    "Neg = Tot - Pos\n",
+    "#This is a large county (population around half a million) and a large death count (120)\n",
+    "#Actual posterior mean\n",
+    "print((a+Pos)/(a+b+Tot))\n",
+    "from scipy.stats import beta\n",
+    "# Plotting histogram\n",
+    "plt.hist(theta_346_samples, bins=50, density=True, alpha=0.6, label=\"Posterior Samples\")\n",
+    "\n",
+    "# Superimposing the Beta density\n",
+    "x = np.arange(0, 8e-4, 1e-6)\n",
+    "y = beta.pdf(x, a+Pos, b+Neg)\n",
+    "plt.plot(x, y, 'r-', lw=2, label=f\"Beta({a+Pos}, {b+Neg}) Density\")\n",
+    "# Labels, legend, and title\n",
+    "plt.xlabel(\"Value\")\n",
+    "plt.ylabel(\"Density\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.title(\"Histogram of Posterior Samples of 346th theta with the actual posterior Beta Density\")\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 22,
+   "id": "50bf37bb",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1000x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#We can compute the posterior means for all theta parameters by simply averaging\n",
+    "#the observed posterior samples\n",
+    "theta_samples = idata.posterior['theta'].values\n",
+    "combined_samples = theta_samples.reshape(-1, N)\n",
+    "theta_means = np.mean(combined_samples, axis=0)\n",
+    "\n",
+    "#We can check if these Bayes estimates obtained from samples generated by \n",
+    "#some kind of a Markov Chain Monte Carlo (MCMC) algorithm match the Bayes estimates\n",
+    "#calculated from the correct Beta posterior densities\n",
+    "\n",
+    "#Plot theta_means against the exact posterior mean Bayes estimates\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.scatter(d['bayesestimate'].values, theta_means, alpha=0.5, s = 15)\n",
+    "\n",
+    "# Add the y=x line\n",
+    "min_val = min(d['bayesestimate'].values.min(), theta_means.min())\n",
+    "max_val = max(d['bayesestimate'].values.max(), theta_means.max())\n",
+    "plt.plot([min_val, max_val], [min_val, max_val], 'r-', lw=2, label=\"y=x line\")\n",
+    "\n",
+    "plt.xlabel(\"Exact Bayesestimates\")\n",
+    "plt.ylabel(\"MCMC Bayesestimates\")\n",
+    "plt.title(\"MCMC Bayes Estimates vs. Exact Bayes Estimates\")\n",
+    "plt.grid(True)\n",
+    "plt.show()\n",
+    "#Clearly the two methods give very nearly the same answers"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "9a79557a",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<!-- Generated by graphviz version 2.43.0 (0)\n",
+       " -->\n",
+       "<!-- Title: %3 Pages: 1 -->\n",
+       "<svg width=\"566pt\" height=\"116pt\"\n",
+       " viewBox=\"0.00 0.00 566.00 116.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 112)\">\n",
+       "<title>%3</title>\n",
+       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 562,-112 562,4 -4,4\"/>\n",
+       "<!-- theta_1 -->\n",
+       "<g id=\"node1\" class=\"node\">\n",
+       "<title>theta_1</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ1</text>\n",
+       "</g>\n",
+       "<!-- X_1 -->\n",
+       "<g id=\"node2\" class=\"node\">\n",
+       "<title>X_1</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X1</text>\n",
+       "</g>\n",
+       "<!-- theta_1&#45;&gt;X_1 -->\n",
+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>theta_1&#45;&gt;X_1</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.7C27,-63.98 27,-54.71 27,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-46.1 27,-36.1 23.5,-46.1 30.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_2 -->\n",
+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>theta_2</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"99\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ2</text>\n",
+       "</g>\n",
+       "<!-- X_2 -->\n",
+       "<g id=\"node4\" class=\"node\">\n",
+       "<title>X_2</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"99\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X2</text>\n",
+       "</g>\n",
+       "<!-- theta_2&#45;&gt;X_2 -->\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>theta_2&#45;&gt;X_2</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M99,-71.7C99,-63.98 99,-54.71 99,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"102.5,-46.1 99,-36.1 95.5,-46.1 102.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_3 -->\n",
+       "<g id=\"node5\" class=\"node\">\n",
+       "<title>theta_3</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"171\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ3</text>\n",
+       "</g>\n",
+       "<!-- X_3 -->\n",
+       "<g id=\"node6\" class=\"node\">\n",
+       "<title>X_3</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"171\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X3</text>\n",
+       "</g>\n",
+       "<!-- theta_3&#45;&gt;X_3 -->\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>theta_3&#45;&gt;X_3</title>\n",
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"174.5,-46.1 171,-36.1 167.5,-46.1 174.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_4 -->\n",
+       "<g id=\"node7\" class=\"node\">\n",
+       "<title>theta_4</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"243\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ4</text>\n",
+       "</g>\n",
+       "<!-- X_4 -->\n",
+       "<g id=\"node8\" class=\"node\">\n",
+       "<title>X_4</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"243\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X4</text>\n",
+       "</g>\n",
+       "<!-- theta_4&#45;&gt;X_4 -->\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>theta_4&#45;&gt;X_4</title>\n",
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"246.5,-46.1 243,-36.1 239.5,-46.1 246.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_5 -->\n",
+       "<g id=\"node9\" class=\"node\">\n",
+       "<title>theta_5</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"315\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"315\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ5</text>\n",
+       "</g>\n",
+       "<!-- X_5 -->\n",
+       "<g id=\"node10\" class=\"node\">\n",
+       "<title>X_5</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"315\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"315\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X5</text>\n",
+       "</g>\n",
+       "<!-- theta_5&#45;&gt;X_5 -->\n",
+       "<g id=\"edge5\" class=\"edge\">\n",
+       "<title>theta_5&#45;&gt;X_5</title>\n",
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"318.5,-46.1 315,-36.1 311.5,-46.1 318.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_6 -->\n",
+       "<g id=\"node11\" class=\"node\">\n",
+       "<title>theta_6</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"387\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ6</text>\n",
+       "</g>\n",
+       "<!-- X_6 -->\n",
+       "<g id=\"node12\" class=\"node\">\n",
+       "<title>X_6</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"387\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X6</text>\n",
+       "</g>\n",
+       "<!-- theta_6&#45;&gt;X_6 -->\n",
+       "<g id=\"edge6\" class=\"edge\">\n",
+       "<title>theta_6&#45;&gt;X_6</title>\n",
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+       "</g>\n",
+       "<!-- theta_7 -->\n",
+       "<g id=\"node13\" class=\"node\">\n",
+       "<title>theta_7</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"459\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"459\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ7</text>\n",
+       "</g>\n",
+       "<!-- X_7 -->\n",
+       "<g id=\"node14\" class=\"node\">\n",
+       "<title>X_7</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"459\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"459\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X7</text>\n",
+       "</g>\n",
+       "<!-- theta_7&#45;&gt;X_7 -->\n",
+       "<g id=\"edge7\" class=\"edge\">\n",
+       "<title>theta_7&#45;&gt;X_7</title>\n",
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"462.5,-46.1 459,-36.1 455.5,-46.1 462.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_8 -->\n",
+       "<g id=\"node15\" class=\"node\">\n",
+       "<title>theta_8</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"531\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"531\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ8</text>\n",
+       "</g>\n",
+       "<!-- X_8 -->\n",
+       "<g id=\"node16\" class=\"node\">\n",
+       "<title>X_8</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"531\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"531\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X8</text>\n",
+       "</g>\n",
+       "<!-- theta_8&#45;&gt;X_8 -->\n",
+       "<g id=\"edge8\" class=\"edge\">\n",
+       "<title>theta_8&#45;&gt;X_8</title>\n",
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"534.5,-46.1 531,-36.1 527.5,-46.1 534.5,-46.1\"/>\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<graphviz.dot.Digraph at 0x7f03f4fc68e0>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#The graphical model here is very simple: \n",
+    "from graphviz import Digraph\n",
+    "\n",
+    "def create_graphical_model(N):\n",
+    "    # Create a new directed graph\n",
+    "    dot = Digraph()\n",
+    "\n",
+    "    # Add theta nodes and X nodes\n",
+    "    theta_nodes = [f\"theta_{i}\" for i in range(1, N+1)]\n",
+    "    X_nodes = [f\"X_{i}\" for i in range(1, N+1)]\n",
+    "    for i in range(N):\n",
+    "        dot.node(theta_nodes[i], label=f\"θ{i+1}\")\n",
+    "        dot.node(X_nodes[i], label=f\"X{i+1}\")\n",
+    "        dot.edge(theta_nodes[i], X_nodes[i])\n",
+    "    return dot\n",
+    "\n",
+    "# Display the graph\n",
+    "display(create_graphical_model(8))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2360ce3a",
+   "metadata": {},
+   "source": [
+    "# Analysis via a Hierarchical Model\n",
+    "\n",
+    "In the above analysis, $a$ and $b$ are estimated from the given data on the proportions for large counties. Large was taken to mean population more than 300000. Of course if we use another definition of large, we will get different (but hopefully similar) results. One way of avoiding such ad-hoc estimation is to incorporate $a$ and $b$ also as unknown parameters in the PyMC model. This can be done in the following way: "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "14a180e6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Auto-assigning NUTS sampler...\n",
+      "Initializing NUTS using jitter+adapt_diag...\n",
+      "Multiprocess sampling (2 chains in 4 jobs)\n",
+      "NUTS: [theta, b, a]\n"
+     ]
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "<style>\n",
+       "    /* Turns off some styling */\n",
+       "    progress {\n",
+       "        /* gets rid of default border in Firefox and Opera. */\n",
+       "        border: none;\n",
+       "        /* Needs to be in here for Safari polyfill so background images work as expected. */\n",
+       "        background-size: auto;\n",
+       "    }\n",
+       "    progress:not([value]), progress:not([value])::-webkit-progress-bar {\n",
+       "        background: repeating-linear-gradient(45deg, #7e7e7e, #7e7e7e 10px, #5c5c5c 10px, #5c5c5c 20px);\n",
+       "    }\n",
+       "    .progress-bar-interrupted, .progress-bar-interrupted::-webkit-progress-bar {\n",
+       "        background: #F44336;\n",
+       "    }\n",
+       "</style>\n"
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "\n",
+       "    <div>\n",
+       "      <progress value='4000' class='' max='4000' style='width:300px; height:20px; vertical-align: middle;'></progress>\n",
+       "      100.00% [4000/4000 01:44&lt;00:00 Sampling 2 chains, 1,007 divergences]\n",
+       "    </div>\n",
+       "    "
+      ],
+      "text/plain": [
+       "<IPython.core.display.HTML object>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "Sampling 2 chains for 1_000 tune and 1_000 draw iterations (2_000 + 2_000 draws total) took 105 seconds.\n",
+      "There were 347 divergences after tuning. Increase `target_accept` or reparameterize.\n",
+      "The acceptance probability does not match the target. It is 0.6992742015685093, but should be close to 0.8. Try to increase the number of tuning steps.\n",
+      "There were 660 divergences after tuning. Increase `target_accept` or reparameterize.\n",
+      "The acceptance probability does not match the target. It is 0.6116679458637905, but should be close to 0.8. Try to increase the number of tuning steps.\n",
+      "The rhat statistic is larger than 1.4 for some parameters. The sampler did not converge.\n",
+      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
+     ]
+    }
+   ],
+   "source": [
+    "kidney_model_ab_unknown = pm.Model()\n",
+    "with kidney_model_ab_unknown:\n",
+    "    a = pm.Uniform('a', lower = 0, upper = 50)\n",
+    "    b = pm.Uniform('b', lower = 0, upper = 200000)\n",
+    "    theta = pm.Beta(\"theta\", alpha=a, beta=b, shape = N)\n",
+    "    Y = pm.Binomial(\"Y\", n=n, p=theta, observed=y_obs)\n",
+    "    #Sample from posterior:\n",
+    "    idata = pm.sample(1000, chains = 2, return_inferencedata = True) "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "982f6e8b",
+   "metadata": {},
+   "source": [
+    "This approach produces posterior samples for $a$ and $b$ (in addition to the $\\theta$ parameters). One can use these samples to obtain point estimates for $a$ and $b$, and also to characterize uncertainty in $a$ and $b$. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 25,
+   "id": "e367ebd5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[17.068281999244608, 1.1274766547362032]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/plain": [
+       "[164737.25252111058, 11262.339137284955]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "a_samples = idata.posterior['a'].values.flatten()\n",
+    "b_samples = idata.posterior['b'].values.flatten()\n",
+    "amean = np.mean(a_samples)\n",
+    "astd = np.std(a_samples)\n",
+    "bmean = np.mean(b_samples)\n",
+    "bstd = np.std(b_samples)\n",
+    "display([amean, astd])\n",
+    "display([bmean, bstd])"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 26,
+   "id": "a28e22e5",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1000x400 with 2 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#plotting the histograms of a_samples and b_samples\n",
+    "fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(10, 4))\n",
+    "\n",
+    "axes[0].hist(a_samples, bins=30, color='blue', alpha=0.7, label='a_samples')\n",
+    "axes[0].set_title('Histogram of a_samples')\n",
+    "axes[0].set_xlabel('Value')\n",
+    "axes[0].set_ylabel('Frequency')\n",
+    "\n",
+    "axes[1].hist(b_samples, bins=30, color='red', alpha=0.7, label='b_samples')\n",
+    "axes[1].set_title('Histogram of b_samples')\n",
+    "axes[1].set_xlabel('Value')\n",
+    "axes[1].set_ylabel('Frequency')\n",
+    "\n",
+    "plt.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "7766a891",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.00019285921452520883\n",
+      "2000\n",
+      "0.00020283055885838032\n"
+     ]
+    },
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Let us investigate the theta samples:\n",
+    "#As before, we can look at the histogram of the posterior samples for theta_346 and\n",
+    "#compare it with the Beta posterior from the previous analysis\n",
+    "theta_346_samples = idata.posterior['theta'][:, :, 346].values.flatten()\n",
+    "print(np.mean(theta_346_samples))\n",
+    "print(len(theta_346_samples))\n",
+    "\n",
+    "#Let us plot this histogram along with Beta(a + Pos, b + Neg) posterior for our previous values of a and b\n",
+    "Tot = round(d.loc[346, 'popm'])\n",
+    "Pos = d.loc[346, 'dct']\n",
+    "Neg = Tot - Pos\n",
+    "#This is a large county (population around half a million) and a large death count (120)\n",
+    "#Actual posterior mean\n",
+    "print((aes+Pos)/(aes+bes+Tot))\n",
+    "from scipy.stats import beta\n",
+    "# Plotting histogram\n",
+    "plt.hist(theta_346_samples, bins=50, density=True, alpha=0.6, label=\"Posterior Samples\")\n",
+    "\n",
+    "# Superimposing the Beta density\n",
+    "x = np.arange(0, 8e-4, 1e-6)\n",
+    "y = beta.pdf(x, aes+Pos, bes+Neg)\n",
+    "plt.plot(x, y, 'r-', lw=2, label=f\"Beta({aes+Pos}, {bes+Neg}) Density\")\n",
+    "# Labels, legend, and title\n",
+    "plt.xlabel(\"Value\")\n",
+    "plt.ylabel(\"Density\")\n",
+    "plt.legend(loc=\"upper right\")\n",
+    "plt.title(\"Histogram of Posterior Samples of 346th theta with the actual posterior Beta Density\")\n",
+    "plt.show()\n",
+    "\n",
+    "#This is similar to our previous result but the histogram has moved slightly to the left. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 28,
+   "id": "892b9cc9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "<Figure size 1000x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#We now compare the Bayes estimates in this random a, b model with \n",
+    "#the Bayes estimates based on estimation of a, b in our previous adhoc way.\n",
+    "theta_samples = idata.posterior['theta'].values\n",
+    "combined_samples = theta_samples.reshape(-1, N)\n",
+    "theta_means = np.mean(combined_samples, axis = 0)\n",
+    "\n",
+    "#Plot theta_means against the exact posterior mean Bayes estimates\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.scatter(d['bayesestimate'].values, theta_means, alpha=0.5, s = 15)\n",
+    "\n",
+    "# Add the y=x line\n",
+    "min_val = min(d['bayesestimate'].values.min(), theta_means.min())\n",
+    "max_val = max(d['bayesestimate'].values.max(), theta_means.max())\n",
+    "plt.plot([min_val, max_val], [min_val, max_val], 'r-', lw=2, label=\"y=x line\")\n",
+    "\n",
+    "plt.xlabel(\"Bayes Estimates with Fixed a, b\")\n",
+    "plt.ylabel(\"Bayes Estimates from random a, b\")\n",
+    "plt.title(\"Bayes Estimates from random a, b vs. Fixed a, b Bayes Estimates\")\n",
+    "plt.grid(True)\n",
+    "plt.show()\n",
+    "\n",
+    "#The results are similar but there are some differences. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "e10a541f",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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+      "text/plain": [
+       "<Figure size 1000x600 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#Plotting the posterior standard deviations\n",
+    "theta_stddevs = np.std(combined_samples, axis = 0)\n",
+    "\n",
+    "d['bayesstddev'] = np.sqrt(((d['dct'] + aes)/(d['popm'] + aes + bes)) * (1 - ((d['dct'] + aes)/(d['popm'] + aes + bes))) * (1/(d['popm'] + aes + bes + 1)))\n",
+    "#Plot theta_means against the exact posterior mean Bayes estimates\n",
+    "plt.figure(figsize=(10, 6))\n",
+    "plt.scatter(d['bayesstddev'].values, theta_stddevs, alpha=0.5, s = 15)\n",
+    "\n",
+    "# Add the y=x line\n",
+    "min_val = min(d['bayesstddev'].values.min(), theta_stddevs.min())\n",
+    "max_val = max(d['bayesstddev'].values.max(), theta_stddevs.max())\n",
+    "plt.plot([min_val, max_val], [min_val, max_val], 'r-', lw=2, label=\"y=x line\")\n",
+    "\n",
+    "plt.xlabel(\"Standard Deviations with Fixed a, b\")\n",
+    "plt.ylabel(\"Standard Deviations from random a, b\")\n",
+    "plt.title(\"Standard Deviations from random a, b vs. Standard Deviations for fixed a, b\")\n",
+    "plt.grid(True)\n",
+    "plt.show()\n",
+    "#From this plot, it is clear that the standard deviations in this random a, b model are\n",
+    "#generally smaller than the standard deviations in the fixed a, b model. \n",
+    "#It appears that this Bayesian Hierarchical Model is able to deduce more information\n",
+    "#about the theta parameters (leading to slightly smaller uncertainty) compared to the\n",
+    "#method where we estimated a and b using only about 300 large counties. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 30,
+   "id": "2af9269d",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<!-- Generated by graphviz version 2.43.0 (0)\n",
+       " -->\n",
+       "<!-- Title: %3 Pages: 1 -->\n",
+       "<svg width=\"566pt\" height=\"188pt\"\n",
+       " viewBox=\"0.00 0.00 566.00 188.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 184)\">\n",
+       "<title>%3</title>\n",
+       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-184 562,-184 562,4 -4,4\"/>\n",
+       "<!-- theta_1 -->\n",
+       "<g id=\"node1\" class=\"node\">\n",
+       "<title>theta_1</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ1</text>\n",
+       "</g>\n",
+       "<!-- X_1 -->\n",
+       "<g id=\"node2\" class=\"node\">\n",
+       "<title>X_1</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X1</text>\n",
+       "</g>\n",
+       "<!-- theta_1&#45;&gt;X_1 -->\n",
+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>theta_1&#45;&gt;X_1</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.7C27,-63.98 27,-54.71 27,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-46.1 27,-36.1 23.5,-46.1 30.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_2 -->\n",
+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>theta_2</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"99\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ2</text>\n",
+       "</g>\n",
+       "<!-- X_2 -->\n",
+       "<g id=\"node4\" class=\"node\">\n",
+       "<title>X_2</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"99\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"99\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X2</text>\n",
+       "</g>\n",
+       "<!-- theta_2&#45;&gt;X_2 -->\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>theta_2&#45;&gt;X_2</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M99,-71.7C99,-63.98 99,-54.71 99,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"102.5,-46.1 99,-36.1 95.5,-46.1 102.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_3 -->\n",
+       "<g id=\"node5\" class=\"node\">\n",
+       "<title>theta_3</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"171\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ3</text>\n",
+       "</g>\n",
+       "<!-- X_3 -->\n",
+       "<g id=\"node6\" class=\"node\">\n",
+       "<title>X_3</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"171\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"171\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X3</text>\n",
+       "</g>\n",
+       "<!-- theta_3&#45;&gt;X_3 -->\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>theta_3&#45;&gt;X_3</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M171,-71.7C171,-63.98 171,-54.71 171,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"174.5,-46.1 171,-36.1 167.5,-46.1 174.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_4 -->\n",
+       "<g id=\"node7\" class=\"node\">\n",
+       "<title>theta_4</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"243\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ4</text>\n",
+       "</g>\n",
+       "<!-- X_4 -->\n",
+       "<g id=\"node8\" class=\"node\">\n",
+       "<title>X_4</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"243\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X4</text>\n",
+       "</g>\n",
+       "<!-- theta_4&#45;&gt;X_4 -->\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>theta_4&#45;&gt;X_4</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M243,-71.7C243,-63.98 243,-54.71 243,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"246.5,-46.1 243,-36.1 239.5,-46.1 246.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_5 -->\n",
+       "<g id=\"node9\" class=\"node\">\n",
+       "<title>theta_5</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"315\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"315\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ5</text>\n",
+       "</g>\n",
+       "<!-- X_5 -->\n",
+       "<g id=\"node10\" class=\"node\">\n",
+       "<title>X_5</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"315\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"315\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X5</text>\n",
+       "</g>\n",
+       "<!-- theta_5&#45;&gt;X_5 -->\n",
+       "<g id=\"edge5\" class=\"edge\">\n",
+       "<title>theta_5&#45;&gt;X_5</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M315,-71.7C315,-63.98 315,-54.71 315,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"318.5,-46.1 315,-36.1 311.5,-46.1 318.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_6 -->\n",
+       "<g id=\"node11\" class=\"node\">\n",
+       "<title>theta_6</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"387\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ6</text>\n",
+       "</g>\n",
+       "<!-- X_6 -->\n",
+       "<g id=\"node12\" class=\"node\">\n",
+       "<title>X_6</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"387\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"387\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X6</text>\n",
+       "</g>\n",
+       "<!-- theta_6&#45;&gt;X_6 -->\n",
+       "<g id=\"edge6\" class=\"edge\">\n",
+       "<title>theta_6&#45;&gt;X_6</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M387,-71.7C387,-63.98 387,-54.71 387,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"390.5,-46.1 387,-36.1 383.5,-46.1 390.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_7 -->\n",
+       "<g id=\"node13\" class=\"node\">\n",
+       "<title>theta_7</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"459\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"459\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ7</text>\n",
+       "</g>\n",
+       "<!-- X_7 -->\n",
+       "<g id=\"node14\" class=\"node\">\n",
+       "<title>X_7</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"459\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"459\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X7</text>\n",
+       "</g>\n",
+       "<!-- theta_7&#45;&gt;X_7 -->\n",
+       "<g id=\"edge7\" class=\"edge\">\n",
+       "<title>theta_7&#45;&gt;X_7</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M459,-71.7C459,-63.98 459,-54.71 459,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"462.5,-46.1 459,-36.1 455.5,-46.1 462.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- theta_8 -->\n",
+       "<g id=\"node15\" class=\"node\">\n",
+       "<title>theta_8</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"531\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"531\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">θ8</text>\n",
+       "</g>\n",
+       "<!-- X_8 -->\n",
+       "<g id=\"node16\" class=\"node\">\n",
+       "<title>X_8</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"531\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"531\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X8</text>\n",
+       "</g>\n",
+       "<!-- theta_8&#45;&gt;X_8 -->\n",
+       "<g id=\"edge8\" class=\"edge\">\n",
+       "<title>theta_8&#45;&gt;X_8</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M531,-71.7C531,-63.98 531,-54.71 531,-46.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"534.5,-46.1 531,-36.1 527.5,-46.1 534.5,-46.1\"/>\n",
+       "</g>\n",
+       "<!-- a -->\n",
+       "<g id=\"node17\" class=\"node\">\n",
+       "<title>a</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"243\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"243\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\">a</text>\n",
+       "</g>\n",
+       "<!-- a&#45;&gt;theta_1 -->\n",
+       "<g id=\"edge9\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_1</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M217.85,-154.91C182.68,-146.1 117.04,-128.57 63,-108 61.16,-107.3 59.28,-106.54 57.4,-105.75\"/>\n",
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+       "</g>\n",
+       "<!-- a&#45;&gt;theta_2 -->\n",
+       "<g id=\"edge11\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_2</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M221.75,-150.67C197.4,-138.83 157.28,-119.33 129.57,-105.86\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"130.86,-102.6 120.33,-101.37 127.8,-108.89 130.86,-102.6\"/>\n",
+       "</g>\n",
+       "<!-- a&#45;&gt;theta_3 -->\n",
+       "<g id=\"edge13\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_3</title>\n",
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+       "<polygon fill=\"black\" stroke=\"black\" points=\"195.41,-109.85 185.8,-105.38 190.53,-114.87 195.41,-109.85\"/>\n",
+       "</g>\n",
+       "<!-- a&#45;&gt;theta_4 -->\n",
+       "<g id=\"edge15\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_4</title>\n",
+       "<path fill=\"none\" stroke=\"black\" d=\"M243,-143.7C243,-135.98 243,-126.71 243,-118.11\"/>\n",
+       "<polygon fill=\"black\" stroke=\"black\" points=\"246.5,-118.1 243,-108.1 239.5,-118.1 246.5,-118.1\"/>\n",
+       "</g>\n",
+       "<!-- a&#45;&gt;theta_5 -->\n",
+       "<g id=\"edge17\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_5</title>\n",
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+       "<g id=\"edge19\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_6</title>\n",
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+       "<!-- a&#45;&gt;theta_7 -->\n",
+       "<g id=\"edge21\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_7</title>\n",
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+       "</g>\n",
+       "<!-- a&#45;&gt;theta_8 -->\n",
+       "<g id=\"edge23\" class=\"edge\">\n",
+       "<title>a&#45;&gt;theta_8</title>\n",
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+       "</g>\n",
+       "<!-- b -->\n",
+       "<g id=\"node18\" class=\"node\">\n",
+       "<title>b</title>\n",
+       "<ellipse fill=\"none\" stroke=\"black\" cx=\"315\" cy=\"-162\" rx=\"27\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"315\" y=\"-158.3\" font-family=\"Times,serif\" font-size=\"14.00\">b</text>\n",
+       "</g>\n",
+       "<!-- b&#45;&gt;theta_1 -->\n",
+       "<g id=\"edge10\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_1</title>\n",
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+       "<g id=\"edge12\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_2</title>\n",
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+       "<g id=\"edge14\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_3</title>\n",
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+       "<g id=\"edge16\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_4</title>\n",
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+       "<g id=\"edge18\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_5</title>\n",
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+       "<title>b&#45;&gt;theta_6</title>\n",
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+       "<g id=\"edge22\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_7</title>\n",
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+       "<!-- b&#45;&gt;theta_8 -->\n",
+       "<g id=\"edge24\" class=\"edge\">\n",
+       "<title>b&#45;&gt;theta_8</title>\n",
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+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<graphviz.dot.Digraph at 0x7f03f7685f10>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "#The graphical model for this model is the following:\n",
+    "from graphviz import Digraph\n",
+    "\n",
+    "def create_graphical_model(N):\n",
+    "    # Create a new directed graph\n",
+    "    dot = Digraph()\n",
+    "\n",
+    "    # Add theta nodes and X nodes\n",
+    "    theta_nodes = [f\"theta_{i}\" for i in range(1, N+1)]\n",
+    "    X_nodes = [f\"X_{i}\" for i in range(1, N+1)]\n",
+    "    for i in range(N):\n",
+    "        dot.node(theta_nodes[i], label=f\"θ{i+1}\")\n",
+    "        dot.node(X_nodes[i], label=f\"X{i+1}\")\n",
+    "        dot.edge(theta_nodes[i], X_nodes[i])\n",
+    "\n",
+    "    # Add nodes a and b\n",
+    "    dot.node(\"a\", \"a\")\n",
+    "    dot.node(\"b\", \"b\")\n",
+    "\n",
+    "    # Add directed edges from a and b to each theta_i\n",
+    "    for theta in theta_nodes:\n",
+    "        dot.edge(\"a\", theta)\n",
+    "        dot.edge(\"b\", theta)\n",
+    "\n",
+    "    return dot\n",
+    "\n",
+    "# Display the graph\n",
+    "display(create_graphical_model(8))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "4115a227",
+   "metadata": {},
+   "source": [
+    "The above is an example of a **Bayesian Hierarchical Model**. $a$ and $b$ are referred to as hyperparameters (to distinguish them from the parameters $\\theta_1, \\dots, \\theta_N$). In the next class, we shall study more Bayesian models and use them for data analysis through PyMC. "
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
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