{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "da61d6ad",
   "metadata": {},
   "source": [
    "# Bayesian Hierarchical Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "id": "6be719f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "from IPython.display import YouTubeVideo\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1628e767",
   "metadata": {},
   "source": [
    "We've seen so far that a Bayesian approach can be useful in cases where we have prior domain knowledge that we want to incorporate into our model. We've also seen that the effect of choosing a prior depends heavily on how much data we have: the less data we have, the more our conclusions tilt toward the prior.\n",
    "\n",
    "In many cases, we may not have as much external prior knowledge, and we want to rely on parts of the dataset that are larger to help offset parts of the dataset that are smaller. We'll make this (very) abstract idea concrete with an example looking at kidney cancer deaths in the US between 1980 and 1989. The data used in this section, as well as inspiration for the modeling and analysis, comes from [Bayesian Data Analysis](http://www.stat.columbia.edu/~gelman/book/) pp 47-51. The cleaned version of the data came from [Robin Ryder](https://github.com/robinryder/BDA-kidney). Note that the dataset suffers from a severe bias: it only contains information on white men. We'll discuss issues with this later in this section.\n",
    "\n",
    "We'll walk through the process of setting up a model for this more complex dataset, and in the process see several advantages and perspectives on Bayesian models."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ee8ef374",
   "metadata": {},
   "source": [
    "## Example: Understanding Kidney Cancer Death Risk\n",
    "\n",
    "Before we can start modeling, we must first understand the data. We'll focus on the following columns:\n",
    "* `state`: the US state\n",
    "* `Location`: the county and state as a string\n",
    "* `fips`, which provides the [FIPS code](https://en.wikipedia.org/wiki/Federal_Information_Processing_Standard_state_code) for each county: this is a standard identifier that can often be used to join datasets with county-level information.\n",
    "* `dc` and `dc.2`: the number of kidney cancer deaths between 1980-1984 and 1985-1989, respectively\n",
    "* `pop` and `pop.2`: the population between 1980-1984 and 1985-1989, respectively"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "5ad47a90",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>state</th>\n",
       "      <th>Location</th>\n",
       "      <th>dc</th>\n",
       "      <th>dc.2</th>\n",
       "      <th>pop</th>\n",
       "      <th>pop.2</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>Autauga County, Alabama</td>\n",
       "      <td>2</td>\n",
       "      <td>1</td>\n",
       "      <td>61921</td>\n",
       "      <td>64915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>Baldwin County, Alabama</td>\n",
       "      <td>7</td>\n",
       "      <td>15</td>\n",
       "      <td>170945</td>\n",
       "      <td>195253</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>Barbour County, Alabama</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>33316</td>\n",
       "      <td>33987</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>Bibb County, Alabama</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>30152</td>\n",
       "      <td>31175</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>Blount County, Alabama</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>88342</td>\n",
       "      <td>91547</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     state                 Location  dc  dc.2     pop   pop.2\n",
       "0  ALABAMA  Autauga County, Alabama   2     1   61921   64915\n",
       "1  ALABAMA  Baldwin County, Alabama   7    15  170945  195253\n",
       "2  ALABAMA  Barbour County, Alabama   0     1   33316   33987\n",
       "3  ALABAMA     Bibb County, Alabama   0     1   30152   31175\n",
       "4  ALABAMA   Blount County, Alabama   3     5   88342   91547"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kc_full = pd.read_csv('kidney_cancer_1980.csv', skiprows=4)\n",
    "# There are many other interesting columns, but we'll focus on these:\n",
    "kc = kc_full.loc[:, ['state', 'Location', 'dc', 'dc.2', 'pop', 'pop.2']]\n",
    "kc.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e92ea20c",
   "metadata": {},
   "source": [
    "For simplicity, we'll focus our analysis on 1980-1984. Our goal will be to understand **in which counties people are at the highest risk of kidney cancer death**. This could help inform public health actions, or could reveal information about underlying carcinogens (e.g., proximity to chemical treatment plants, etc.) that should be investigated and remedied."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "925d1dc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='rate_naive', ylabel='Count'>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kc['rate_nopool'] = kc['dc'] / kc['pop']\n",
    "sns.histplot(kc, x='rate_nopool')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f0c59ec",
   "metadata": {},
   "source": [
    "From this, it appears that most counties have a rate between 1 in 100,000 ($0.00001$) and 1 in 10,000 ($0.0001$), but a sizeable number have a rate of 0.\n",
    "\n",
    "If our goal is merely to characterize exactly what happened in each county from 1980-1984, this visualization could be enough. However, our goal is to understand the risk of kidney cancer death in each county, in a way that could help inform public health. This motivates the definition of our parameter of interest: **for county $i$, what is each person's average risk of dying from kidney cancer?** \n",
    "\n",
    "Intuitively, we can see that in counties with very low population, this dataset will provide a poor estimate of this parameter. Take, for example, a hypothetical county with only 10 people. Because the rate we're interested in is close to 1 in 10,000, we're very likely to see 0 deaths, but that doesn't mean that the risk for these 10 people is 0! We can see this empirically:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "68e0bf57",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='pop', ylabel='rate_naive'>"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(kc, x='pop', y='rate_nopool', alpha=0.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0000aa5",
   "metadata": {},
   "source": [
    "For larger counties, our estimates are consistently between $0.00002$ and $0.00008$, but for the small counties, the estimates have much higher variability.\n",
    "\n",
    "Here, we have a situation where we have a very large amount of data (in fact, our dataset contains a census of the entire population of interest), but we're trying to quantify a relatively rare phenomenon. Next, we'll see how Bayesian inference can help us leverage the more certain information from large counties to make good inferences for small counties."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8782f152",
   "metadata": {},
   "source": [
    "## Bayesian Inference as a Middle Ground\n",
    "\n",
    "We can consider the approach we took earlier as one extreme of a spectrum: we estimated the death rate for each county separately, and didn't pool or share any information across counties at all.\n",
    "\n",
    "On the opposite extreme of the spectrum, we could pool all the data from all the counties together:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "82892dfb",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.856485743364176e-05"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_pop = kc['pop'].sum()\n",
    "total_dc = kc['dc'].sum()\n",
    "overall_rate = total_dc / total_pop\n",
    "overall_rate"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f68cf3c",
   "metadata": {},
   "source": [
    "While this provides a good estimate of the rate overall, it obscures variability across counties, and prevents us from making county-level inferences or finding locations most in need of targeting. \n",
    "\n",
    "To achieve a middle ground between these two extremes, we'll use a **Bayesian hierarchical model**:\n",
    "* For each county, let $\\theta_i \\in [0, 1]$ be a random variable indicating the risk of kidney cancer death for an individual in that county. \n",
    "* We'll use the same prior distribution for each county: a Beta$(a, b)$ (for values of $a$ and $b$ yet to be determined), but each is a separate random variable and will have a separate posterior distribution.\n",
    "* Let $y_i$ be a **binomial** random variable for each county indicating the number of kidney cancer deaths for that county, with parameters $n_i$ (the county population) and $\\theta_i$ (the county-level risk).\n",
    "\n",
    "Notationally, we can write the above bullet points as \n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "\\theta_i &\\sim \\mathrm{Beta}(a, b), & i \\in \\{1, 2, \\ldots\\} \\\\\n",
    "y_i &\\sim \\mathrm{Binomial}(\\theta_i, n_i), & i \\in \\{1, 2, \\ldots, C\\}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "We saw in the last section that if the likelihood for a sequence of random variables $x_i$ is Bernoulli$(\\theta)$ and the prior for $\\theta$ is Beta$(a, b)$, then the posterior for $\\theta$ is Beta$\\left(a + \\sum x_i, b + n - \\sum x_i\\right)$. We can also show that **if the likelihood a random variable $y$ is Binomial$(n, \\theta)$ and the prior for $\\theta$ is Beta$(a, b)$, then the posterior for $\\theta$ is Beta$(a + y, b + n - y)$.** In other words, just as the Beta distribution is the conjugate prior for the Bernoulli likelihood, it is also the conjugate prior for the binomial likelihood. (It also happens to be the conjugate prior for the geometric likelihood as well!)\n",
    "\n",
    "Putting all this together, we can now compute the posterior distribution. Instead of a single parameter $\\theta$, we now have $C$ parameters, $\\theta_1, \\ldots, \\theta_C$. The posterior distribution is the joint distribution of all of these random variables, conditioned on all of the observed data:\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "p(\\theta_1, \\ldots, \\theta_C | y_1, \\ldots, y_C) \n",
    "    &\\propto \\overbrace{p(y_1, \\ldots, y_c | \\theta_1, \\ldots, \\theta_C)}^{\\text{likelihood}}\\,\n",
    "             \\overbrace{p(\\theta_1, \\ldots, \\theta_C)}^{\\text{prior}} \\\\\n",
    "    &= \\prod_{i=1}^C \\theta_i^{a+y_i}(1-\\theta_i)^{b + n_i - y_i}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "From this, we can conclude that we can compute the posterior independently for every county: \n",
    "\n",
    "$$\n",
    "\\theta_i | y_i \\sim \\mathrm{Beta}(a + y_i, b + n_i - y_i)\n",
    "$$\n",
    "\n",
    "Note that according to the posterior distribution $p(\\theta_1, \\ldots, \\theta_C | y_1, \\ldots, y_C)$, the distribution for each county's parameter is independent of all other counties, because the joint distribution can be written as a product of the marginal distributions. But, they all share the parameters $a$ and $b$ in common.\n",
    "\n",
    "Just as in the earlier example, we're now left with a critically important question: **how do we choose $a$ and $b$**? We'll examine four approaches, in increasing order of complexity and sophistication:\n",
    "\n",
    "1. Uninformative prior\n",
    "2. Educated guess\n",
    "3. Empirical Bayes\n",
    "4. Hierarchical model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "394463e5",
   "metadata": {},
   "source": [
    "#### Uninformative Prior\n",
    "\n",
    "If we don't know anything about the data, we can choose an **uninformative prior**: in other words, one that provides as little information as possible. In this example, we might choose a uniform distribution over $[0, 1]$ (i.e., $a = b = 1$). While this avoids the problem of specifying a prior, it also isn't particularly useful. If we use such a weak prior, we're saying that risk values closer to $0.8$ are just as likely as values closer to $0.0001$: this clearly does not align with what we already know about the problem, and if we compute the posterior distributions, we'll see that the results won't be significantly different from the no-pooling estimates earlier."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "420cb14e",
   "metadata": {},
   "source": [
    "#### Educated Guess\n",
    "\n",
    "A good prior distribution should encode our knowledge about the quantity of interest. In this case, everything we know comes from what we've done here: above, we estimated an overall rate of about 4.9 in 10,000. If we choose $a = 5$ and $b = 9995$, then the mean of the prior is $5 \\times 10^{-5}$. So, one possible option is Beta$(5, 9995)$.\n",
    "\n",
    "Note that this is fairly arbitrary: we could have just as easily chosen $a = 10$ and $b = 19990$, or $a = 50$ and $b = 99950$, and obtained the same mean. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68abfc19",
   "metadata": {},
   "source": [
    "#### Empirical Bayes\n",
    "\n",
    "Empirical Bayes is a hybrid Bayesian-frequentist approach that uses frequentist methods to find guesses or prior distributions for quantities of interest. In this case, we'll use a frequentist approach to make a better guess for $a$ and $b$.\n",
    "\n",
    "In particular, we saw earlier that the smaller counties produced naive estimates that varied too much. What if we just looked at the larger counties? We'll start by deciding on a (somewhat arbitrary) threshold of big versus small counties. From the scatterplot above, we can see that after a certain size, the non-pooled estimates seem to be much less variable. We can zoom in to decide on a threshold:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "26641ae1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.scatterplot(kc, x='pop', y='rate_nopool', alpha=0.6);\n",
    "plt.vlines(3e5, 0, 0.0004, color='black', ls='--')\n",
    "plt.axis([0, 1e6, 0, 0.0004]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "982f3126",
   "metadata": {},
   "source": [
    "Based on this, we'll use 300,000 as a cutoff (the dotted line), and ignore counties smaller than this when estimating the parameters of the prior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "143fc601",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='rate_naive', ylabel='Count'>"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kc_large_counties = kc[kc['pop'] > 300000]\n",
    "sns.histplot(kc_large_counties, x='rate_nopool')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ec8e5be",
   "metadata": {},
   "source": [
    "We'll use this empirical distribution (or rather, a close approximation of it) as our prior: this is where the \"empirical\" in empirical Bayes comes from. Since we want to use a Beta prior, we need to fit a Beta distribution to this data. In other words, we need to find parameters $a$ and $b$ that are a good fit for this sequence of observations (in the histogram above). \n",
    "\n",
    "This is exactly the problem we solved in the last section using maximum likelihood! We'll use maximum likelihood to fit a Beta distribution to these data. This time, instead of deriving the MLEs for the Beta distribution, we'll use scipy to do it for us:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "76527a8f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "9.270228244533358 195581.04114706165\n"
     ]
    }
   ],
   "source": [
    "from scipy import stats\n",
    "# The last two arguments tell scipy that it shouldn't try to shift or scale our Beta distribution\n",
    "a_hat, b_hat, loc_, scale_ = stats.beta.fit(kc_large_counties['rate_nopool'], floc=0, fscale=1)\n",
    "print(a_hat, b_hat)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1f0826d7",
   "metadata": {},
   "source": [
    "Using this approach, our prior would be Beta$(9.27, 195581)$. To summarize what we did:\n",
    "\n",
    "* We want to find the parameters $a$ and $b$ of the prior, using our data to help us since we don't have any domain knowledge\n",
    "* We determined that we trust the data from the large counties, but not the smaller counties (because they are too variable). Note that this is an implicit **assumption** which could lead us astray: for example, if larger counties are biased toward lower or higher rates, then using them to estimate parameters of the prior is a bad idea.\n",
    "* We looked at the naively estimated rates for the large counties only, and fit a Beta distribution to those, and then used that Beta distribution as our prior.\n",
    "\n",
    "Let's compare the results for these two approaches. For ease of visualization, we'll look at a histogram of each county's LMSE estimate:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "53dd0943",
   "metadata": {},
   "outputs": [],
   "source": [
    "a_guess, b_guess = 5, 19995  # educated guess\n",
    "a_eb, b_eb = a_hat, b_hat  # empirical bayes\n",
    "\n",
    "def compute_posterior(kc, prior_a, prior_b):\n",
    "    posterior_a = prior_a + kc['dc']\n",
    "    posterior_b = prior_b + (kc['pop'] - kc['dc'])\n",
    "    return posterior_a, posterior_b\n",
    "kc['posterior_a_guess'], kc['posterior_b_guess'] = compute_posterior(kc, a_guess, b_guess)\n",
    "kc['posterior_a_eb'], kc['posterior_b_eb'] = compute_posterior(kc, a_eb, b_eb)\n",
    "\n",
    "# For a Beta(a, b) distribution, the mean is a / (a + b)\n",
    "kc['lmse_guess'] = kc['posterior_a_guess'] / (kc['posterior_a_guess'] + kc['posterior_b_guess'])\n",
    "kc['lmse_eb'] = kc['posterior_a_eb'] / (kc['posterior_a_eb'] + kc['posterior_b_eb'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "id": "e575a137",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x176c5e950>"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(0, 0.0003, 100)\n",
    "sns.histplot(kc, x='lmse_eb', stat='density', label='Empirical Bayes prior', bins=bins)\n",
    "sns.histplot(kc, x='lmse_guess',  stat='density', label='Educated guess prior', bins=np.linspace(0, 0.0003, 100))\n",
    "plt.xlabel(\"LMSE estimate for each county's risk\")\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6bb8795",
   "metadata": {},
   "source": [
    "In both cases, we no longer see estimates of 0. Note that because the empirical Bayes prior was stronger (i.e., less variable due to larger values of $a$ and $b$), the posterior estimates fall in a narrower range."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cce6f558",
   "metadata": {},
   "source": [
    "#### Full Hierarchical Model\n",
    "\n",
    "Philosophically, taking a Bayesian approach means that we're deciding to treat unknown quantities as random variables, rather than fixed parameters. From what we've seen so far, in this model, $a$ and $b$ are important unknown quantities that have a fairly significant effect on the outcome of our inference. So, we'll now try treating them as random variables. Note that we now have two levels of unknown random variables: $\\theta_i$, which we've already established, are the county-level risk probabilities. $a$ and $b$ are now US-level average parameters that reflect the risk across all counties. This is a common feature of hierarchical models: one set of variables is closely linked to the data for each group (in this case, county), and one set of variables represents more global information (in this case, the entire US).\n",
    "\n",
    "But this leads to yet another modeling question: **what prior distribution do we choose for $a$ and $b$**?\n",
    "\n",
    "Unfortunately, there is no convenient distribution that is a conjugate prior for the parameters of the Beta distribution. We'll use a uniform distribution, but we're still left with the question of how to choose the parameters of that uniform distribution. Since we know that $b >> a$, we'll make the somewhat arbitrary choice of saying $a \\sim \\mathrm{Uniform}(0, 50)$ and $b \\sim \\mathrm{Uniform}(0, 200000)$. We can then write out the full model:\n",
    "\n",
    "\n",
    "$$\n",
    "\\begin{align*}\n",
    "a &\\sim \\mathrm{Uniform}(0, 50) \\\\\n",
    "b &\\sim \\mathrm{Uniform}(0, 300000) \\\\\n",
    "\\theta_i &\\sim \\mathrm{Beta}(a, b), & i \\in \\{1, 2, \\ldots\\} \\\\\n",
    "y_i &\\sim \\mathrm{Binomial}(\\theta_i, n_i), & i \\in \\{1, 2, \\ldots\\}\n",
    "\\end{align*}\n",
    "$$\n",
    "\n",
    "Unfortunately, there is no convenient way to compute the posterior distribution here: we must resort to approximate techniques. We'll return to this model in the next section, after we develop tools for approximate inference. In the remainder of this section, we'll explore different hierarchical models as well as a unifying framework for them known as graphical models.\n",
    "\n",
    "#### Attempting to compute the posterior for the full hierarchical model\n",
    "\n",
    "*Coming soon*"
   ]
  },
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   "cell_type": "markdown",
   "id": "804836f2",
   "metadata": {},
   "source": [
    "### Bias in the Kidney Cancer Dataset\n",
    "\n",
    "*The content in this section is under active development and is subject to change.*\n",
    "\n",
    "As mentioned earlier, the dataset as provided only contains data about white men. However, kidney cancer risk is not uniform, as seen in this data from the NIH's National Cancer Institute:\n",
    "\n",
    "![explorer-graph.png](explorer-graph.png)\n",
    "\n",
    "From this, we can see that there are clearly racial disparities in kidney cancer occurrence. Further, any county-level effects that we see may have racial disparities as well. How might we solve this? Unfortunately, in this case, because we don't have much insight into how the data were collected, and because they were collected so long ago, we can't improve our analysis."
   ]
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   "cell_type": "markdown",
   "id": "04250f6a",
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   "source": [
    "## Example: Gaussian Mixture Model for Exoplanet Habitability\n",
    "\n",
    "*Coming soon*"
   ]
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