lab6.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "collect-panic",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: coda\n",
      "\n",
      "Linked to JAGS 4.3.0\n",
      "\n",
      "Loaded modules: basemod,bugs\n",
      "\n"
     ]
    }
   ],
   "source": [
    "library(rjags)\n",
    "\n",
    "### 1\n",
    "\n",
    "#Binomial data with Beta prior\n",
    "\n",
    "#  beta(p,q):  p=alpha, q= beta\n",
    "\n",
    "bb.sum<-function(y,z,alfa,beta)\n",
    "{\n",
    "  # binomial - beta conjugate pairs\n",
    "  #bb.sum(data, maximum value of the observation, prior parameter_a,prior parameter_b)\n",
    "  #The function gives the parameters of the posterior distribution (Beta)  \n",
    "  \n",
    "  #bb.sum(data,havainnon maksimiarvo,priorialfa,prioribeta)\n",
    "  #Funktio laskee posteriorijakauman parametrit (betajakauma)\n",
    "  #sekä keskiarvon, varianssin ja moodin.\n",
    "  #Binomiotos, priori betajakauma.\n",
    "  n<-length(y)\n",
    "  s<-sum(y)\n",
    "  m<-n*z\n",
    "  if(z>=max(y) & alfa>0 & beta>0 & min(y)>=0 & max(abs(y-round(y,digits=0)))==0\n",
    "     & z-round(z,digits=0)==0)\n",
    "  {\n",
    "    alfa1<-alfa+s\n",
    "    beta1<-beta+m-s\n",
    "    ka<-alfa1/(alfa1+beta1)\n",
    "    var<-alfa1*beta1/(alfa1+beta1)**2/(alfa1+beta1+1)\n",
    "    mo<-min(1,max(0,(alfa1-1)/(alfa1+beta1-2)))\n",
    "    list(alfa1=alfa1,beta1=beta1,Mean=ka,Var=var,Mode=mo)\n",
    "  }\n",
    "  else\n",
    "    (\"Datan arvojen pitää olla ei-negatiivisia kokonaislukuja ja pienempiä tai yhtä suuria kuin \")\n",
    "  #maksimiarvo, alfan ja betan pitää olla positiivisia lukuja\")\n",
    "}\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "governmental-drove",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$alfa1</dt>\n",
       "\t\t<dd>13</dd>\n",
       "\t<dt>$beta1</dt>\n",
       "\t\t<dd>9</dd>\n",
       "\t<dt>$Mean</dt>\n",
       "\t\t<dd>0.590909090909091</dd>\n",
       "\t<dt>$Var</dt>\n",
       "\t\t<dd>0.0105102407473949</dd>\n",
       "\t<dt>$Mode</dt>\n",
       "\t\t<dd>0.6</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$alfa1] 13\n",
       "\\item[\\$beta1] 9\n",
       "\\item[\\$Mean] 0.590909090909091\n",
       "\\item[\\$Var] 0.0105102407473949\n",
       "\\item[\\$Mode] 0.6\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$alfa1\n",
       ":   13\n",
       "$beta1\n",
       ":   9\n",
       "$Mean\n",
       ":   0.590909090909091\n",
       "$Var\n",
       ":   0.0105102407473949\n",
       "$Mode\n",
       ":   0.6\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$alfa1\n",
       "[1] 13\n",
       "\n",
       "$beta1\n",
       "[1] 9\n",
       "\n",
       "$Mean\n",
       "[1] 0.5909091\n",
       "\n",
       "$Var\n",
       "[1] 0.01051024\n",
       "\n",
       "$Mode\n",
       "[1] 0.6\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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iJ5oCxPZdMRQZE8UJansumIoEgeKMtT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\nHxtuYvAnv3kpAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Posterior (black), prior (red)\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### a)\n",
    "\n",
    "# x=12, n=20\n",
    "grave.dat <- c(rep(1, 12), rep(0, 8))\n",
    "\n",
    "# prior: Unif(0, 1)=Beta(1, 1)\n",
    "bb.sum(grave.dat, 1, 1, 1)\n",
    "\n",
    "# posterior inference for theta\n",
    "\n",
    "# $alfa1\n",
    "# [1] 13\n",
    "# \n",
    "# $beta1\n",
    "# [1] 9\n",
    "# \n",
    "# $Mean\n",
    "# [1] 0.5909091\n",
    "# \n",
    "# $Var\n",
    "# [1] 0.01051024\n",
    "# \n",
    "# $Mode\n",
    "# [1] 0.6\n",
    "\n",
    "# posterior distribution is Beta(13, 9)\n",
    "\n",
    "theta <- seq(0, 1, 0.01)\n",
    "th.pr <- dbeta(theta, 1, 1) # prior density\n",
    "th.ps <- dbeta(theta, 13, 9) # posterior density\n",
    "\n",
    "\n",
    "# overlaid plots of prior and posterior distributions\n",
    "plot(theta, th.ps, type = 'l', col='1', main=\"Posterior (black), prior (red)\", ylab=\"density\", xlab = \"theta\")\n",
    "lines(theta, th.pr, lty=2, col='2')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "tough-campus",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$alfa1</dt>\n",
       "\t\t<dd>22</dd>\n",
       "\t<dt>$beta1</dt>\n",
       "\t\t<dd>10</dd>\n",
       "\t<dt>$Mean</dt>\n",
       "\t\t<dd>0.6875</dd>\n",
       "\t<dt>$Var</dt>\n",
       "\t\t<dd>0.00651041666666667</dd>\n",
       "\t<dt>$Mode</dt>\n",
       "\t\t<dd>0.7</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$alfa1] 22\n",
       "\\item[\\$beta1] 10\n",
       "\\item[\\$Mean] 0.6875\n",
       "\\item[\\$Var] 0.00651041666666667\n",
       "\\item[\\$Mode] 0.7\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$alfa1\n",
       ":   22\n",
       "$beta1\n",
       ":   10\n",
       "$Mean\n",
       ":   0.6875\n",
       "$Var\n",
       ":   0.00651041666666667\n",
       "$Mode\n",
       ":   0.7\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$alfa1\n",
       "[1] 22\n",
       "\n",
       "$beta1\n",
       "[1] 10\n",
       "\n",
       "$Mean\n",
       "[1] 0.6875\n",
       "\n",
       "$Var\n",
       "[1] 0.006510417\n",
       "\n",
       "$Mode\n",
       "[1] 0.7\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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xBSVuZcHv3L4KTuiZCwxqyM3K+GImK7EyFl5Ne2yyyims5dVudaofbrtC7HjEof\nOxQhpeTn1VGeGRESlpjK6F9OdxdGyOxRXCNlYPJolHVENZFdipCS9zWjzI9Eb3PfMzWFkBI3\ntpPUAVFRh9OSCCl+XzNCn/1BiZBSZczH3tGcypHROInzuy9L9vIQhUPEzwwi4kD0m6uUvIZ0\n+dvVs787XFwNkYtXQ+0RKPfb2wu4ScljSPeNeds6GSILzZHoHzcTVhseyedScY10MMXpWn90\nOxfm4GKItD3m/3nkISBLK1tSEVJhrq+Pr6ZwMUQCOqdqz3A6AUHO2DXmLypC6q318CmYrm/L\nGN3Bkvrvry0AUWYZFSFxREK6/F4jnW/1R1wjITU+b39vO8fIzd3JEEAYfl9HOtSvIxW7P15H\nQlp4ZwMggJAAAYQECCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAA\nQgIEEBIggJAAAUpDAiKzYi+XDyeKsRmf8UXHJyTGZ3xtC4tobMZnfEJifMbXNj4hMT7ja1tY\nRGMzPuMTEuMzvrbxCYnxGV/bwiIam/EZn5AYn/G1jU9IjM/42hYW0diMz/jJhAQkg5AAAYQE\nCCAkQAAhAQIICRBASIAAQgIEEBIggJAAAYQECCAkQAAhAQIICRBASIAAQgIEeA/pUJjicJ/6\ngufxj5uw4z9cPM7CYPzr3pj9Ldj4d8/z/5jw/tYWGt93SNv6L/vfTHzB8/iH+guFr5kce7r3\nwt8sDMY/h33+t6IZ31/J1/6/NSG1/3kO6WKKa3ktzOXrFzyPfzX7e/VLah9o/MpuzT8jIjV+\n8fjCfWcOgcbf1yMffG3/shq8u7XF9j/PIR3M+fH/J/P39Quex981G8DXrjz2dE+r/j0eofFP\n9Y58N0Wg8Y3f7f/4lbntjSW2/3kOaWeqY/jV7L5+wfP4LV8TOTL+7WNq/Y6/N1dfY4+O357V\n+gq5fPze6G1tsf3Pc0iDX0CefyN9Ge5utsHG35qbv5AG429M+VfUp7dhxv9rT+08nZGU14/J\nF9v/CKlyrA/wQcb/Myd/JzZj239XX+yHGr88VncbiqOn8T8GJySx8Wu3wtOZ5XD8+qQiaEjV\nzYa9ryPC2C+Siq8D0sfghCQ2fuVeeDqxGzu1qm48Bw2puka6+Xr9YTD+sTq1e4Ts8ZCUREjF\n53oPvuB5/MrW26tYg/H39Tmlv5AGz9/zL7LB+BtTXZ7d/b2Q+PFcxfa/IHftbp937W5+79r1\nhrtttv5eDfwc3+YfpJcY3/ft/8H4vm9/f44ltv95Dumv/g18fr/+N/iC5/EfH3s7rxsZ33dI\nX6E58OQAAAJ4SURBVLb/zddGGIzfHBG8vY5V6W1rsf0v93c2eNuFvoxfC/jOhsfV0b26RjkF\nGv9gqve5HXz9Iq0k8c6Gxzlxpd55myfU+UKI8fd+jwjD59//yP/4f2G3f/teN5+/zZ5bW3b/\n8x1S82bfZmjz8YUQ43s+tRo+//5HAcY/b0Nu//bd197GLz9Dktr/fIcEJImQAAGEBAggJEAA\nIQECCAkQQEiAAEICBBASIICQAAGEBAggJEAAIQECCAkQQEiAAEICBBASIICQAAGEBAggJEAA\nIQECCAkQQEiAAEICBBASIICQAAGEBAggJEAAIQECCAkQQEiAAEICBBASIICQ4lD9k8Ff/mW/\ns981wShCisKmnqfRkDZMoQbMQhTM95A8/gO0+I5ZiAIhaccsxKD9d9cf/zuY4q/+0nFjiuP7\nW+V5Zzz/6+DoIqQYvELaVR9U/dQfmO3rW3/1fw0lhUJIUXie2m3v5dFsHsef6qP71pzf3zqV\n5YnTvGDY8lF41nJpP96Z++Oju9n1r5EIKRi2fBS6Nxuak7zWO57b+W9LSMGw5aPwO6Tt83ME\nwZaPwjCkj2/tzeZ4vhFSMGz5KHyGtDPnkW8RUjhs+SgYcyu7zZxMcS3LY3OzofnWpbxyjRQO\nWz4KG2OK3sGnuSQqbs9vHdprpkvgFc0WIUXhsvkIqXpng9nfXt96XCSZ7eVcHaIQAiEBAggJ\nEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJ\nEEBIgABCAgQQEiCAkAABhAQIICRAACEBAggJEEBIgABCAgQQEiCAkAABhAQI+A8ECFi4zZP/\njwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Posterior (black), prior (red)\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### b)\n",
    "\n",
    "# prior: Beta(10, 2)\n",
    "bb.sum(grave.dat, 1, 10, 2)\n",
    "\n",
    "# posterior inference for theta\n",
    "\n",
    "# $alfa1\n",
    "# [1] 22\n",
    "# \n",
    "# $beta1\n",
    "# [1] 10\n",
    "# \n",
    "# $Mean\n",
    "# [1] 0.6875\n",
    "# \n",
    "# $Var\n",
    "# [1] 0.006510417\n",
    "# \n",
    "# $Mode\n",
    "# [1] 0.7\n",
    "\n",
    "# posterior distribution is Beta(22, 10)\n",
    "\n",
    "th.pr <- dbeta(theta, 10, 2) # prior density\n",
    "th.ps <- dbeta(theta, 22, 10) # posterior density\n",
    "\n",
    "\n",
    "# overlaid plots of prior and posterior distributions\n",
    "plot(theta, th.ps, type = 'l', col='1', main=\"Posterior (black), prior (red)\", ylab=\"density\", xlab = \"theta\")\n",
    "lines(theta, th.pr, lty=2, col='2')\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "wound-midwest",
   "metadata": {},
   "outputs": [],
   "source": [
    "### c)\n",
    "\n",
    "# In a), a flat non-informative prior Unif(0, 1) is used with equal possibilities for all\n",
    "# values of theta. \n",
    "# \n",
    "# In b) an informative prior Beta(10, 2) which reflects specific information about theta is used.\n",
    "\n",
    "# The overlaid plots of the prior and posterior distributions in a) show that the\n",
    "# non-informative prior has less influence on the resulting posterior which makes the \n",
    "# posterior density to look nothing like the prior density since very little specific information is\n",
    "# known about theta. \n",
    "\n",
    "# The overlaid plots of the prior and posterior distributions in b) show that the \n",
    "# informative prior has more influence on the resulting posterior which makes the \n",
    "# posterior density to look like the prior density since the prior reflects specific \n",
    "# information about theta.\n",
    "\n",
    "# The posterior inference for theta shows that the prior in a) resulted in a smaller posterior mean\n",
    "# than that in b) but with bigger variability.\n",
    "\n",
    "# From the results obtained above it clearly shows that a non-informative prior has less influence on the \n",
    "# posterior with a smaller posterior mean but bigger variability since only a little information is known\n",
    "# about the unknown variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "phantom-floating",
   "metadata": {},
   "outputs": [],
   "source": [
    "### 2)\n",
    "\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    " # likelihood\n",
    " \n",
    " for (i in 1:N){\n",
    " \n",
    "  x[i] ~ dnorm(mu1, psi1)    # psi: precision not the variance\n",
    "  y[i] ~ dnorm(mu2, psi2)\n",
    "  \n",
    " }\n",
    " \n",
    " # prior\n",
    " \n",
    " \n",
    " psi1 ~ dgamma(0.35, 1.01)\n",
    " psi2 ~ dgamma(0.35, 1.01)\n",
    " \n",
    " mu1 ~ dnorm(0, 0.003*psi1)\n",
    " mu2 ~ dnorm(0, 0.003*psi2)\n",
    "\n",
    " tau1 <- 1/psi1\n",
    " tau2 <- 1/psi2\n",
    " delta <- mu1-mu2\n",
    " var.ratio <- tau1/tau2\n",
    " \n",
    "\n",
    "}\",\n",
    "    \n",
    "    file = \"blood.jag\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "fossil-gabriel",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling model graph\n",
      "   Resolving undeclared variables\n",
      "   Allocating nodes\n",
      "Graph information:\n",
      "   Observed stochastic nodes: 30\n",
      "   Unobserved stochastic nodes: 4\n",
      "   Total graph size: 46\n",
      "\n",
      "Initializing model\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 10:10000\n",
       "Thinning interval = 10 \n",
       "Number of chains = 1 \n",
       "Sample size per chain = 1000 \n",
       "\n",
       "1. Empirical mean and standard deviation for each variable,\n",
       "   plus standard error of the mean:\n",
       "\n",
       "               Mean        SD  Naive SE Time-series SE\n",
       "delta     1.925e+01 7.363e+00 2.329e-01      2.329e-01\n",
       "mu1       1.771e+02 5.148e+00 1.628e-01      1.628e-01\n",
       "mu2       1.578e+02 5.167e+00 1.634e-01      1.634e-01\n",
       "psi1      2.572e-03 8.948e-04 2.830e-05      2.685e-05\n",
       "psi2      2.759e-03 9.808e-04 3.102e-05      3.102e-05\n",
       "tau1      4.423e+02 1.762e+02 5.572e+00      5.268e+00\n",
       "tau2      4.156e+02 1.759e+02 5.562e+00      5.562e+00\n",
       "var.ratio 1.211e+00 6.516e-01 2.061e-02      2.061e-02\n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "               2.5%       25%       50%       75%     97.5%\n",
       "delta     4.998e+00 1.406e+01 1.946e+01 2.422e+01 3.290e+01\n",
       "mu1       1.669e+02 1.739e+02 1.770e+02 1.804e+02 1.871e+02\n",
       "mu2       1.478e+02 1.544e+02 1.578e+02 1.612e+02 1.679e+02\n",
       "psi1      1.105e-03 1.923e-03 2.490e-03 3.113e-03 4.537e-03\n",
       "psi2      1.178e-03 2.079e-03 2.632e-03 3.277e-03 5.063e-03\n",
       "tau1      2.204e+02 3.213e+02 4.016e+02 5.200e+02 9.047e+02\n",
       "tau2      1.975e+02 3.052e+02 3.799e+02 4.810e+02 8.486e+02\n",
       "var.ratio 3.835e-01 7.723e-01 1.083e+00 1.450e+00 2.798e+00\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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8hGSvkPZIMhz6n+jA9k5ZNWvRYCcF0g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\nIABEAkCA/wN3SNtzz+S6xgAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Density of psi1\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LJixVwo0pLtEpFOlnD5goqduQU4a/A3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\n",
      "text/plain": [
       "Plot with title \"Density of var.ratio\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### a-b)\n",
    "\n",
    "blood.inits = list(mu1=160.0, mu2=160.0, psi1=1, psi2=1)\n",
    "\n",
    "blood.data = list(x=c(210, 169, 187, 160, 167, 176, 185, 206, 173, 146, 174, 201, 198, 148, 154),\n",
    "                  y=c(201, 165, 166, 157, 147, 145, 168, 180, 147, 136, 151, 168, 179, 129, 131), N=15)\n",
    "\n",
    "blood.pressure <- jags.model(file = 'blood.jag', data = blood.data, n.chains = 1, inits = blood.inits, n.adapt = 2000)\n",
    "\n",
    "blood.par <- c(\"mu1\", \"mu2\", \"delta\", \"psi1\", \"psi2\", \"tau1\", \"tau2\", \"var.ratio\")\n",
    "\n",
    "blood.res <- coda.samples(blood.pressure, var=blood.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(blood.res)\n",
    "\n",
    "# 1. Empirical mean and standard deviation for each variable,\n",
    "# plus standard error of the mean:\n",
    "#   \n",
    "#             Mean        SD  Naive SE Time-series SE\n",
    "# delta     1.863e+01 7.548e+00 2.387e-01      2.552e-01\n",
    "# mu1       1.765e+02 5.307e+00 1.678e-01      1.762e-01\n",
    "# mu2       1.579e+02 5.291e+00 1.673e-01      1.673e-01\n",
    "# psi1      2.642e-03 9.694e-04 3.065e-05      3.065e-05\n",
    "# psi2      2.763e-03 9.940e-04 3.143e-05      3.143e-05\n",
    "# tau1      4.396e+02 2.018e+02 6.383e+00      6.383e+00\n",
    "# tau2      4.161e+02 1.750e+02 5.535e+00      5.535e+00\n",
    "# var.ratio 1.223e+00 7.838e-01 2.478e-02      2.478e-02\n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#               2.5%       25%       50%       75%     97.5%\n",
    "# delta     3.657e+00 1.374e+01 1.873e+01 2.366e+01 3.347e+01\n",
    "# mu1       1.666e+02 1.731e+02 1.766e+02 1.801e+02 1.869e+02\n",
    "# mu2       1.471e+02 1.544e+02 1.579e+02 1.614e+02 1.686e+02\n",
    "# psi1      1.099e-03 1.939e-03 2.530e-03 3.214e-03 4.851e-03\n",
    "# psi2      1.187e-03 2.053e-03 2.647e-03 3.357e-03 4.896e-03\n",
    "# tau1      2.062e+02 3.111e+02 3.952e+02 5.158e+02 9.102e+02\n",
    "# tau2      2.042e+02 2.979e+02 3.778e+02 4.872e+02 8.425e+02\n",
    "# var.ratio 3.793e-01 7.234e-01 1.043e+00 1.488e+00 3.072e+00\n",
    "\n",
    "plot(blood.res)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "innocent-singles",
   "metadata": {},
   "outputs": [],
   "source": [
    "### c)\n",
    "\n",
    "# marginal posterior 95% hpd interval for mu\n",
    "\n",
    "# (166.6, 186.9) for mu1\n",
    "# (147.1, 168.6) for mu2\n",
    "\n",
    "\n",
    "### d)\n",
    "\n",
    "# Since the difference between mu1 and mu2 is 18.63, \n",
    "# we found evidence that mu2 is less than mu1. Therefore,\n",
    "# we can conclude that the blood pressures after taking \n",
    "# the drug are less than the blood pressures before\n",
    "# taking the drug, and so the drug is effective."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "opened-native",
   "metadata": {},
   "outputs": [],
   "source": [
    "### 3)\n",
    "\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    " # likelihood\n",
    " for (i in 1:N){\n",
    "  mpg[i] ~ dnorm(mu[i], psi)\n",
    "  mu[i] <- beta0 + beta1*weight[i] + beta2*sixcyl[i] + beta3*eightcyl[i]\n",
    " \n",
    " }\n",
    " \n",
    "  # priors\n",
    " beta0 ~ dnorm(0.0, 1.0E-04)\n",
    " beta1 ~ dnorm(0.0, 1.0E-04)\n",
    " beta2 ~ dnorm(0.0, 1.0E-04)\n",
    " beta3 ~ dnorm(0.0, 1.0E-04)\n",
    " psi ~ dgamma(0.01, 0.01)\n",
    " sigma2 <- 1.0/psi # variance\n",
    " \n",
    " # predictive\n",
    " mu.new <- beta0 + beta1 * weight.new + beta2 * sixcyl.new + beta3 * eightcyl.new\n",
    " mpg.new ~ dnorm(mu.new, psi)\n",
    " \n",
    "\n",
    "}\",\n",
    "    \n",
    "    file = \"mpg.jag\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "hawaiian-lunch",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Compiling model graph\n",
      "   Resolving undeclared variables\n",
      "   Allocating nodes\n",
      "Graph information:\n",
      "   Observed stochastic nodes: 32\n",
      "   Unobserved stochastic nodes: 6\n",
      "   Total graph size: 208\n",
      "\n",
      "Initializing model\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 10:10000\n",
       "Thinning interval = 10 \n",
       "Number of chains = 3 \n",
       "Sample size per chain = 1000 \n",
       "\n",
       "1. Empirical mean and standard deviation for each variable,\n",
       "   plus standard error of the mean:\n",
       "\n",
       "          Mean      SD  Naive SE Time-series SE\n",
       "beta0  33.8675 2.05621 0.0375410      0.0705334\n",
       "beta1  -3.1702 0.77848 0.0142131      0.0295732\n",
       "beta2  -4.2523 1.45807 0.0266206      0.0313000\n",
       "beta3  -6.0902 1.66620 0.0304205      0.0487384\n",
       "psi     0.1529 0.04191 0.0007652      0.0008081\n",
       "sigma2  7.1238 2.87104 0.0524178      0.0550514\n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "           2.5%     25%     50%     75%   97.5%\n",
       "beta0  30.00979 32.6984 33.9024 35.1442 37.6198\n",
       "beta1  -4.66692 -3.6706 -3.1732 -2.6934 -1.6393\n",
       "beta2  -7.04085 -5.2368 -4.2342 -3.2909 -1.5081\n",
       "beta3  -9.36271 -7.1815 -6.0600 -5.0061 -2.8136\n",
       "psi     0.08166  0.1233  0.1493  0.1786  0.2445\n",
       "sigma2  4.09067  5.6000  6.6999  8.1128 12.2458\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DkIIEGQgwASBDkIIEGQgwASBDkIIEGQgwASBDkIIEGQgwASBDkIIEGQgwASBDkI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\nAalXP7tRjEBkAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Density of beta2\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SX5MK2mzs8OSDG3asd5pKsvWgVI8wswjoYsUjV8LFEnl/TyVYZYmRfzsnRup8RI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\nCYIcBJAgyEEACYIcBJAgyEH/B4iPzdX3Yr2PAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Density of sigma2\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mpg.inits <- list(list(beta0=2, beta1=1, beta2=2, beta3=2, psi=1), list(beta0=2, beta1=5, beta2=2, beta3=1, psi=0.5), \n",
    "                  list(beta0=2, beta1=1, beta2=1, beta3=1, psi=0.05))\n",
    "\n",
    "mpg.data = list(mpg=c( 21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2, 17.8, 16.4, 17.3, 15.2, 10.4, 10.4, 14.7,\n",
    "                       32.4, 30.4, 33.9, 21.5, 15.5, 15.2, 13.3, 19.2, 27.3, 26.0, 30.4, 15.8, 19.7, 15.0, 21.4), \n",
    "                weight=c( 2.620, 2.875, 2.320,3.215, 3.440, 3.460, 3.570, 3.190, 3.150, 3.440, 3.440, 4.070, 3.730,\n",
    "                          3.780, 5.250, 5.424, 5.345, 2.200, 1.615, 1.835, 2.465, 3.520, 3.435, 3.840, 3.845, 1.935, 2.140,\n",
    "                          1.513, 3.170, 2.770, 3.570, 2.780), \n",
    "                sixcyl=c( 1, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0), \n",
    "                eightcyl=c(0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0), N=32, \n",
    "                weight.new = 3.5, sixcyl.new = 0, eightcyl.new = 0)\n",
    "\n",
    "mpg.model <- jags.model(file = \"mpg.jag\", data = mpg.data, inits = mpg.inits, n.chains = 3, n.adapt = 2000)\n",
    "\n",
    "mpg.par <- c(\"beta0\", \"beta1\", \"beta2\", \"beta3\", \"psi\", \"sigma2\")\n",
    "\n",
    "mpg.res <- coda.samples(model = mpg.model, variable.names = mpg.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(mpg.res)\n",
    "\n",
    "# 1. Empirical mean and standard deviation for each variable,\n",
    "# plus standard error of the mean:\n",
    "#   \n",
    "#         Mean      SD  Naive SE Time-series SE\n",
    "# beta0  33.9976 2.13389 0.0389593      0.0862392\n",
    "# beta1  -3.2096 0.82422 0.0150481      0.0357609\n",
    "# beta2  -4.2675 1.48671 0.0271435      0.0323638\n",
    "# beta3  -6.0628 1.73952 0.0317592      0.0552862\n",
    "# psi     0.1532 0.04095 0.0007477      0.0008118\n",
    "# sigma2  7.0710 2.74553 0.0501263      0.0607342\n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#           2.5%     25%     50%     75%   97.5%\n",
    "# beta0  30.09684 32.7537 34.0498 35.3103 37.7739\n",
    "# beta1  -4.78099 -3.7364 -3.2271 -2.6991 -1.6301\n",
    "# beta2  -7.18468 -5.2255 -4.3027 -3.3119 -1.3492\n",
    "# beta3  -9.33034 -7.1878 -6.0658 -4.9379 -2.6243\n",
    "# psi     0.08551  0.1237  0.1503  0.1784  0.2415\n",
    "# sigma2  4.14164  5.6050  6.6545  8.0816 11.6948\n",
    "\n",
    "plot(mpg.res)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "assigned-princess",
   "metadata": {},
   "outputs": [],
   "source": [
    "### b)\n",
    "\n",
    "# i)\n",
    "\n",
    "#  95% equal tail probability interval for beta0\n",
    "\n",
    "# p(30.09684 < 33.9976(mean of beta0) < 37.7739) = 0.95\n",
    "\n",
    "# (30.09684, 37.7739): the probability that this interval contains the true value of beta0 is 0.95\n",
    "\n",
    "# ii)\n",
    "\n",
    "#  95% equal tail probability interval for beta1\n",
    "\n",
    "# p(-4.78099 < -3.2096 < -1.6301) = 0.95\n",
    "\n",
    "# (-4.78099, -1.6301): the probability that this interval contains the true value of beta1 is 0.95\n",
    "\n",
    "\n",
    "# iii)\n",
    "\n",
    "#  95% equal tail probability interval for beta2\n",
    "\n",
    "# p(-7.18468 < -4.2675 < -1.3492) = 0.95\n",
    "\n",
    "# (-7.18468, -1.3492): the probability that this interval contains the true value of beta2 is 0.95\n",
    "\n",
    "\n",
    "# iv)\n",
    "\n",
    "#  95% equal tail probability interval for beta3\n",
    "\n",
    "# p(-9.33034 < -6.0628 < -2.6243) = 0.95\n",
    "\n",
    "# (-9.33034, -2.6243): the probability that this interval contains the true value of beta3 is 0.95\n",
    "\n",
    "\n",
    "# v)\n",
    "\n",
    "#  95% equal tail probability interval for psi\n",
    "\n",
    "# p(0.08551 < 0.1532 < 0.2415) = 0.95\n",
    "\n",
    "# (0.08551, 0.2415)\n",
    "\n",
    "\n",
    "# vi)\n",
    "\n",
    "#  95% equal tail probability interval for sigma2\n",
    "\n",
    "# p(4.14164 < 7.0710 < 11.6948) = 0.95\n",
    "\n",
    "# (4.14164, 11.6948)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "better-trading",
   "metadata": {},
   "outputs": [],
   "source": [
    "### c)\n",
    "\n",
    "# Looking at the regression coefficients beta2 and beta3 for\n",
    "# sixcyl and eightcyl variables respectively, it clearly shows that moving\n",
    "# from six cylinders (beta2 = -4.2675) to eight cylinders (beta3 = -6.0628)\n",
    "# reduces the mpg by 1.7953. Therefore, we can say that the mpg of a car\n",
    "# increases with decreasing number of cylinders."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "convinced-testament",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 10010:20000\n",
       "Thinning interval = 10 \n",
       "Number of chains = 3 \n",
       "Sample size per chain = 1000 \n",
       "\n",
       "1. Empirical mean and standard deviation for each variable,\n",
       "   plus standard error of the mean:\n",
       "\n",
       "          Mean             SD       Naive SE Time-series SE \n",
       "      22.75212        2.88016        0.05258        0.05530 \n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       " 2.5%   25%   50%   75% 97.5% \n",
       "17.24 20.82 22.76 24.62 28.44 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SrXI6GPhG/UfKQakchHoow06yONaSRzh0bi5RNVH0mJtCmWEikJYXHBmiQSayTI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      "text/plain": [
       "Plot with title \"Density of mpg.new\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "### d)\n",
    "\n",
    "\n",
    "mpg.par <- c(\"mpg.new\")\n",
    "\n",
    "mpg.res <- coda.samples(model = mpg.model, variable.names = mpg.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(mpg.res)\n",
    "\n",
    "# 1. Empirical mean and standard deviation for each variable,\n",
    "# plus standard error of the mean:\n",
    "#   \n",
    "#   Mean             SD       Naive SE Time-series SE \n",
    "# 22.8177         2.9794         0.0544         0.0544 \n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#   2.5%   25%   50%   75% 97.5% \n",
    "# 16.68 20.85 22.85 24.78 28.61 \n",
    "\n",
    "plot(mpg.res)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "double-accommodation",
   "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": "4.1.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}