Hierarchical Bayes With Gibbs Sampling.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "ename": "ERROR",
     "evalue": "Error in library(coda): there is no package called ‘coda’\n",
     "output_type": "error",
     "traceback": [
      "Error in library(coda): there is no package called ‘coda’\nTraceback:\n",
      "1. library(coda)"
     ]
    }
   ],
   "source": [
    "library(tidyr)\n",
    "library (coda)\n",
    "library(car)\n",
    "library(reshape2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "       NS1      NS2      NS3      NS4      NS5      NS6      NS7      NS8\n",
      "1 5.743003 5.869297 5.545177 5.560682 5.318120 6.380123 5.730100 5.497168\n",
      "2 5.605802 5.846439 5.648974 5.683580 5.605802 5.743003 5.897154 5.480639\n",
      "3 5.857933 5.950643 5.768321 5.723585 5.521461 5.655992 5.924256 5.627621\n",
      "4 5.655992 5.834811 5.613128 5.676754 5.560682 5.736572 5.627621 5.568345\n",
      "5 5.590987 5.710427 5.780744 5.575949 5.749393 6.656727 5.902633 5.583496\n",
      "6 5.793014 5.743003 5.590987 5.669881 5.730100 5.897154 5.736572 5.537334\n",
      "       NS9     NS10     NS11\n",
      "1 5.446737 5.762051 5.480639\n",
      "2 5.568345 5.780744 5.676754\n",
      "3 5.438079 5.641907 5.857933\n",
      "4 5.402677 5.897154 5.537334\n",
      "5 5.347108 5.655992 5.981414\n",
      "6 5.648974 5.834811 6.063785\n"
     ]
    }
   ],
   "source": [
    "#raw data\n",
    "header <- sprintf(\"NS%d\",seq(1:11))\n",
    "df <- log(t(read.csv('http://www.stat.columbia.edu/~gelman/book/data/schiz.asc',sep = ' ',\n",
    "                     skip=4, nrows=11, header=F)))\n",
    "colnames(df) <- header; rownames(df) <- c(1:30)\n",
    "yBar <- colMeans(df)\n",
    "yVar <- apply(df,2,var)\n",
    "ySD <- sqrt(yVar)\n",
    "n <- 30\n",
    "s <- 11\n",
    "ySS <- yVar*(n-1)+n*yBar^2   # sum of squares\n",
    "print(head(df))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "#weak priors (given)\n",
    "mu0 <- log(250)   # typical reaction time to visual stimulus is 0.25 sec\n",
    "sigma0 <- .22\n",
    "tau.sh.0 <- sig.sh.0 <- 1/2    # Use small virtual sample size (Shape)\n",
    "tau.sc.0 <- sig.sc.0 <- 50     # prior scale gives expected precision of 25 (Scale)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "sim <- 5000\n",
    "theta.mcmc <- matrix(nrow = sim, ncol = s)\n",
    "theta.mcmc[1,] <- yBar   # initial value for theta\n",
    "mu.mcmc <- mean(yBar)    # initial value for mu\n",
    "tau.mcmc <- sd(yBar)     # initial value for tau\n",
    "sig.mcmc <- mean(ySD)    # initial value for sigma"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gibbs Sampler with Semi Conjugate prior"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#MCMC algo\n",
    "for (k in 2:sim) {\n",
    "  mu1 <- (mu0/sigma0^2+sum(theta.mcmc[k-1,])/tau.mcmc[k-1]^2)/(1/sigma0^2+s/tau.mcmc[k-1]^2)\n",
    "  sigma1 <- (1/sigma0^2+s/tau.mcmc[k-1]^2)^(-.5)\n",
    "  mu.mcmc[k] <- rnorm(1,mu1, sigma1)    # sample new mu\n",
    "  \n",
    "  tau.sh.1 <- tau.sh.0 + 0.5*s  # this is the same every iteration\n",
    "  tau.sc.1 <- (1/tau.sc.0 + 0.5*sum((theta.mcmc[k-1,]-mu.mcmc[k])^2))^-1\n",
    "  tau.mcmc[k] <- rgamma(1,shape=tau.sh.1,scale=tau.sc.1)^(-.5)\n",
    "  \n",
    "  sig.sh.1 = sig.sh.0 + 0.5*s*n  # this is the same every iteration\n",
    "  # In the formula below, sum(ySS - n*yBar^2 + n*(theta.mcmc[k-1,]-yBar)^2) is\n",
    "  # equal to the sum of squared deviatons of each subject's observations and\n",
    "  # that subject's theta value. \n",
    "  sig.sc.1 = (1/sig.sc.0 + 0.5*sum(ySS - n*yBar^2 + n*(theta.mcmc[k-1,]-yBar)^2))^-1\n",
    "  sig.mcmc[k] = rgamma(1,shape=sig.sh.1,scale=sig.sc.1)^(-1/2)\n",
    "  \n",
    "  mu2 <- (mu.mcmc[k]/tau.mcmc[k]^2+yBar*n/sig.mcmc[k]^2)/(1/tau.mcmc[k]^2+n/sig.mcmc[k]^2) # vector of posterior means\n",
    "  tau2 <- (1/tau.mcmc[k]^2+n/sig.mcmc[k]^2)^(-1/2)  # vector of posterior SDs\n",
    "  theta.mcmc[k,] = rnorm(s,mu2,tau2)\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              2.5%     97.5%\n",
      "theta_1  5.6751084 5.7860260\n",
      "theta_2  5.8297843 5.9445431\n",
      "theta_3  5.6547643 5.7651808\n",
      "theta_4  5.6504224 5.7617949\n",
      "theta_5  5.5211609 5.6326730\n",
      "theta_6  5.7373484 5.8504667\n",
      "theta_7  5.8009607 5.9152744\n",
      "theta_8  5.5324073 5.6445497\n",
      "theta_9  5.4956760 5.6063450\n",
      "theta_10 5.7179365 5.8307824\n",
      "theta_11 5.6603075 5.7716979\n",
      "mu       5.6243562 5.7911852\n",
      "tau      0.0860066 0.2116579\n",
      "sig      0.1482716 0.1730829\n"
     ]
    }
   ],
   "source": [
    "#Generate Credible Intervals\n",
    "theta.hat <- colMeans(theta.mcmc)\n",
    "th025<-th975<-NULL\n",
    "for (i in 1:s) {\n",
    "  th025[i] = quantile(theta.mcmc[,i],0.025)\n",
    "  th975[i] = quantile(theta.mcmc[,i],0.975)\n",
    "}\n",
    "\n",
    "# Table of credible intervals\n",
    "results<-as.data.frame(th025)\n",
    "results$th975<-th975\n",
    "colnames(results)<-c(\"2.5%\",\"97.5%\")\n",
    "rownames(results) <- paste(\"theta\",c(1:11),sep=\"_\")\n",
    "mu025<-quantile(mu.mcmc,0.025)\n",
    "mu975<-quantile(mu.mcmc,0.975)\n",
    "tau025<-quantile(tau.mcmc,0.025)\n",
    "tau975<-quantile(tau.mcmc,0.975)\n",
    "sig025<-quantile(sig.mcmc,0.025)\n",
    "sig975<-quantile(sig.mcmc,0.975)\n",
    "\n",
    "results[12,]<-c(mu025,mu975)\n",
    "results[13,]<-c(tau025,tau975)\n",
    "results[14,]<-c(sig025,sig975)\n",
    "rownames(results)[12:14] = c(\"mu\",\"tau\",\"sig\")\n",
    "print(results)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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V5MbyPVetM9iJRVbvstjMg0aZj9rdZf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\nRK5CYII=",
      "text/plain": [
       "Plot with title “Means for 11 Non-schizophrenic Subjects”"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Caterpillar plot for Theta\n",
    "plot(yBar,theta.hat,main = \"Means for 11 Non-schizophrenic Subjects\",\n",
    "     ylab=\"Posterior Interval\",xlab=\"Sample Mean\", ylim = c(5.5,5.95))\n",
    "lines(yBar,yBar)\n",
    "for (i in 1:s) {\n",
    "  lines(c(yBar[i],yBar[i]),c(results$`2.5%`[i],results$`97.5%`[i]))\n",
    "}\n",
    "lines(1:11,array(mean(theta.hat),11))  # Plotting this line shows clearly that means are different\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "R",
   "language": "R",
   "name": "ir"
  },
  "language_info": {
   "codemirror_mode": "r",
   "file_extension": ".r",
   "mimetype": "text/x-r-source",
   "name": "R",
   "pygments_lexer": "r",
   "version": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}