AM207_HW7_Nikhila_Ravi.ipynb

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   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import scipy\n",
    "from scipy import stats\n",
    "from scipy.stats import norm\n",
    "from scipy.stats import beta\n",
    "from scipy.stats import distributions\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import time\n",
    "sns.set_style('white')\n",
    "sns.set_context('paper')\n",
    "from scipy.special import gammaln"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# APMTH 207: Advanced Scientific Computing: \n",
    "## Stochastic Methods for Data Analysis, Inference and Optimization\n",
    "## Homework #7\n",
    "**Harvard University**<br>\n",
    "**Spring 2017**<br>\n",
    "**Instructors: Rahul Dave**<br>\n",
    "**Due Date: ** Thursday, March 23th, 2017 at 11:59pm\n",
    "\n",
    "**Instructions:**\n",
    "\n",
    "- Upload your final answers as well as your iPython notebook containing all work to Canvas.\n",
    "\n",
    "- Structure your notebook and your work to maximize readability."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Problem 1: Kidney Cancer Data Revisited\n",
    "In this problem we will work with the US Kidney Cancer Data set (by county). This is a dataset of kidney cancer frequencies across the US over 5 years on a per county basis. \n",
    "\n",
    "In lecture, we've discussed the potential (and significant) draw backs of drawing conclusions based on raw cancer rates. Addressing these draw backs, we proposed using a Bayesian model to model the data. In the following, you will implement two Bayesian models and examine the adjusted cancer rates per county resulting from these models.\n",
    "\n",
    "### Part A: Empirical Bayes\n",
    "Let $N$ be the number of counties; let $y_j$ the number of kidney cancer case for the $j$-th county, $n_j$ the population of the $j$-county and $\\theta_j$ be the underlying kidney cancer rate for that county. The following is a Bayesian model for our data:\n",
    "\\begin{aligned}\n",
    "y_j &\\sim Poisson(5 \\cdot n_j \\cdot \\theta_j), \\quad j = 1, \\ldots, N\\\\\n",
    "\\theta_j &\\sim Gamma(\\alpha, \\beta), \\quad j = 1, \\ldots, N\n",
    "\\end{aligned}\n",
    "where $\\alpha, \\beta$ are hyper-parameters of the model.\n",
    "\n",
    "(1) Using Empirical Bayes and moment matching, choose appropriate values for the hyperparameters. To do this, consider the **prior-predictive** distribution (also called evidence, the denominator normalization of bayes theorem) of the model: \n",
    "\n",
    "$$p(y) = \\int p(y \\vert \\theta) p(\\theta) d \\theta$$.\n",
    "\n",
    "(This is as opposed to the posterior predictive: $\\int p( y \\vert \\theta) p(\\theta \\vert D) d\\theta$. Not that in conjugate models such as ours, these two distributions have the same form)\n",
    "\n",
    "For this model, the prior-predictive is a negative binomial. By matching the mean and the variance of the negative binomial to that from the data you can find $\\alpha$ and $\\beta$. (Hint: You need to be careful with the $5n_j$ multiplier.) Why the prior-predictive? Because you then \"havent seen\" individual county data yet.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
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   "outputs": [],
   "source": [
    "cancer_data = pd.read_csv('./kcancer.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
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    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>state</th>\n",
       "      <th>fips</th>\n",
       "      <th>county</th>\n",
       "      <th>countyfips</th>\n",
       "      <th>dc</th>\n",
       "      <th>pop</th>\n",
       "      <th>pct_mortality</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>AUTAUGA</td>\n",
       "      <td>1001</td>\n",
       "      <td>1.0</td>\n",
       "      <td>64915.0</td>\n",
       "      <td>0.000015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>BALDWIN</td>\n",
       "      <td>1003</td>\n",
       "      <td>15.0</td>\n",
       "      <td>195253.0</td>\n",
       "      <td>0.000077</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>BARBOUR</td>\n",
       "      <td>1005</td>\n",
       "      <td>1.0</td>\n",
       "      <td>33987.0</td>\n",
       "      <td>0.000029</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>BIBB</td>\n",
       "      <td>1007</td>\n",
       "      <td>1.0</td>\n",
       "      <td>31175.0</td>\n",
       "      <td>0.000032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>BLOUNT</td>\n",
       "      <td>1009</td>\n",
       "      <td>5.0</td>\n",
       "      <td>91547.0</td>\n",
       "      <td>0.000055</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>BULLOCK</td>\n",
       "      <td>1011</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8197.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>BUTLER</td>\n",
       "      <td>1013</td>\n",
       "      <td>1.0</td>\n",
       "      <td>31722.0</td>\n",
       "      <td>0.000032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>CALHOUN</td>\n",
       "      <td>1015</td>\n",
       "      <td>12.0</td>\n",
       "      <td>233021.0</td>\n",
       "      <td>0.000051</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>CHAMBERS</td>\n",
       "      <td>1017</td>\n",
       "      <td>0.0</td>\n",
       "      <td>57813.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>ALABAMA</td>\n",
       "      <td>1</td>\n",
       "      <td>CHEROKEE</td>\n",
       "      <td>1019</td>\n",
       "      <td>0.0</td>\n",
       "      <td>43828.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     state  fips    county  countyfips    dc       pop  pct_mortality\n",
       "0  ALABAMA     1   AUTAUGA        1001   1.0   64915.0       0.000015\n",
       "1  ALABAMA     1   BALDWIN        1003  15.0  195253.0       0.000077\n",
       "2  ALABAMA     1   BARBOUR        1005   1.0   33987.0       0.000029\n",
       "3  ALABAMA     1      BIBB        1007   1.0   31175.0       0.000032\n",
       "4  ALABAMA     1    BLOUNT        1009   5.0   91547.0       0.000055\n",
       "5  ALABAMA     1   BULLOCK        1011   0.0    8197.0       0.000000\n",
       "6  ALABAMA     1    BUTLER        1013   1.0   31722.0       0.000032\n",
       "7  ALABAMA     1   CALHOUN        1015  12.0  233021.0       0.000051\n",
       "8  ALABAMA     1  CHAMBERS        1017   0.0   57813.0       0.000000\n",
       "9  ALABAMA     1  CHEROKEE        1019   0.0   43828.0       0.000000"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cancer_data.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Estimate $\\alpha$ and $\\beta$ based on the prior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From matching the mean and the variance of the prior to the moments of the gamma distribution, the values of $\\alpha$ and $\\beta$ can be calculated:\n",
    "\n",
    "$$ \\mu = \\frac{\\alpha}{\\beta} $$\n",
    "$$ \\sigma^2 = \\frac{\\alpha}{\\beta^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mu = (cancer_data['dc']/(5*cancer_data['pop'])).mean()\n",
    "sigma2 = (cancer_data['dc']/(5*cancer_data['pop'])).var()\n",
    "sum_yi = cancer_data['dc'].sum()\n",
    "N = cancer_data.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1573104708217248e-05, 1.0113340787478882e-10)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu, sigma2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "beta_emp = mu/sigma2\n",
    "alpha_emp = mu*beta_emp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.3243571575594935, 114434.04263154732)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha_emp,beta_emp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "thetas = []\n",
    "for i in range(N):\n",
    "    y_j = cancer_data['dc'].iloc[i]\n",
    "    n_j = cancer_data['pop'].iloc[i]\n",
    "    thetas.append(np.random.gamma(alpha_emp+y_j, 1/(beta_emp+5*n_j), size=10000).mean())\n",
    "thetas = np.array(thetas) # need the per year rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimate $\\alpha$ and $\\beta$ based on the prior predictive\n",
    "\n",
    "The negative binomial is parameterised by r and p. For this example the prior predictive values of y are given by:\n",
    "\n",
    "$$ y_j \\sim NegBin (\\alpha, \\frac{\\beta}{5n_j}) $$\n",
    "\n",
    "where:\n",
    "\n",
    "$$ r = \\alpha $$\n",
    "$$ p =  \\frac{5n_j}{5n_j+ \\beta}$$\n",
    "\n",
    "The mean and variance of a negative binomial are given by:\n",
    "\n",
    "$$ \\mu = \\frac{rp}{1-p} $$\n",
    "\n",
    "$$ \\sigma^2 = \\frac{rp}{(1-p)^2} $$\n",
    "\n",
    "$$ \\sigma^2 = \\frac{\\mu}{(1-p)} $$\n",
    "\n",
    "Substituting r and p we get:\n",
    "\n",
    "$$ \\mu = \\frac{\\alpha * 5n_j}{\\beta} $$\n",
    "\n",
    "$$ \\sigma^2 = \\frac{\\mu(\\beta + 5n_j)}{\\beta}$$\n",
    "\n",
    "Resulting in the following experessions for alpha and beta:\n",
    "\n",
    "$$ \\beta = \\frac{5n_j \\mu}{\\sigma^2 - \\mu} $$\n",
    "\n",
    "$$ \\alpha = \\frac{\\mu \\beta}{5n_j} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu_ = cancer_data['dc'].mean()\n",
    "sigma2_ = cancer_data['dc'].var()\n",
    "n_j_mean = cancer_data['pop'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "beta1 = (5*cancer_data['pop']*cancer_data['dc']).mean()/(sigma2_ - mu_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "113737.85828851341"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "beta1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "alpha1 = ((beta1*cancer_data['dc'])/(5*cancer_data['pop'])).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.3163001432613421"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "thetas = []\n",
    "for i in range(N):\n",
    "    y_j = cancer_data['dc'].iloc[i]\n",
    "    n_j = cancer_data['pop'].iloc[i]\n",
    "    thetas.append(np.random.gamma(alpha1+y_j, 1/(beta1+5*n_j), size=10000).mean())\n",
    "thetas = np.array(thetas) # need the per year rate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The values of alpha and beta obtained using the prior and prior predictive are very similar. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "(2) Produce a scatter plot of the raw cancer rates (pct mortality) vs the county population size. Highlight the top 300 raw cancer rates in red. Highlight the bottom 300 raw cancer rates in blue. Finally, on the same plot again, scatter plot the posterior mean cancer rate estimates (pct mortality) vs the county population size, highlight these in green. \n",
    "\n",
    "(**Note:** This is the plot (without the corrected green estimates) shown in the lecture notes for this dataset. We have provided the code to produce this plot, which you are free to use or to ignore.)\n",
    "\n",
    "\n",
    "(3) Using the scatter plot, explain why using the posterior means (from our model) to estimate cancer rates is preferable to studying the raw rates themselves.\n",
    "\n",
    "(**Hint:** You might find it helpful to review the in-class discussion on this dataset. You might also find it helpful to follow the Rat Tumor Baysian model example.)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# data_df is the dataframe of your data\n",
    "# estimates is a numpy array of cancer rate estimates, one for each county\n",
    "def scatter_plot_cancer_rates(data_df, estimates):\n",
    "    ax = data_df.plot(kind='scatter', x=\"pop\",y=\"pct_mortality\", alpha=0.05, color=\"grey\", figsize=(10,10))\n",
    "    # NOTE:if you have an older pandas version you should use \n",
    "    # \"data_df.sort\" instead of \"data_df.sort_values\"\n",
    "    bot_kcancer_counties = data_df.sort_values(by='pct_mortality',ascending=True)[:300]\n",
    "    top_kcancer_counties = data_df.sort_values(by='pct_mortality',ascending=False)[:300]\n",
    "    top_kcancer_counties.plot(kind='scatter',x=\"pop\",y=\"pct_mortality\",alpha=0.07, color=\"blue\", ax=ax, logx=True)\n",
    "    bot_kcancer_counties.plot(kind='scatter',x=\"pop\",y=\"pct_mortality\",alpha=0.07, color=\"red\", ax=ax, logx=True)\n",
    "    ax.plot(data_df['pop'], 5 * estimates, '.', alpha=0.1, color=\"green\")\n",
    "    ax.set_ylim([-0.0001, 0.0003])\n",
    "    ax.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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WiOaWrtvI5cob06EOwmHXUOen02WkUkbrfNu2e1bibk6zumBZAlIpA0BnaxZR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rOf7LPpFlMnms3mXfdfLi/zSx/9Jfr/p88zvWfoDXqYosnhrcN3VB1FUeT40nFEXaTn9vA9n6Ew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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11450c7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot_cancer_rates(cancer_data, np.array(thetas))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explain why using the posterior means (from our model) to estimate cancer rates is preferable to studying the raw rates themselves\n",
    "\n",
    "The raw cancer mortality rates are skewed by the population size of the county. For counties with very small populations, even small numbers of cancer deaths can result in the mortality rate being very large. It therefore does not provide a useful metric for comparing mortality rates between counties. \n",
    "\n",
    "When the mortatlity rates are assumed to come from a common prior gamma distribution with the empirically estimated parameters, there is a pooling effect where all the mortality rate are pushed towards the group mean (~0.000005) and there are fewer extreme values. The population size has a smaller effect on the percentage mortality. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Part B: Full Bayes\n",
    "Rather than estimating the hyperparameters $\\alpha, \\beta$ from the data, in a full Bayesian model we would put additional priors on quantities of which we are uncertain. That is, we can model the kidney cancer rates using a *hierarchical model*.\n",
    "\\begin{aligned}\n",
    "y_j &\\sim Poisson(5 \\cdot n_j \\cdot \\theta_j), \\quad j = 1, \\ldots, N\\\\\n",
    "\\theta_j &\\sim Gamma(\\alpha, \\beta), \\quad j = 1, \\ldots, N\\\\\n",
    "\\alpha &\\sim Gamma(a, b)\\\\\n",
    "\\beta &\\sim Gamma(c, d)\n",
    "\\end{aligned}\n",
    "where $a, b, c, d$ are hyperparameters. \n",
    "\n",
    "\n",
    "(1) Analytically derive the full conditional, up constants that are inconsequential for sampling, for each variable in the model. \n",
    "  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Start with the joint and then derive the individual conditionals \n",
    "\\begin{aligned}\n",
    "p(\\theta_j, y_j, \\mu, \\sigma,\\alpha, \\beta, a,b,c,d) =  p(y_j|\\theta_j)*p(\\theta_j|\\alpha, \\beta)*  p(\\alpha|a,b)*p(\\beta|c,d)*p(a)*p(b)*p(c)*p(d)\n",
    "\\end{aligned}\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j,  \\mu, \\sigma) = p(y_j|\\theta_j)*p(\\theta_j|\\alpha, \\beta) \\\\\n",
    "\\end{aligned}\n",
    "\n",
    "We know that the prior is modelled with a Gamma function and the likelihood with a poission distribution, therefore by conjugacy of the Poission-Gamma model the posterior for $\\theta$ is a Gamma function as well. We can prove this as follows:\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j, \\mu, \\sigma) \\propto \\left(\\frac{{5n_j\\theta_j}^y_j e^{-5n_j\\theta_j}}{y_j!}\\right)* \\left(\\frac{{\\beta}^\\alpha}{\\Gamma(a)}\\right)\\theta_j^{\\alpha -1}e^{-\\beta\\theta_j}\\\\\n",
    "\\end{aligned}\n",
    "\n",
    "Grouping similar terms together:\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j, \\mu, \\sigma) \\propto \\theta_j^{y_j+\\alpha -1} e^{-(5n_j + \\beta)\\theta_j}\\\\\n",
    "\\end{aligned}\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j, \\mu, \\sigma) \\propto \\theta_j^{y_j+\\alpha -1} e^{-(5n_j + \\beta)\\theta_j}\\\\\n",
    "\\end{aligned}\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j, \\mu, \\sigma) \\propto \\left(\\frac{(\\beta+5n_j)\\theta_j^{y_j+\\alpha -1} e^{-(5n_j + \\beta)\\theta_j}}{\\Gamma(\\alpha + y_i)}\\right)\\\\\n",
    "\\end{aligned}\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j, \\alpha, \\beta) \\propto Gamma\\left(\\theta_j; y_j + \\alpha, \\beta + 5n_j\\right)\\\\\n",
    "\\end{aligned}\n",
    "\n",
    "For $\\alpha$ and $\\beta$ the conditional distribution can be derived as follows:\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\alpha, \\beta|\\theta_j, y_j, \\sigma^2) =  \\prod_j p(\\theta_j|\\alpha, \\beta)*p(\\alpha| a,b)*p(\\beta| c,d)\n",
    "\\end{aligned}\n",
    "\n",
    "Substituting in gamma pdfs:\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\alpha, \\beta|\\theta_j, y_j, \\sigma^2) =  \\prod_j \\left(\\frac{{\\beta}^\\alpha}{\\Gamma(\\alpha)}\\theta_j^{a-1}e^{-\\theta_j \\beta}\\right) \\left(\\frac{{b}^a}{\\Gamma(a)}\\alpha^{a-1}e^{-\\alpha b}\\right) \\left(\\frac{{d}^c}{\\Gamma(c)}\\beta^{c-1}e^{-\\beta d}\\right)\n",
    "\\end{aligned}\n",
    "\n",
    "This can be rearranged to the form:\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\alpha, \\beta|\\theta_j, y_j, \\sigma^2) =  \\left(\\frac{{b}^a}{\\Gamma(a)}\\alpha^{a-1}e^{-\\alpha b}\\right) \\left(\\frac{{d}^c}{\\Gamma(c)}\\beta^{c-1}e^{-\\beta d}\\right) \\frac{{\\beta}^{N\\alpha}}{\\Gamma(\\alpha)^N} \\prod_j \\left(\\theta_j^{a-1}e^{-\\theta_j \\beta}\\right)\n",
    "\\end{aligned}\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\alpha, \\beta|\\theta_j, y_j, \\sigma^2) =  \\left(\\frac{{b}^a}{\\Gamma(a)}\\alpha^{a-1}e^{-\\alpha b}\\right) \\left(\\frac{{d}^c}{\\Gamma(c)}\\beta^{c-1}e^{-\\beta d}\\right) \\beta^{N\\alpha}\\Gamma(\\alpha)^{-N} \\prod_j \\left(\\theta_j^{a-1}\\right)e^{-\\beta\\sum_j\\theta_j}\n",
    "\\end{aligned}\n",
    "\n",
    "\\begin{aligned}\n",
    "p(\\alpha, \\beta | y_j, \\theta_j, \\sigma^2) &\\propto \\beta^{N\\alpha}\\Gamma(\\alpha)^{-N}\\prod_j\\theta_j^{\\alpha} \\exp\\left\\{ - \\beta\\sum_j \\theta_j \\right\\} * Gamma\\left(\\alpha; a, b \\right) * Gamma\\left(\\beta; c, d \\right) \\\\\n",
    "\\end{aligned}\n",
    "\n",
    "The term: \n",
    "\n",
    "$$\\beta^{N\\alpha}\\Gamma(\\alpha)^{-N}\\prod_j\\theta_j^{\\alpha} \\exp\\left\\{ - \\beta\\sum_j \\theta_j \\right\\}$$\n",
    "\n",
    "is the product of gamma pdfs evaluated at each value of theta. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A possible set of correct final forms of your conditionals looks like the following:\n",
    "      \n",
    "\\begin{aligned}\n",
    "p(\\theta_j | y_j, \\mu, \\sigma) &\\propto Gamma\\left(\\theta_j; y_j + \\alpha, \\beta + 5n_j\\right)\\\\\n",
    "p(\\alpha, \\beta | y_j, \\theta_j, \\sigma^2) &\\propto \\beta^{N\\alpha}\\Gamma(\\alpha)^{-N} \\prod_j\\theta_j^{\\alpha} \\exp\\left\\{ - \\beta\\sum_j \\theta_j \\right\\} * Gamma\\left(\\alpha; a, b \\right) * Gamma\\left(\\beta; c, d \\right) \\\\\n",
    "\\end{aligned}\n",
    "\n",
    "\n",
    "\n",
    "(2) Implement a Metropolis-Hastings-in-Gibbs sampler (like in rat tumors) to produce sets of theta-values, $\\{ \\theta_j: j = 1, \\ldots, N\\}$. Note that for updating some variables, you may need to use a Metropolis-Hastings step (see Rat Tumor example). \n",
    "\n",
    "  We suggest the following settings for your MH-in-Gibbs sampler, but please feel free to use your own:\n",
    "  \n",
    "  - Gibbs sweeps: 100,000\n",
    "  - $a = 9, b = 6, c = 9, d = 0.00001$\n",
    "  - Starting points: $\\alpha_0 = \\alpha_{\\text{emperical bayes}}, \\beta_0 = \\beta_{\\text{emperical bayes}}$\n",
    "  - proposal distribution: $\\mathcal{N}\\left([\\alpha, \\beta], \\left[\\begin{array}{cc} 0.1 & 0 \\\\ 0 & 1000\\end{array}\\right]\\right)$\n",
    "  - burn in: 10%\n",
    "  - thinning: 10\n",
    "  \n",
    "  We do not guarantee convergence after 100,000 sets of samples under these conditions. In fact, ***convergence in a untweaked sampler maybe unlikely after only 100,000 Gibbs sweeps***. \n",
    "\n",
    "  You are responsible for performing your own convergence tests and diagnostics.\n",
    "\n",
    "  **Note:** to sanity check your implementation, you may wish to implement this model in PyMC3 and compare your results. Note that because you model is hand tuned to deal with the conditionals and to sample straight away from the Gamma's, it will likely run faster)\n",
    "  \n",
    "  \n",
    "\n",
    "- **Extra Credit:** Tweak the settings in your sampler (including number of sweeps) in order to achieve convergence. For example, do you need to sample $\\alpha$ and $\\beta$ jointly? Can sampling them individually speed up your sampler? Only do this after you have a complete homework. It is a rabbit hole.\n",
    "\n",
    "\n",
    "\n",
    "(3) Using your samples, produce a pct mortality vs county population scatter plot exactly as in Part A."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "a = 9\n",
    "b = 6\n",
    "c = 9\n",
    "d = 0.00001\n",
    "\n",
    "def proposal(alp,bet):\n",
    "    cov = [[0.001, 0], [0, 1000]]\n",
    "    return np.random.multivariate_normal([alp,bet], cov)\n",
    "\n",
    "prior_a = stats.gamma(a,scale=1.0/b)\n",
    "\n",
    "prior_b = stats.gamma(c,scale=1.0/d)\n",
    "\n",
    "likelihood_theta = lambda alp, bet: stats.gamma(alp,scale=1.0/bet)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "numthetas=cancer_data.shape[0]\n",
    "\n",
    "# sampling from conditional posterior for the theta\n",
    "draw_thetas = lambda a_,b_: stats.gamma.rvs(a_+cancer_data['dc'],scale=1.0/(b_+5*cancer_data['pop']), size=numthetas)\n",
    "\n",
    "# conditional posterior (pdf) for alpha beta\n",
    "def log_cond_alpha_beta(alp,bet, thetas):\n",
    "    return np.sum(np.log(likelihood_theta(alp, bet).pdf(thetas))) + np.log(prior_a.pdf(alp)) + np.log(prior_b.pdf(bet))\n",
    "\n",
    "# using the above pdfs we draw for alpha and beta in MH fashion\n",
    "def draw_alpha_beta(alp,bet,thetas,proposal, accepts):\n",
    "    alp_star, bet_star = proposal(alp, bet)  # propose a new alpha and beta\n",
    "    num = log_cond_alpha_beta(alp_star,bet_star, thetas) \n",
    "    den = log_cond_alpha_beta(alp,bet, thetas)\n",
    "    R=np.random.rand()\n",
    "    if (np.log(R) <= num - den): \n",
    "        accepted=1\n",
    "    else:\n",
    "        accepted=0\n",
    "    accepts['alpha_beta'] = accepts['alpha_beta'] + accepted\n",
    "    if accepted:\n",
    "        return alp_star, bet_star\n",
    "    else:\n",
    "        return alp, bet"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "totaltraces=100000\n",
    "burnin=0.1*totaltraces\n",
    "\n",
    "alphas=np.empty(totaltraces)\n",
    "betas=np.empty(totaltraces)\n",
    "thetas=np.empty((totaltraces, numthetas))\n",
    "\n",
    "# start positions\n",
    "alphas[0]=alpha_emp\n",
    "betas[0]=beta_emp\n",
    "thetas[0,:] = 0.0001\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10000\n",
      "20000\n",
      "30000\n",
      "40000\n",
      "50000\n",
      "60000\n",
      "70000\n",
      "80000\n",
      "90000\n",
      "('sampling took: ', 525.695029, ' seconds.')\n"
     ]
    }
   ],
   "source": [
    "start = time.clock()\n",
    "accepteds={'alpha_beta':0}\n",
    "for m in np.arange(1,totaltraces):\n",
    "    if (m%10000 == 0):\n",
    "        print(m)\n",
    "    alphas[m], betas[m] = draw_alpha_beta(alphas[m-1],betas[m-1],thetas[m-1,:], proposal, accepteds)\n",
    "    thetas[m,:] = draw_thetas(alphas[m],betas[m])\n",
    "\n",
    "print(\"sampling took: \", time.clock()-start, \" seconds.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61603"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accepteds['alpha_beta']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "accepteds['alpha_beta']/totaltraces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "((9900, 3113), (9900,))\n"
     ]
    }
   ],
   "source": [
    "#remove burnin samples and thin\n",
    "thin=10\n",
    "burnin=1000\n",
    "alphatrace=alphas[burnin+1:totaltraces:thin]\n",
    "betatrace=betas[burnin+1:totaltraces:thin]\n",
    "thetastrace=thetas[burnin+1:totaltraces:thin,:]\n",
    "print(thetastrace.shape, alphatrace.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1ac801450>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PMpkMLi4u8PX1xccff4yCggJ8+OGHsLa2xvz58xEdHY1+/fpBLpejc+fOCAsL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\nAAAYRMAGAAAADPo/tV8nZBp7nXcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ac5cca50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[12,6])\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(alphas)\n",
    "plt.ylabel('alpha')\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(betas)\n",
    "plt.ylabel('beta')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The alpha and beta values do not appear to have converged within 100000 iterations but due to time constraints, the sampler was only run for this duration. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ad0cf810>]"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lv6ezi3DyvDxP7zQOmfXUP8avlGQ/Srft2+Ug9ymrcOeG8yGi8wZ356m49TGn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\nIsUwCBERkWIYhIiISDEMQkREpJj/B1jZWacoz29CAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1accca110>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(thetastrace[:, 100])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def corrplot(trace, maxlags=50):\n",
    "    plt.acorr(trace-np.mean(trace),  normed=True, maxlags=maxlags);\n",
    "    plt.xlim([0, maxlags])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ifa7w2Wef6Y477lBJSYkuXbrE2lzl3nvvVSgUUigU0rZt21ytz6hGw+/3D3z6MBaL8d+M\nXCUvL0+//vqrpL8+pXn152BuNefPn9fq1atVUlKiefPmsTZXOXr0qLKzs7V161Z1dXXp7Nmzklgf\nSdqzZ48OHTqkXbt2qa2tTadPn5bE2lx25MgR9ff3S5Kys7MHPqhtWZ9RPeU2Go0qFAopNzdXxcXF\nevrpp0frodPe4sWL1dTUpPfff18///yzYrGY1q1bp9zc3FSPljKvvfaajh8/Lr/fr8zMTN1zzz2s\nzRW+++47bdmyRZMnT9Ztt92myZMnsz5X2b17t8aOHavTp0+zNlc4fPiwmpqalJeXp2nTpqm/v9+8\nPnxOAwBgxim3AAAzogEAMCMaAAAzogEAMCMaAAAzogEAMCMaAACz/wJ+PCRgDrFP7QAAAABJRU5E\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1149efe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "corrplot(thetastrace[:, 100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After burnin and thinning therer is no autocorrelation in the trace of the thetas. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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0pS/h4sWLzjEPP/ww7r///mm9NaKZ0bl9mCCs7Wj7MMMwcO1aDs2mALfbxvHjCci7iBTH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2AAAg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1ad12b5d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "scatter_plot_cancer_rates(cancer_data, np.mean(thetastrace, axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "With a full bayesian model, there are hyperpriors on  alpha and beta which themselves are uncertain and have variability. \n",
    "\n",
    "Compared to the purely empirical Bayes, with the fully Bayesian model, the perecent mortality has slightly more variation with population and there is a larger distribution of mortality rates about the group mean. \n",
    "\n",
    "Overall, the result of the model is to reduce the extreme values of of percentage mortality caused by having either very small or very large population sizes. There is a smaller overall range in the mortality rates comapred to the raw estimates of mortality based purely on the counts of incidence and population. "
   ]
  }
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