lab5.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "described-course",
   "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": [
    "### Lab 5\n",
    "\n",
    "library(rjags)\n",
    "\n",
    "# 1\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    "  # pi ~ dbeta(0.01, 0.01) # prior1\n",
    "  # pi ~ dunif(0, 1) # prior2\n",
    "  pi ~ dbeta(0.5, 0.5) # prior3\n",
    "  r ~ dbin(pi, N) # likelihood\n",
    "  \n",
    "  # number of replying immoral in new survey\n",
    "  r.new ~ dbin(pi, N)\n",
    "  pi.new <- r.new/N # new probability for group responding 'immoral'\n",
    "\n",
    "}\",\n",
    "  \n",
    "  file = \"gallup.jag\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "religious-zoning",
   "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: 1\n",
      "   Unobserved stochastic nodes: 2\n",
      "   Total graph size: 6\n",
      "\n",
      "Initializing model\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 2010:12000\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",
       "     0.1997843      0.0206652      0.0006535      0.0005290 \n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "  2.5%    25%    50%    75%  97.5% \n",
       "0.1571 0.1864 0.1997 0.2130 0.2384 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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9dv7yBSKBDJILRI10akzEcKRAoHIhkE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\nAJEAHIBIAA74H+g1EyHqi4K+AAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Density of pi.new\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a)\n",
    "\n",
    "gal.data1 = list(N=751, r=150)\n",
    "\n",
    "gal.inits = list(pi=0.5, r.new=0)\n",
    "\n",
    "gal1 <- jags.model(file = \"gallup.jag\", data = gal.data1, n.chains = 1, inits = gal.inits, n.adapt = 2000)\n",
    "\n",
    "gal1.par <- c(\"pi.new\")\n",
    "\n",
    "res.gal1 <- coda.samples(gal1, var=gal1.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "# results for prior1 Beta (0.01,0.01)\n",
    "summary(res.gal1)\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",
    "# 0.1997044      0.0209795      0.0006634      0.0006387 \n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#   2.5%    25%    50%    75%  97.5% \n",
    "# 0.1598 0.1851 0.1984 0.2130 0.2423\n",
    "\n",
    "# posterior mean = 0.1997044\n",
    "\n",
    "# 95% posterior credible interval on pi = (0.1598, 0.2423)\n",
    "\n",
    "\n",
    "\n",
    "plot(res.gal1)\n",
    "\n",
    "# results for prior2 uniform(0,1)=Beta(1,1)\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",
    "# 0.2003555      0.0208431      0.0006591      0.0006591 \n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#   2.5%    25%    50%    75%  97.5% \n",
    "# 0.1637 0.1864 0.1997 0.2144 0.2437\n",
    "\n",
    "plot(res.gal1)\n",
    "\n",
    "# posterior mean = 0.2003555\n",
    "\n",
    "# 95% posterior credible interval on pi = (0.1637, 0.2437)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "organic-breeding",
   "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: 1\n",
      "   Unobserved stochastic nodes: 2\n",
      "   Total graph size: 6\n",
      "\n",
      "Initializing model\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 2010:12000\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",
       "      0.053250       0.101024       0.003195       0.003753 \n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       " 2.5%   25%   50%   75% 97.5% \n",
       "0.000 0.000 0.000 0.125 0.375 \n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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LbPkYrdgedIPqico4gkyCrSdykQSRWI\nJEAkn0LOKERaM4jkU8gZhUhrBpF8CjmjEGnNIJJPIWcUIq0ZRPIp5IxCpDWDSD6FnFGItGYQ\nyaeQMwqR1gwi+RRyRiHSmkEkn0LOKERaM4jkU8gZhUhrBpF8CjmjEGnNIJJPIWcUIq0ZRPIp\n5IxCpDWDSD6FnFGItGYQyaeQMwqR1gwi+RRyRiHSmkEkn0LOKERaM4jkU8gZhUhrBpF8Cjmj\nEGnNIJJPIWfUykXS2cpsIJJPIWcUIq0ZRPIp5IxCpDWDSD6FnFGItGYQyaeQMwqR1gwi+RRy\nRiHSmkEkn0LOKERaM4jkU8gZhUhrBpF8CjmjEGnNIJJPIWcUIq0ZRPIp5IxCpDWDSD6FnFGI\ntGYQyaeQMwqR1gwi+RRyRiHSmkEkn0LOKERaM4jkU8gZhUhrBpF8CjmjEGnNIJJPIWcUIq0Z\nRPIp5IxCpDWDSD6FnFGItGYQyaeQMwqR1gwi+RRyRiHSmkEkn0LOKERaM4jkU8gZhUhrBpF8\nCjmjEGnNIJJPIWcUIq2Z9YrkrgWRxkAkASL5FHJGIdKaQSSfQs4oRFoziORTyBmFSGsGkXwK\nOaMQac0gkk8hZxQirRlE8inkjEKkNYNIPoWcUYi0ZhDJp5AzCpHWDCL5FHJGIdKaQSSfQs4o\nRFoziORTyBm1dpF0NjMXiORTyBmFSDO0Qg2I5FPIGfVDIh03xuxO7hhEEiCSTyFn1C+I1PXK\n1rSU7tAJe1YEIvkUckb9jEilKau6vpbm6AydsGdFIJJPIWfUz4hUmKrZrszGGTphz4pAJJ9C\nzqifEanvGncXIZIAkXwKOaN+RqR9L1LhDJ2wZ0Ugkk8hZ9RviLQ7HE/m77ZZle67DYgkmEWk\nkUmMSEGNiYG5024WlTN0wp4VgUg+hZxRvyBSfbkcj7tde8uhdHqESJKMIhmJdwpEUgUiCTKK\ndC4QaeEiuQdQTTPnIOfSrtqZ7bWtgaWdFypnKCIJ8l4j/Zn2hhAi+aFyhiKSIPPNhuvW7CpE\n8kTlDEUkQfa7dgdTnBDJj/y3v4OuYxEpeZEhl83ICH1KgUjpOSJSIPlFar6CgkheZJyhl2I7\nMRKRBHOIFJgCkXJwGfk1pAeIJEAkn0LOqN8Q6ba6u0yKQyTBXCLxQNYDlTMUkQR6RBq9ykUk\nVSCSgKWdTyFnFCLN0Ao1IJJPIWcUIs3QCjUgkk8hZxQizdAKNWQV6XzYtVdAu/IckAKRVIFI\ngowiVZvB3QT3Yz9ECmhMZhBJkFGk0hR/3SOK66nw/e8B1IikDEQSZBSpGDzpu/j+F2pqRFIG\nIgkyiiSmLg9kPVA5QxFJwBnJp5AzCpFmaIUa8l4jndrfNOcayROVMxSRBDlvf28Hd+02nv/N\ntBqRlIFIgpwi1eeyfY5U7A48R/JB5QxFJEFWkb5LgUiqQCQBIvkUckYh0gytUAMi+RRyRiHS\nDK1QAyL5FHJGrV4kne3MBCL5FHJGIZLKdmYCkXwKOaMQSWU7M4FIPoWcUYiksp2ZQCSfQs4o\nRFLZzkwgkk8hZxQiqWxnJhDJp5AzCpFUtjMTixDJtPP+baK+NuRDw5wimQ8hb3sG2Z9lhlHG\nJdKjyLtIRlZrU1zlBEUkASLZQxBpDEQSIJI9BJHGQCQBItlDEGkMRBIgkj0EkcZAJAEi2UMQ\naQxEEiCSPQSRxkAkASLZQxBpDEQSIJI9BJHGQCQBItlDEGkMRBIgkj0EkcZAJAEi2UMQaQxE\nEiCSPQSRxkAkASLZQxBpDEQSIJI9BJHGQCQBItlDEGkMRBIgkj0EkcZAJAEi2UMQaQxEEiCS\nPQSRxkAkASLZQxBpDEQSIJI9BJHGQCQBItlDEGkMRBIgkj0EkcZAJAEi2UMQaQxEEiCSPQSR\nxkAkASLZQxBpDEQSIJI9BJHGQCQBItlDEGkMRBIgkj0EkcZAJAEi2UMQaQxEEiCSPQSRxkAk\nASLZQxBpDFujVDY0D4hkD0GkMRBJgEj2EEQaA5EEiGQPQaQxEEmASPYQRBoDkQSIZA9BpDEQ\nSYBI9hBEGgORBIhkD0GkMRBJgEj2EEQaA5EEiGQPQaQxEEmASPYQRBoDkQSIZA9BpDEQSYBI\n9hBEGgORBIhkD0GkMRBJgEj2EEQaA5EEiGQPQaQxEEmASPYQRBoDkQSIZA9BpDEQSYBI9hBE\nGgORBIhkD0GkMRBJgEj2EEQaA5EEiGQPQaQxEEmASPYQRBoDkQSIZA9BpDEQSYBI9hBEGgOR\nBDOIdCzM5uiVApEUgkiCnCJddqY41gfTsPVJgUgKQSRBRpEurUGl2Vf1dWec5yREcjdGA4gk\nyCjS3pR1XZqi2a7MxiMFIikEkQQZReomiNkNXkxMgUgKQSRBdpH+ujVdd2KamAKRFIJIgqxL\nu9vVUUfVLvMmp0AkhSCSIKNIVWGec8V5QkKkkcZoAJEEGUWq67LXp3CejxBprDEaQCRBVpFC\nUyCSQhBJgEj2EEQaA5EEiGQPQaQxEEkwl0g8R3qJ/gmRdLY0C3pEMkPeMiKSNhBJwNLOHoJI\nYyCSAJHsIYg0BiIJEMkegkhjIJIgq0jnw669AtqVZ68UiKQQRBJkFKnaDO4m8It9L9GItGwy\nilSa4u/Sbl1PBV9afYlGpGWTUaTCXB7bF36N4iUakZZNRpGMfdpNSIFICkEkAWckewgijYFI\ngrzXSKdru8U10nvFiLRsMopUbwd37TaVKxKR3I3RACIJcopUn8v2OVKxO/Ac6bViRFo2WUUK\nTYFICkEkASLZQ1YrUui3Txw7VwEi2UNWKlL4t08cO1cBItlDVipS+LdPHDtXASLZQ1YqUviz\nPsfOVYBI9pCVihT+7RPHzlWASPaQlYrEGSkURLKHrFSk8G+fOHauAkSyh6xUpPBvnzh2rgJE\nsoesVaTgb584dq4CRLKHrFakySCSAJHsIYhkw/HfHrwH5G6RGhDJHoJIYyCSAJHsIYg0BiIJ\nEMkegkhjIJIAkewhKxXJmNHLoEfo5J2rAJHsISsV6YhIgSCSPWSlItWXwv3LE08QSYBI9pC1\nilRf3F8MeoJIAkSyh6xWpNvq7jIeVCPSC4hkD1mvSFNBJAEi2UMQaYwP3Zq5FWpAJHsIIo2B\nSAJEsocg0hiIJEAkewgijYFIAkSyhyDSGIgkQCR7CCKNgUgCRLKHINIYiCRAJHsIIo2BSAJE\nsocg0hiIJEAkewgijYFIAkSyhyDSGIgkQCR7CCKNgUiCJYnUT7lOKvGbZ92ex6R8TvJn0X7n\nfSqboQ5ihrfVP6ruq3rUaR7/G85+l0hmUNA8G3ZPej+K/kdt+YU6lbMTkQSIhEhhIJIAkRAp\nDEQSIBIihYFIAkRCpDAQSYBIiBQGIgkQCZHCQCQBIiFSGIgkQCRECgORBIiESGEgkgCRECkM\nRBIgEiKFgUgCREKkMBBJgEiIFAYiCRAJkcJAJAEiIVIYiCRAJEQKA5EEiIRIYSCSAJEQKQxE\nEiASIoWBSAJEQqQwEEmASIgUBiIJEAmRwvjQKJVtzQAiIVIYiCRAJEQKA5EEiIRIYSCSAJEQ\nKQxEEiASIoWBSAJEQqQwEEmASIgUBiIJEAmRwkAkASIhUhiIJEAkRAoDkQQ5Rar2xmxP90qc\ntSCSqzt0gEiCjCJVRTv3d10liIRIv0RGkUpzvNl0LLZtJYiESL9ERpGKruC12FwRCZF+jIwi\n9fOj2m4RCZF+jIwibUzVb20RCZF+i4wiHc3+vnU1W0RCpJ8io0h1+Zghp/fJ4kqBSApBJEFO\nkerLrt+67hEJkX6JrCKFpkAkhSCSAJEQKQxEEiASIoWBSIK5ROJmAyL9FHpEMkPeMiKSNhBJ\nMJdIXikQSSGIJEAkRAoDkQSIhEhhIJIgq0jnw66d/rvy7JUCkRSCSIKMIlWbwd2ErU8KRFII\nIgkyilSa4u/Sbl1PhSk9UiCSQhBJkFGkwlwe2xdTeKRAJIV8apTKxqYno0hifrxNFlcKRFII\nIgk4IyFSGIgkyCjS7RrpdG23uEZCpF8jo0j1dnDXblO5ImUKM0Ek86VIzxnezWSHSCZUJINI\nv0tOkepz2T5HKnYHr+dI2UQyfV2TRBpmfFb41vq+DYj002QVKTAFIk3qtMwgkgCRECkMRBIg\nEiKFgUgCREKkMBBJgEiIFAYiCRAJkcJAJAEiIVIYiCRAJEQKA5EEiIRIYSCSAJEQKQxEEiAS\nIoWBSAJEQqQwEEmASIgUBiIJEAmRwkAkASIhUhiIJEAkRAoDkQSIhEhhIJIAkRApDEQSIBIi\nhYFIAkRCpDAQSYBIiBQGIgkQCZHCQCQBIiFSGB8bpbK1yUEkRAoDkQSIhEhhIJIAkRApDEQS\nIBIihYFIAkRCpDAQSYBIiBQGIgkQCZHCQCQBIiFSGIgkQCRECgORBIiESGEgkgCRECkMRBIg\nEiKFgUgCREKkMBBJgEiIFAYiCRAJkcJAJAEiIVIYiCRAJEQKA5EEiIRI7xw3xuxO7hhEEiAS\nIg0ztam2bd+a0h3q/cZPg0iINMzUpCpNWdX1tTRHZ6j3Gz8NIiHSMFOTqjBVs12ZjTPU+42f\nBpEQaZhp0DX1Wzu6Pu/5WEey1mkGkRBpmKlJte+7sXCGer/x0yASIg0zmd3heDJ/t82qdN9t\nQCQBIiHSMNNz2WZMUTlDvd/4aRAJkYZcLsfjbtckLEqnR45GrdIkREKkMBBJgEiIFAYiCRAJ\nkcJAJAEiIVIYiCRAJEQKA5EEiIRIYSCSQLtIplfGPMy5/3zsfezq/3lo9YgwwzJPc/pyj9hh\nNYNK+6L14P/DRg1yP8OfrhlxGE+B6kH5h0iDo8rZ4/4gkmA5IvUzbqJIL5PcIZKRIkn7pINv\nIgmhRkXqDa+HB1Uj0i+ASIgUBiIJEAmRwkAkASIhUhiIJEAkRAoDkQSIhEhhIJIAkRApDEQS\nIBIihYFIAkRCpDAQSYBIiBQGIgkQCZHCQCQBIiFSGIgkyCjS69yblAKRvujxpCCSIKNIR0RC\npJ8l59LuUmy9UyDSNz2eEkejVLY3MVmvkS4jf+DAkgKRvurxhCCSIO/NhqO5eKZApO96PB2I\nJMgrkn8KRMrT4/4gkgCRECkMRBIgEiKFgUgCREKkMBBJMJdIxlkLIiHSwtAjkpyYwzhEitHj\nsUEkAUs7RAoDkQSIhEhhIJIAkRApDEQSZBXpfNi182RXnqemQKSvejwhiCTIKFK1Gcw899dX\nEQmRFkZGkUpT/HVftbueiql/MRuRvujxpCCSIKNIxeAbqxdTTEuBSF/0eFIQSZBRJDE5jLMW\nREKkhcEZCZHCQCRB3muk07Xd4hrpt0XS2eC0ZBSp3g5m3qaalgKRvunxlCCSIKdI9blsnyMV\nuwPPkRDpt8gqUkAKRMrT4/4EiWSMymOJACIhUhghIpmRcgsGkRApDEQSIBIihREgkhktuFwQ\nCZHCQCQBIiFSGIgkQCRECsNfJON8d+EgEiKFgUgCREKkMBBJgEiIFEa4SDqP50sQCZHC8BbJ\nuN9eOIiESGEgkgCRECkMRBIgEiKF4WyU7U3jfnvhIBIiheErknG/vXQQCZHCQCQBIiFSGIgk\nQCRECgORBIiESGF8I5LOI/oKREKkMDxFMiPvLx1EQqQwEEmASIgUBiIJfkAky7x+n+RWkZ4R\nFpGEHLU9x6fMvTX3cu8iGbdI5tdF0nlI34BIBpGCQCQBIhlECsJPpNcdKg/pGxDJIFIQiCRA\nJINIQSCSAJEMIgXhbtSYOCoP6RsQySBSEN+JpPOYvgCRDCIF4SXSe7DKY/oCRDKIFAQiCRDJ\nIFIQiCRAJINIQSCSAJEMIgXxpUg6DyocRDKIFISPSLZYlQcVDiIZRAoCkQSIZBApCEQSIJJB\npCBGGjV6ACoPKhxEMogUxLci6TyqYBDJIFIQHiLZQ1UeVTCIZBApCEQSIJJBpCAQSYBIBpGC\nQCQBIhlECuJrkXQeViiIZBApiOkifYpUeVihIJJBpCAQSYBIBpGCGGuUsWz51bAoEMkgUhCI\nJEAkg0hBTBbpc6DK4woEkQwiBYFIAkQyiBQEIgkQySBSEIgkQCSDSEFMFckRp/K4AkEkg0hB\njDbKjMepPLAwEMkgUhCIJEAkg0hB5BBJ5YHbQSSDSEFMFMkZ5n7TdKO0DBDJIFIQMUSacCdC\n5bFbQCSDSEGMN8qMh31+14xG6AKRDCIFkUkknQf/DiIZRAoirUhmQowqEMkgUhATGmXGoz68\nb+oly+0AAAx0SURBVMZDlIFIBpGCmNIoMxpkDzATYpSBSAaRgojTqCki6Tz+FxDJIFIQkRpl\nq+Z1n8rjfwGRDCIFkU6k910qO0CSVaTzYddOkl15npoCkb7q8YTkFElnDwgyilRtBlNtOzEF\nIn3R40mJ1ai3eqYs9vSRUaTSFH+Xdut6Kkw5LQUifdHjSUkl0qTbD/rIKFJhLo/tiymmpUCk\nL3o8KdEaZZwvo6dLREaRxOQwzloQabUifapWZR8M4IxkECmIeI0yH7Y98tl6LS95r5FO13aL\nayREstfkqtThmHnfyk1GkertYKptqmkpZhJpIohUe7bOGmw+vD3x6skM352m0vdt/qrG4CJ3\nzmX7HKnYHWZ5juTBxDPSx+KINFbKtvdVgtdgW+FHGa+z0sJFCkgxJpLv9DZZlnaWxEsRyf+h\neYxJ2ffRSPD7DuvJbFylNYo0MkfHp/P810iWYkpFCnloHmdS2ib/+66Xfhm++vyOpZbXHnby\nIyLNco0UV6SXM9KHAhpECnloHv/T3RX8XMq9qPC6LLQXfswAD51UizTykSHi5IxbvkiWpZ2t\nisg9PomQRxR5RRrYMBIsol7KvC55PmZxDcuEtjpJJJK9vR+Ox4fQOiaU86z60zrvU3jUHp+E\nXCw5x+hfz3NrAr8bHNDZXwyUnhRLQvcZCRq0XyNBnfkayf+hOdSItAgydkfIQ3OoM4sU8It9\nUGd+juT/0BzqrCIF/WIf1Eq7Q2Wj5iOjSEG/2Ae10u5Q2aj5yCgSd4RCUdkdKhs1HxlFGnlG\nESPFj6KyO1Q2aj44Iy0Ald2hslHzkfcaiWcUQajsDpWNmo+ct795RhGIyu5Q2aj5yPsciWcU\nQajsDpWNmg++2bAAVHaHykbNByItAJXdobJR84FIC0Bld6hs1Hwg0gJQ2R0qGzUfiLQAVHaH\nykbNByItAJXdobJR84FIC0Bld6hs1Hwg0gJQ2R0qGzUfiLQAVHaHykbNByItAJXdobJR86FU\nJBCk73F/5u4TbQT0YPxBiZksRwmtzZqFKe1cc0yawumTIVJmtE1cbTFpCqdPhkiZ0TZxtcWk\nKZw+GSJlRtvE1RaTpnD6ZIiUGW0TV1tMmsLpkyFSZrRNXG0xaQqnT4ZImdE2cbXFpCmcPhki\nZUbbxNUWk6Zw+mSIlBltE1dbTJrC6ZMhUma0TVxtMWkKp0+GSJnRNnG1xaQpnD4ZImVG28TV\nFpOmMAB0IBJABBAJIAKIBBABRAKIACIBRACRACKASAARQCSACCASQAQQCSACiAQQAUQCiAAi\nAUQAkQAigEgAEUgn0nFjirJqN8tiZDOUy96Y/TVhjmPfP6PVRzia2Xhre+DBvBUbzIGv6rlx\nDpipb/UM5ktskolUtv9V/6I5jG27uak/boZySp3j0v9dgtHqIxzNbLy1PfBg3ooN5sBX9dyo\nCv+Z+lbPKaw9k0gl0sXsq+YDfd98lhSX+lKY86fNYIpbFdXOlKly3Ip2/TNafYyjmYu3tgce\nzFuxwRz4qp6Gnf+fWnmv5zlf4pNKpF1XcXP4pTndtv7M4dNmKH9tl1SmSJTjaLb34RutPsLR\nzMZb2wMP5q3YYA58VU/7yl+kt3oG8yU+iW82NIe/M82q9GJ2nzZD2ZtLv5kkx63f78M3Wn2E\no5mNt7YHHsynYr4KWOq5Pj7SvqlnMF/ik1akymwfHdn8sG+GsjH1oWiXD2lyXF5r+Fx9hKOZ\njbe2Bx7Mh2LtHPiynq25+nftWz2D+RKftCN/bM6uyaaeMbv24rFOlwORvqino50D39VzMH8B\nXWs5rsd8iU/Skb8WzWk1oUjNxeO+WQQjUjhpRermwFf1tKuzKCI95kt8Uo58VbQn9YQiNWve\na3ODE5HCSSrSfQ58Vc+muWEdRaTHfIlPypHfdi0ungdk3wzFjFX8fY570dHqIxzNbLy1PfBg\nrMW2/rP2tZ59uzb079q39iT9tEs38tfNtnuG3N09uT5vbr1uhjK4vZoqx73TR6uPcDSz8db2\nwIOxFHvMgW/qMQ++bE/g7fhpJBPp9LhZc2g/UU7NTXz7ZihdFdcmUaoc904frT7C0czGW9sD\nD+a92Mn3hp21nlCRPhzXNahRo6QSadDcZN8FuK12q+bi8S9djvvg8c2GkHoCp6w9vf95xNKe\nx3yJTyqR9oNPkU270XaqfTOUw1jFX+foh2+0+ghHMxuDtnfHG3gwr/UM58BX7ZFb4fUcEg5S\nKpGGp+Oq/RZuu9u+Gcxp66746xz98I1WH+No5mLQ9u54Aw/mtZ7AJdl7e+TWF/U850t0lnib\nCUAdiAQQAUQCiAAiAUQAkQAigEgAEUAkgAggEkAEEAkgAogEEAFEAogAIgFEAJEAIoBIABFA\nJIAIIBJABBAJIAKIBBABRAKIACIBRACRACKASAARQCSACCASQAQQCSACiAQQAUQCiAAiAUQA\nkQAigEgAEUAkgAggEkAEEAkgAj8gUvfX2E7jgadnNNwx5tRvuAOP/fvtn8GrHJuWHO1fnBz9\nk7SWJgx2tZuTh/CtPYMdx83wvXNXWyVLnH2nyQ9Mq/vfqR2N60IQSWBM0W844y79+9vWis3n\nTVuOjstoW1y7ms3JQ/jWnsGOst0s7s5URVvbtej2XsVeD35gWt3/Xum0OJDcJs/hvuEKuxRT\n/767NUfzbzn6V5DdTWjeNRNFcv2h9ovZV80Jdt+9s+tq25uybaPc68EPTC5E+oLbp7S5dhuO\nqKPZ3t8v26XgX2OffdOaY/jD1Zaxd6eK9NaewY6daM2fEXW+7PXgByZX18P3Q2/Wv8dub7Ux\nu9uq+vbh0v4l63vII2xzD7vuTNF2+Ok2WbYTLrV+ituCq+mlkdl5+7i+v79rtWvL2DetObof\n7SLyMR7Drm+uYJoU5+6McOou3Pa312bw7mAIy76gnbf2vDewq/naf0IUwzY+9nrwYyLtuuva\ndu9tu6wP3fK8lCJtB2Ht4vjQfOq2HOc9mNzcumPfroCeM8c8eERdXj+ynx9Jr5v2HHVzUmi6\n9jkeg67vxqNZThWDdVYzq5+jtRuKtBMj9d7gt/a87ai6hebWXLt9h/vS7iD2evAjIvW37sy2\nqqtt84Fmms3mx197pn6ENP/+3VfMf/ewY3MVWjQXw3+fLph/lVt3VO0xO0WqvxTpIY8cj77r\n+/Ewt/n8V/d3QJqF2HC0Bku7vuCnBo+LdGxPek26+75jY3W3mBnsnc5vibQzjTxVcwY3wyvf\nF5F2bS+emg8l8/g4ftwIXhXNkR+bD/exmfO9SNvLYE897Ppdu3W6bV6bMTnfzjiX9rzw8u5j\nCOUpdKyxlh3XolnkXbqJ0u7pTpWHl73T+S2RBh9Nzz47HbYvIr1Ngebf8rZiuIzdof052uPf\n3D5/korU/Hu630Rzj8f21pTydt126Jz6OFrfiVQV7cJu09wDv180NyfMat98pAz2evDzIm0f\nJ/0RkepDMXiQsBbaI2+u8Scu7Ypn19k3P+VoPumb2TsyHqebQsWm3my6Vd4kkd4b/Naelx3b\ndlm4b9cg3b7NfS2zEXs9+DWR5N6mszbH03WSSLdRLDcrvEaqm9XTxTUvn4H321/X5626182P\nObqfY+NRm835dnIom3uuVbBIb+0RO66b7fW13DOJ/fBH+S2Rds/rnOHgvA5cf420sw1Ktnar\noDveq9lMXNod7l1Xftr8XLRqbiE4xqO7112a5pRwuv27f3936tLurT3DHaf+yfBQme6UVbU3\nClcuUvMh097gua13dwORzvVlOwhpNsVdu76KTXc/aZVnpPZSe1Jg+Dcbqm33EGIwHv2bp+d9\nuUaY7lT0WGGdhnftrvUUkVzfbLi+fMOiq6c0zffsyod6q13abbpbpt0KvLnQufdEef90Ofch\n7f7hc6S+ir9H4JroJ0wxUaSmF+9d92HTVrSjqMR4DHxonwvt+6uV5rNs2z0afXl3MITuqT5o\nT19rv2P/csK5b2zlEaxWpPOm6/njrcf2z4+ttt+253YV14V0+4/F45sNj3/bbzaszKNHN52m\nitR9S9qxaSvaatR9tfo5HkMfDsXjyxPdo9FD/9hJvDscQmeDB+25nw8fO15Xbv2GPII1igQw\nP4gEEAFEAogAIgFEAJEAIoBIABFAJIAIIBJABBAJIAKIBBABRAKIACIBRACRACKASAARQCSA\nCCASQAQQCSACiAQQAUQCiAAiAUQAkQAigEgAEUAkgAggEkAEEAkgAogEEAFEAogAIgFEAJEA\nIoBIABFAJIAI/AdboWF8JEvnjQAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Density of pi.new\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b)\n",
    "\n",
    "gal.data2 = list(N=8, r=0)\n",
    "\n",
    "gal.inits = list(pi=0.5, r.new=0)\n",
    "\n",
    "gal2 <- jags.model(file = \"gallup.jag\", data = gal.data2, n.chains = 1, inits = gal.inits, n.adapt = 2000)\n",
    "\n",
    "gal2.par <- c(\"pi.new\")\n",
    "\n",
    "res.gal2 <- coda.samples(gal2, var=gal2.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(res.gal2)\n",
    "\n",
    "# results for prior1  Beta (0.01,0.01)\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",
    "# 0.0018750      0.0152017      0.0004807      0.0006555 \n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#   2.5%   25%   50%   75% 97.5% \n",
    "# 0     0     0     0     0\n",
    "\n",
    "# posterior mean = 0.0018750\n",
    "\n",
    "# 95% posterior credible interval on pi = (0, 0)\n",
    "\n",
    "\n",
    "plot(res.gal2)\n",
    "\n",
    "\n",
    "\n",
    "# results for prior2 uniform(0,1)=Beta(1,1)\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",
    "# 0.098750       0.131280       0.004151       0.004151 \n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#   2.5%   25%   50%   75% 97.5% \n",
    "# 0.000 0.000 0.000 0.125 0.375\n",
    "\n",
    "# posterior mean = 0.098750\n",
    "\n",
    "# 95% posterior credible interval on pi = (0.000, 0.375)\n",
    "\n",
    "\n",
    "\n",
    "plot(res.gal2)\n",
    "\n",
    "# results for prior3 Beta (0.5,0.5)\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",
    "# 0.053750       0.107663       0.003405       0.003577 \n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#   2.5%   25%   50%   75% 97.5% \n",
    "# 0.000 0.000 0.000 0.125 0.375\n",
    "\n",
    "# posterior mean = 0.053750\n",
    "\n",
    "# 95% posterior credible interval on pi = (0.000, 0.375)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "sitting-dancing",
   "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: 66\n",
      "   Unobserved stochastic nodes: 4\n",
      "   Total graph size: 77\n",
      "\n",
      "Initializing model\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 2\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    " # likelihood\n",
    " for (i in 1:N){\n",
    " y[i] ~ dt(mu, sigma, 4)\n",
    " \n",
    " }\n",
    " \n",
    " # prediction\n",
    " for(j in 67:68){\n",
    " y.new[j] ~ dt(mu, sigma, 4)\n",
    " }\n",
    " \n",
    " # prior\n",
    " \n",
    " mu ~ dnorm(0, 1.0E-06)\n",
    " sigma ~ dgamma(0.0001, 0.0001)\n",
    " tau <- 1/sigma\n",
    "\n",
    "}\",\n",
    "    \n",
    "    file = \"light.jag\"\n",
    ")\n",
    "\n",
    "light.inits = list(mu=10, sigma=1)\n",
    "\n",
    "light.data = list(y=c(28,26,33,24,34,-44,27,16,40,-2,29,22,24,21,25,30,23,29,31,19,24,20,36,32,\n",
    "                      36,28,25,21,28,29,37,25,28,26,30,32,36,26,30,22,36,23,27,27,28,27,31,27,26,\n",
    "                      33,26,32,32,24,39,28,24,25,32,25,29,27,28,29,16,23), N=66)\n",
    "\n",
    "\n",
    "light.deviations <- jags.model(file = 'light.jag', data = light.data, n.chains = 1, inits = light.inits, n.adapt = 2000)\n",
    "\n",
    "light.par <- c(\"mu\", \"tau\", \"y.new\")\n",
    "\n",
    "res.light <- coda.samples(light.deviations, var=light.par, n.iter = 10000, thin = 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "waiting-organic",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 2010:12000\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",
       "mu        27.48 0.6834  0.02161        0.02161\n",
       "tau       21.22 5.2647  0.16648        0.16648\n",
       "y.new[67] 27.47 6.5416  0.20686        0.20686\n",
       "y.new[68] 27.18 6.3416  0.20054        0.20054\n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "           2.5%   25%   50%   75% 97.5%\n",
       "mu        26.20 27.02 27.49 27.92 28.87\n",
       "tau       12.68 17.54 20.51 24.09 33.21\n",
       "y.new[67] 14.30 23.74 27.37 30.94 40.79\n",
       "y.new[68] 14.17 23.87 27.26 30.93 38.48\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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V6UtBn98PecttT25spG5shSYR37Kc6N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\nAAEgEgACQCQABIBIAAjwf7uTeK90NYRHAAAAAElFTkSuQmCC",
      "text/plain": [
       "Plot with title \"Density of y.new[68]\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a), c)\n",
    "\n",
    "summary(res.light)\n",
    "\n",
    "plot(res.light)\n",
    "\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",
    "# mu        27.48 0.6802  0.02151        0.02151\n",
    "# tau       21.47 5.5027  0.17401        0.17401\n",
    "# y.new[67] 27.69 6.3905  0.20209        0.20209\n",
    "# y.new[68] 27.39 6.4683  0.20455        0.20455\n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#           2.5%   25%   50%   75% 97.5%\n",
    "# mu        26.15 27.05 27.49 27.94 28.77\n",
    "# tau       12.96 17.47 20.66 24.61 33.77\n",
    "# y.new[67] 15.63 24.15 27.58 31.07 39.82\n",
    "# y.new[68] 15.27 23.89 27.31 30.82 40.57\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "textile-antarctica",
   "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: 66\n",
      "   Unobserved stochastic nodes: 4\n",
      "   Total graph size: 76\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",
       "mu         26.19  1.398  0.04421        0.04421\n",
       "tau       119.05 21.486  0.67944        0.67944\n",
       "y.new[67]  26.07 10.914  0.34513        0.34513\n",
       "y.new[68]  26.11 11.488  0.36329        0.36329\n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "            2.5%    25%    50%    75%  97.5%\n",
       "mu        23.462  25.24  26.14  27.16  28.90\n",
       "tau       83.752 103.46 116.65 131.58 166.05\n",
       "y.new[67]  4.155  18.77  25.83  33.10  47.82\n",
       "y.new[68]  3.969  18.00  26.04  33.65  48.51\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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mnjUmcixfL4B704jmkUimT2m3nDbYXJRKyJgUiRxlqRjP6bRGLHoh0kL9L2MdpY\nXp8eDTRwqVORNjeAkinikeg+KYhnyRRJOSKpdZH8a8EpRepYo4nKMlUXyd0nI1LGEX86Wzy4\nWSQvf1hutkiLc/I+JEXqXqOJijIJiZS7/nZD7sDZ1hQpmism0nKe84t0Eo0mUmEpXY1AimTO\ndbnairSv5PDAukgZFRUTSehhQ+MvPneRPnG5KgRSjKkiX7EsFCAmUi5FRdpHXCS58ne0IZ3u\njBppaOFKcrxwgRSKLXCahEERci7S5VohWf6xGanSEqkGtI28MgVSqEuKlME5RIreI80x8287\nU9op1/i/nvjHt3TzpjZPJ6k/OCfzT6cgf19Gx8iM4nOLVJreHjaAEMxIJwAi9U+Nhw3gKJmD\nujKQMZHAUbb3v+hg1s3bqNpWTU4VuTTk5eakgrPdqRoNkZrkrb3YOlVMli8aIvVULUQqW/K5\nGg2RmuStHX6nisnyRUOknqrtVKTK9UGkAkWeMCpP2OS+6oNIBYo8YVSesMmpIvHUrmXJEKlJ\nXvmRXPoe6WQxWb7o3kUC7VgWCZQG3X4RIFJb0O0XASK1Bd1+FTb/VBgoAfodAAEgEgACQCQA\nBIBIAAgAkQAQACIBIICcSPmPXucc0bcNufdmPVLt7rx0tOa9zI/ExWuJnJB40cLtLtrvcq3M\nLm3OEX3bkJsSJZSsdnde9uec9p7wTsi+isZNeEKiRRdod9l+byjSnK2JSJUldP6E4BVEip2Q\naNHFLgAQKZLvNCKpZiK5ZytccMGYLNVuiBTLt1MG2j2bzQvrM4nktFiyYOWfkGzRhdp9VZEO\nTCu7s1Ik07VnpBK11JiRihR9SZGS4bUh4wEHn0gkVaqWwiKpIkXXaLRIQZmlEXvJOr/555wh\n0jYgEiv4giIRz5h9fpiRtoClnVtu/yLlf8FF7ndu+EK2CKVqiZxQ50XH402KwosKAJ4DiASA\nABAJAAEgEgACQCQABIBIAAgAkQAQACIBIABEAkAAiASAABAJAAEgEgACQCQABIBIAAgAkQAQ\nACIBIABEAkAAiASAABAJAAEgEgACQCQABIBIAAhwFZEWz+MqJ9kB7HfDRQ+t/qox/UuxkmU7\n2xQe8ctyNu1r0d9xFmtL3eqKQalTucoJdgL/40WRI+u//HLNxGAXxY94GZxf/pisoSBXiTOI\nVAdKBfbCn4Dy0kV2qtROiFSb+Y+16FdF86b54yDmgF6BtGzteeEikbuEyhXJHxFW9rxFelh1\nIrfOwCNWYfXhvUo8sUsXKfPn/MI3WrvKgUVs/8UObRFJixCMCHki8XGM1hneIqmYZHW4Sjh5\nIp9N/A4AACAASURBVAV7wzewh+MisdfYwJC1SPnDGqnQXdOZPfUH+CohZRdw9g+9UXJiwtJu\nL3bhJbG0yxfJq9Nb30Gkw7jrNW9yCkdFXefM68JFih5SLKAXRUqMT8aMxMpTboUNxvYq4RQu\n7Ya3paXdVc68LvNcnzqUJ1I4PulLYGS80ks7iLSbeViUvZGdb179p3ZY2h2CxW30UMYXskSO\nJ94AmV3MtqBGlset9+BZ7gDxBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAA\nEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAA\nIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJA\nJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgQM8ikSE3\n588r0duu+pT6eqHbh61c7an/GZi65/V7PZ1SvwuDcZGx6jlG9ot0e+R531Wfeh0r/OxicLpG\nd9DHarrpX4qLjFXvMbKvY/bn+qa3u/rRl8gX+t5d2tWZeuU/ot+tafOPLefqaqx6j5G5Y4i+\nby+Pqfxx+Xr/U/N6YNx4oZcfnfjvfTpsZjG6jftvupDf9/kKOmd7obt6XNceJd8fL0Oet2GP\n5pP+Y20ADnOvfI3TiR4G1sUft3HZpeaJgtyxuNxY9R4jRqRhIf1F07v6HTfe9cZ8TbzfxvG6\n28H5GK9S3/PyY14AsGzD8ftj6z6mGfLcbt+v9DYVOAwYawNwmHvlPghghsF28Zte92mR3LG4\n3Fj1HiNGpE91f1ytftTfsOf90ZW/08bvY2NeYn8MG+/z4I38jt37Mpv2GJf7IKPNNgzJY3Hy\nuJgNwzSt5q2a80UOIkXRveIMg+3iIeJ/9P3R+MDBGYvLjVXvMWJEmmbxn89X5+b1xhYNjw/3\n+Qppjr+Mo/CqWCHjtUxnewzeG709EryYIf8YRvnNlKcgUhwuku1P08WP9djntz4+pnXG4nJj\n1XuMGJGG15/bvBAw3aUf17BEzvFhBf9O3+HxOdsrPWa4x9z2NwygzTm+/thBLX2WZ4Qv7Ux/\n2u77exnC/5v1anIs5gLPPVa9x4gj0gt9/t49kVjayFXuPnT9zUns5P8cL3GPlfZj6TjfwJqU\nn/QVqQTMzL3yPa3onJ3T69/Xux6LcYczFpcbq95jxBHpcTUalsnT4vpnWFObjYFw3T18tN90\n2MEx2X7GRfew9P6Zjvw3rM0/x7uuN/0QAyLFmHrl+zb0kulPHv/z/ayVgY/F5caq9xhxRBqf\nBA3XsulJzpd+pDM///7TT4JYdw69/6f8pYDNNj4Guk+rw/Hl1dzA6ge1ECnKvOQaQ9/0J49/\n+9RuuM95t2MxcLmx6j1GHJEeo3P7+BtG5+eFbuNkPmz8pxPr7yZ4d75Mq2d/Ta2zvY2HX8c7\n1un4B9Hrr+KFQKQYk0bzjwjp/mRdzL5HGuatoYNf9J2Mut5YXT1G7jda/WkwTWoQIJIMa2Nx\n6rG6eIzYZ+PbEke6I74XZLM2Fuceq4vHyI1e/9ZTzXQ3ONdibSzOPVaIEQAEgEgACACRABAA\nIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJA\nJAAEgEgACACRABAAIl0F/XvmWrfjSUG/XwQKNkBN0O0XASK15XC3EziKxDguitT6BC/A9v4/\nPIBgJxVEEqnhmYFIJ0CoBxeunRijo0CklmzsmvI92OcYZa6dmgKRWlJXpCEY/YjsN0r9RnXa\nTE1JkfodpF6oKhLpks5wjxSPmo6D6eozUrcdPwKR4iz40qtLEKklECnKcmv6NAki1SnjUMnP\n9fh7XZQeVYJI8mVsT1/5YUO6tI4ic1NTOmrvTO8iLWReKZeOV76togPp8fg7oJsuyaSJSBlF\n9ijSWpm9inSGL2Q3N6S35R1EWk91EZGi90h9fUWR045e2jzTSKR9Fx7vG7pEbc6twLYV9z6R\nUrnOJJJoDUfJc6Mvk1qLtBbC5xMp4yqRSpk7BWZW1q9Imcn7aPWElEg5628qIBIrsIBI5FUR\na07QgHTda2f/nCLt8KKHZs8IiZQ1SMSCPRWM5viqSJ4wU5FUXCRKlD2dHNFS3esibZl7s+n7\nYcOu+aWDds90KpI9vlUk7c26SGGJrJJolE1arIpEc1k0v66KlIqdQiIt0EFA7mtCBw2faCeS\nDrdocY5IRgnvB5dNGptjjl8n11J7dohk5ifHLDMDTQqFIsUuCBDpeAvat3zi5CKR0uYcFInc\nHV5rrEhk6+Nm2aVcXCSK1Oqej3u8qEhbxqg2+xvQvOkTQiLteNigwy1MTTqyaUUkXc5UvV5P\nhSKll4RMJLIzixfgYiJxW/kkZ1PoY882Ix2pv3XbJ6REiuaMyKX98ETiayvKEolWRCLlnQLx\nKnUiO0nO7eIN3i6SUYipadL4Iulc+iSJ+DG/0wrRxxeyx6pv3foRWZGiaSMi0Rz7SyKZJPIi\nsfnD1GNFMoHFpjtlXreLZBvhicQS2/ZUEKnbp3ZHTbiQSEv/Zb0vktaDWDQGIrEkZsnEQm1O\n6YikzSQjhmIimRp0K3kQC4ikPU6KZE5kRSRda+4QrELBhnQNOzleeQcmSc1IboynCzgokrtA\nSojE5zrjn538ApFM+nWRTMrtIvGZz27aEp5eJImVWfvVnZRIykbKYgGhSF7g8NA2ItmZQ/Fw\nJHNoVSTmrK5eKS8zq3uDSCYRMycUifRlwGjliGSvJlakuaQdQ7BMtyKJFNLaJDmRdMAtF+CJ\npOPIzhmuF6FIPDL3i+TMBkFe7YixwRPJKpAWyeiaFilyknb/viFYHJ6F4hqGoVDVrU2SFCln\nRuJBtEMkE/jO5JUWSce4qZ2JFOZNiUR+2xUTyTTEFYkCkbyaqokULVq2hh2ICdDYJFmR1gtw\nRDIWWIWCELMZrD58XcgKckLURC0XiTJFMlnURpHcYlyR2NIxIZI7UQsOQd4Y1USy4qYm9SKS\nCboFkawhvkiRKN4lklOOL1IwldrdvhZu05VTa1gXsfOuLVKktprIVtxyUupDJBN0/rqOKCpS\nGNJ+DFuRdJlxkaJ5nVoWRXJnMX/DlLAuUtgGySHIG6OKSNfbcIkqkCKngKRIlBQpDN4Fkdxk\noUj6JbZSc1vmCKzSIkXyByKFNSw4rHcJDkHeGNVDvtp2c6tAipwCnBBOipRacIXBu4Qbtusi\nuVk36RrWx5u/UySzIBQbgrwxqkaJWluZVFmk3NjshcgTBftaqErBIcgao2oUqrSNSh3MSEHM\nUmT9xz9H1n9uBCZyssKTU4Pd602XUZEiFUdmH/vRJkieuk0hOAR5Y1SJYgFPLVTqSCQWRsoL\n2iDsWP5Am2MimZLjIinzMV5wWiR9ECKVr7OBSfVFcsOVfUyLFC4JlY3mqEhrM5bN5N8sxUXS\nKdk3QuFVQM0laxGcAiKnHrTzmUQqG+v1TWp0j+R9/bIgkloRKXy0HMw4kbnBzoxLIimnidOJ\n6CDPFEl5IkWbZtLOOcSGYGFwTKdUpnSNtU+ppEiRQeJhyfzZIJK/2kuKpKxI8cv+ZpEcI5lI\nyhdpTqp8kdhKzp678wzPbWEDkarVUL/CuufUakaybphYYpdw832TDV/vAs/C14nmebZIiBTM\nG4q/sXuc6YmGjfSYSE7qLSI5+9MiqScQqUp9VSelBiLZaFZOxPL7D/11qi+SYjHI93P3lFuU\nH6k6l9bDKKDVMK87RGKPFJXSeXyReJOJXw24SKJDsEp36yCZaiqeVmWRdLyquEh6Qxl9SGez\nlqREUkmR2BygJdC68rmEGab0klLbYhtmjDG5ddvZSeqSFMuSFMmZQZ9BpHq19VRTXZHslV1F\nRJpLWBPJbC2I5KigeJvYtGVaZyp0RdJtTInkZmHti4jEpjKjYKwHi1BVpJqVVZuU6ovEX1ZE\nUgmR2H5lwlYfM1tOgWy1FYjkFOWLZNdw/AxCkbyTTIhkLwDmbJQRie2+skg1F1z1aqstkl24\nEQvFUCQvqw1tVyTFC4pe+5UfuXbX/HJMJBUTSXki2QNswoyKpC4vUlWNxgqr1NiPSGx3mJWL\n5IduSiS32lAkXUNKJJYiUyS3USpyRs5TlPnd6BQWFtknS7XorjsdVayzb5FsLl8kr8jg4u8X\n44gUzZsvkj4ej/5skVQLkYjYLWZ5Gmik6pjUlUgLZRwXKV5HKJKpjaXYJxKrI9wVF2lzAXtY\nkKZOgLeYjmrV3E4kvjharYWFdhORwpKFRHKnraIiUbAhXcNK/e08qmBSdZGc/Xki6WxLIqVq\nzRLJX4zxQ5GnAWsiRat9OpFaalSh/jOKtFBHWqRET7oZlkTycjgiZfNsIjWdjUwj2hZeTKSc\nskVEWm5BSiQFkQ7X3INGquykJCXSvhtZcZGya/JEiqcuI5KbeakQofFv9LChE4tGyrVFSKTS\nV7s1kfYX7GxtmRHik1Z2tQ1EalFDL5ORoVR7Sook+B3F1UTaJlC0/gNVRsaj6PdI3Vk0UqZR\nZ5mRZIuLlbZVJOGK64lU+R6pT4tGSjTtfCKVBCIJ0bFFI/Lta/uwYTMQSa7G4iL1btGEcCul\nRCpZQD0aiCSddkMpJUWq+YN7h5FsK0TawDVEKr5qOJNDGrFGQ6RGNBCpVA2Vf4JcHonmQ6RG\nnH5GIsvhlnXBsfOBSI3o5B5pDp1/W6HwE43/0x+n7UeJOir/2QBlm9X4F/k0v45Nprn5ZM4t\ncopbKD+KEOkoJ3rY8LRgRjoBEKl/aogEjnJ0CKZxCDYwRoJs73/Rwaybt1G1rZqcKnJ9yAVq\nPV5EDyUU6H+I1CRvm8VWFxHYQwkQqadqIdJpS4BIPVXbqUgLRXcRgT2UAJF6qrZTkcrW2oMG\nXZxG0RJPGJUnbHLTWnvQoIvTKFriCaPyhE1OFYmndlWLKFniCaPyhE1eKRH3SHWKKF4iaMIW\nkUA50O0XASK1Bd1+ESBSW9DtV2HzT4WBEqDfARAAIgEgAEQCQACIBIAAEAkAASASAALIiZT/\n6HXOEX3bkHtv1iPV7s5LR2s+ikRtB5sqcsJHSyjV62KlUXZpc47o24bclCihZLW789o/AL37\nhI8hUdvBpoqcMBv2do1IFixWUH5pjUSqLOGUqKVIrBmtRJJogoxIMqcSLViooHoijSlPI5KC\nSFJNgEipbPVFot2z2by0hkjtmnBYJDo6qaUKliwou7QD08rurBTJ9BQz0tEAEmjq8fnkaAnO\n6AvSVqRkeG3IeGhp91QizQ+oWBN2lnMksymhsUjTy8VEIvaSdYbzzzlDpAzIfTlUQqMmuMN+\npAnXEol4xuwzxIyUhdPZB4o40FSBJjzBjJT/FZf+z2fwhWwNj9zO3l9I4yaoo13W/ReyADwz\nEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAA\nIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABDgKiItnsdVTrID2O+mix5a/VVj+pdy\nJct2tik84pUVbNb7FWduWyrXVwpKncpVTrAT7G8/jh5Z/+WXayYGuyh+xFbmbpb5FfnrXCXO\nIFIdKBXYC38CyksX2alSOxdF8suDSALMf65DvyqaN80f8TAH9AqkZWvPCxeJ3GVarkj+iLCy\n5y3Sw6oTBXUGIh3+uy97uUo8sUsX2ctS+EZbrnIgie2/2KEtImkRghEhTyQ+jskFh7mLMn9y\nA/dIh/BECvaGb2APx0Vir7GBIWuR8oc1UamtlzcPM9Iu7ALOLpIpOTFhabcXu/CSWNrlixSp\n07xDJAHc9Zo3OYWjoq5z5nXhIkUP2eMrIiXGJ2tGcoUiiT+gtJerhFO4tBvelpZ2Vznzusxz\nfepQnkjh+KQvgbHxInfLcRQi7WMeFmVvZOebV/+pHZZ2hyD2GjuU8YUskeOJN0BmF7MtUZRb\nU6Le0iCeABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAA\nEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAA\nIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJA\nJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAE6FkkMuTm/HklettVn1JfL3T7\neHz6fpTx+q33Ap9pZIYeWkun1O/CYFxkrHqOkf0i3R553nfVp17HCj/V11TzfxApgR6bj9V0\n078UFxmr3mNkX8fsz/VNb3f187hE3ujrccWj2+7Srs7UK/8R/W5Nm39sOVdXY9V7jMwdQ/R9\ne3l01uPy9f6n5vXAuPFCLz868d/7dNjMYmPfDhe9uZDf9/kKOmd7obt6XNceJd8fL0Oet2GP\nrXh8hUgx5l75GqcTPQysiz9u07LrkW6aMJyxuNxY9R4jRqRhIT1N4Y8F9e+48a435mvi/TaO\n190OzgcNS/jvefkxr0VYtuH4/bF1H9MMeW63x3r77XcYpfEq96YgUpy5V+6DAGYYbBe/6XWf\nFskdi8uNVe8xYkT6VPfH1epH/Q173h9d+Ttt/D425iX2x7DxPg/eyO9wAXtcy37nQt7vg4w2\n2zAk/42r62GYptX8PG5/4wL8lbUBOOhecYbBdvEQ8T/6/mh84OCMxeXGqvcYMSJNs/jP56tz\n83pji4bHh/t8hTTHX8ZReFWskPFaprM9Bu+N3h4JXsyQfwyj/Kb+pkvmn4JIcbhItj9NFz/W\nY5/f+viY1hmLy41V7zFiRBpef27zQsB013xR4mmd48MK/p2+w+Nztld6zHCPue1vGECb8/E6\nLxdeFUSKw5d2pj9tF/+9DLH9zXo1ORZzgeceq95jxBHphT5/755ILG3kKncfuv7mJHbyf46X\nuMdK+7F0nG9g5zQ93MB2zdwr39OKztk5vf59veuxGHc4Y3G5seo9RhyRHlejYZk8La5/hjW1\n2RgI193DR/tNh+1vk+1nXHQPS++f6ch/w9r881HQ/Ej1RUGkOFOvfN+GmxrTnzz+5/tZKwMf\ni8uNVe8x4og0PgkarmXTk5wv/Uhnfv79p58Ese4cel+vne3g2GzjY6A72avZ63wD+z2tKL4V\nRIozL7nG0Df9yePfPrUb7nPe7VgMXG6seo8RR6TH6Nw+/obR+Xmh29ewZ9j4TyfW303w7nyx\nT3PYCsBkexsPv7JHpx9Er8OTo+GrqtcfpSBSnCl45x8R0v3Juph9jzTMW0MHv+hHCep6Y3X1\nGLnfaPWnwTSpQYBIMqyNxanH6uIxYp+Nb0sc6Y74XpDN2lice6wuHiM3ev1bTzXT3eBci7Wx\nOPdYIUYAEAAiASAARAJAAIgEgAAQCQABIBIAAkAkAASASAAIAJEAEAAiASAARAJAAIgEgAAQ\nCQABIBIAAkAkAASASAAIAJEAEAAiASAARAJAAIgEgAAQCQABtomkf6tm4cYAcFY2uUHBBjsG\njiI3mqnxA0dZ7+NNA7GQGrPUUSqIVLyGqwORTkDBHtx8PQXLVBcJQ5YPZiRNv94LibR0hhDp\nKDJ9Nv/1hg1j1Cu26f2pJCVSNGdMru564ATIiUSJ4s4wKm4g9TYtic1IauPVrq/Tj9FfCyGS\nijSxL5ME75G2DVJXZx+lvxZCpHgLe1LpoiIla9lwvqVaeGCNLFP/8EeJE8V1FJFR0n81rJeW\nn0+kvKeI/t7oAW/xnd2kbbQWSc1xd8KHDQtj0otJko+/jU1LBawWt5aA0h8plcju3SGS1Eh1\nIFLDGo6w3Lo+VOrv8Xd1kSghkv++mdQyJLccgZxuMfP4kLevzy9mDOuN66H5JR9/RwtoJdI8\nXcZFckPLK+OoSLac1IyYWeBOtq8aumKLJR1cCa4gErmH4rFiRQqXbr2IlDooKFLyYtIpWw1p\nblJbkWKHaCmDCuI7JpJTBJuKQpGmvc6Kp7BI5Dc3nXF1/65m+f0rWIM8GX40PoUORVr5UYg8\nkSgtEpl/UZFcoYhtrxG20DalvUjR4OxTpLxppu2k1EokSh1a/ZkiLUWGSPqhL5ktnToUyTwh\n5iKR2+wViLw3NtUSLRRWVqSlKbZLkXIb1dSkxiKF85OoSNPm7AbFRSIjkq7fqYDqiUQU2bm5\n1kN0KNIOLVqa1EikObpMsNo3JhKbKMgpIBSJl5MUiRIizV/5bxYp7BH3smAM0n7qNjKRYs4Y\nkSLXDgk2f0XRA/ta1O48+hbJRJUnEilXJKccsrdZvki0WSQqL1L4zW9ZkSjYUItyNWVvg5qd\nSEmRFv4zCjIrLRY4VqRpZ0QkG4Jk5ckTyQl3u9fGvRVJ/8+d4pwdtigJkVJT1VIvbyYqkmgN\nchwIOsFWyNZbbkZiIs220A6R7K2PnUN2ijRNkp5IZJqpbOsCkUg3fS6ZbEk6AxHZ5rKGsGLM\nBLnUg3s5j0hHJshWk2tnIhETiaxIPPjnaCQjAhfJyqF0iabIJZFYiWmRiC0DzSxjdzOR9CXB\nnJPNq5vj6KlbRKwKySFwS+ldpIMutDmXhiLZ67Ivko5ocy9kAlRf+pMi8clFmeBlL55IhjWR\nmIu+SGanFcnMmXb6sbVwkfh8W1gke82IHJKpQYajjWlyMk1E4rODJ5IdaxvjOviZSDrczBsX\nyUbLgkh+JVGReDOZSGx5ptZEYva4m8RF4udXTKQFOhLp+NrsaUSywc7XOoqHmfJFYkGp3Gj0\nl01GJBuVzgtzLFckt0pWOitM5Yuk7fYOCQ5B5hi15LhHbe6TaovkRG+WSKsflfu2JBKlRCK7\nIAvXYa4BgUi2XvN5g0hUX6Su75FEWgKRzJEMkRJBGoa6WQsmRaKoSEShSOHmEZHCk3rWGUnq\ndlCmGNEat7XJxu9yAeHKjEXYMZHcwxGRlC9SIrM3xc2bCw2KNi6YCKfNcGJrKpLtmy4Qa0f1\nExISiYKNRAGpKPTjSPGA9K/6y7hLvIhIdVBuS7Qu/pwUNFd/zB2CDYOky14Zo3bINQMi1SFZ\nnfPo0EmvKjcydwjkxqgZkq2oPclWFmlrDLkTCp9TiO0PtszHaE1sRtogki/OkkixtWdiNRg8\nooicx7wAzRsCsTFqhmzsX1ukRZMcX8yKxxMpssw7LJKzulIRERQFYsRb7n7MFcks/6ZTyBsC\nuTFqhHQb6p5T/YcN6Ui0X9RmieQXykVybFP2+6FoWCuWMEek4GF4eBqbRZovy/R8Ismvxaqe\nVMnH3zZAwn2xOcE8dXaSbRApLMsRSelidomkdVgUSfGS9HmqoLmKvPpJkc1aWKTNF7smyHtU\n96wkZ6RE6lWR7GLKiUNi+0wI5IjkLNJiInlaKZM6LlLikbwyIrFFmS+SYmW2EmmBDkQ6TaF7\nq9p+j0Tx1BtEUnOsu3GYI5JbnNnniaQkRFIssSOS2iSS27TWIrFObEmhBlQ8L9GHDbQqkrNK\n02G5KBLbZiJxR1RaJGUnISOS/WyqdErfLpKeh1ZEYrt4I+yJY0YqFvD1TBIVaQ7hhQLMuksp\nHr1WJK2kmR88kWww6wlr2udMVVokW6dx3LiodKTzomxo23szIxKre1EkfQK2aXzTNMKt7alF\nKhnutc5MVqRol6REMlf/jSKZKHQnL10SM8wXSUVF0tXZuc98XhZJN4+L5PeT47gWyZy4sqdq\nRXJzPZFIRSuvNScJiWRNWi7Axq4yYWMuzDkiKSfYyAR+XCQTuza6d4tkm+dtuSdtlLANXRLJ\npHbfk50qTEuRCtddySQpkTYW4IqklBthgUhMNBWKZEs2azdiBfki8WaQcjIrLhKbwqxIRhtB\nkZzm+QI9jUgVTq7G2bUUiR87JpJiU45bkDKR6rdJSCRvrmOFevbY04yKpD88mUh1grxCJZVF\n0p9Dkfw0EZF0ImJpeKk2JGVE0hOckSIlUuQMQldMXV7Spxap1rqrfD29iBSkMQopPkWEaaIV\nhcXmiGTLNiLZtMTeVCryc0RabfqFRar1JKBCTY1EWis8ItJKSWo5Glf2JEXylmbRp9OJGqLn\n1ptI5juDBlSttfQ5NhYpnccTKa+kbJH8vcQjvoJIy7muOSPVtrdsfQ1E2panc5E21NmdSAuz\nT32RWsyCJavsVCQVFelAlZlF0HLE7xdpT2OEwpyCDekaMmizmCxYbUmRDq2/uUi7Mq/tWSkA\nIpWkkUcFJ8JTzEgCVQqLtGUfRErRTKOClT+LSNkFrN7MHKjzyUVq6pEqNCt1LVKbp0lTvdcT\nqZOHDY2etXttkC9SIEXpAhqwQ6Ss0sumz6feGHWg0YB4MyBSlLIi5VJwRqr8hWwnGg0IN0VK\npD6WDWJcUaT290gdaTQgev0QEqn9IEkDkYTp4d7IR3AuhkgJIJIoPWo0IuUSRErQU6tPLlKr\nH4rdjEQDIVKCnlp93sffzX6yPJujLcXDhgQ9tfp0j79pIRx65kCb8fg7QU+tPseMRAyB4pqx\n7xwkZ6RE6nP2ak+tLniPNAfNv40kEpLzTtM/+jeUq0unf3NFwws15B97Z438p/f4Z7m1b2RG\n0UgUGaSeQvKcnPxhw1Mg+rCBMEhFgEj9I/vULvrj2i3m74uRNaSrA4kxKsH2/t+SaK28sg8Y\ne6u2VZNTRW4d8njuIzW3yduqyUdKJO/9UGHieZ8sCIrwZH3YSqQKhZ2wRyFS07ynFansl1In\n7NE+RdpX9JP1IUTqqNpORdrHk/UhROqoWojUNu9pRSpb2Al7tC+R8NSuUt4KJT5Zj3Yl0tL3\nSDnZz5P3wiKBdhwUCRwE3X4RIFJb0O0XASK1Bd1+FY49bAAHQb8DIABEAkAAiASAABAJ1Ct4\nugAAAy5JREFUAAEgEgACQCQABJATKf/R65wj+rYh996sR6rdnZeO1lyQQw3Z3fxjp787a6le\nFyuNskubc0TfNuSmRAklq92ddxq8AzUX5FBDdjf/2Omz0a9Z7VrBYgXt6JE2IlWWcErUqUhq\nakFlkQ7VelCko81eKFiooHoijSlPI5KCSMK1QqQgW32RaPdsNi+tIRLLtyfX8Vr3i0S7Z7OV\ngiUL2jMOe6eG3VkpkunZZ6TdsXWo+Qemld1ZndEXpK1IyfDakPHQ0g4izc2yv9O9vki7az0i\n0vRyMZGIvWSd4fxzzhBJBnJf9mWtV6s7+rsqvZZIxDNmnyFmJCmccdiTd1fzj9R65Rkp/ysu\n/Z/P4AvZxh6547Ajd/1a1e6e6/4LWQCeGYgEgAAQCQABIBIAAkAkAASASAAIAJEAEAAiASAA\nRAJAAIgEgAAQCQABIBIAAkAkAASASAAIAJEAEAAiASAARAJAAIgEgAAQCQABIBIAAkAkAASA\nSAAIcBWRFs/jKifZAey30UUPrf6qMf1ruJJlO9sUHvHKcjeP/Y6vI1wlxih1Klc5wU6wv+I4\nemT9l1+umRjsovgRWxnfPPZbJ49wlTiDSHWgVGAv/AkoL11kp0rtXBTJLw8iCTD/uQ79qmje\nNH/EwxzQK5CWrT0vXCRyl2m5Ivkjwsqet0gPq04U1Ompw1eCEGkX7NJFyvxBt/CNtlzlQBLb\nf7FDW0TSIgQjQp5IfBwTdRqldIVEPEtNrhJOnkjB3vAN7OG4SOw1NjBkLVL+sKZq9etV5o9V\n1OMqIWUXcPYPslFyYsLSbi924SWxtMsXaXlpp8K3Wlwlntz1mjc5haOirnPmdeEiRQ/Z4ysi\nJcbn0IykwrdaXCWcwqXdOMOv+wSymOf61KE8kcLxSV8CI+NFTnlevbWH9yrhNA+Lsjey882r\n/9QOS7tDsLiNHsr4QpbI8cQbILOL2RbUyPL49R48z2wQTwAIAJEAEAAiASAARAJAAIgEgAAQ\nCQABIBIAAkAkAASASAAIAJEAEAAiASAARAJAAIgEgAAQCQABIBIAAkAkAASASAAIAJEAEAAi\nASAARAJAgP8BTzAALC0V8bQAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"Density of y.new[68]\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b), c)\n",
    "\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    " # likelihood\n",
    " for (i in 1:N){\n",
    " y[i] ~ dnorm(mu, sigma2)\n",
    " \n",
    " }\n",
    " \n",
    " # prediction\n",
    " for(j in 67:68){\n",
    " y.new[j] ~ dnorm(mu, sigma2)\n",
    " }\n",
    " \n",
    " # prior\n",
    " \n",
    " mu ~ dnorm(0, 1.0E-06)\n",
    " sigma2 ~ dgamma(0.0001, 0.0001)\n",
    " tau <- 1/sigma2\n",
    "\n",
    "}\",\n",
    "    \n",
    "    file = \"light1.jag\"\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "light.inits1 = list(mu=10, sigma2=1)\n",
    "\n",
    "light.deviations1 <- jags.model(file = 'light1.jag', data = light.data, n.chains = 1, inits = light.inits1, n.adapt = 2000)\n",
    "\n",
    "light.par1 <- c(\"mu\", \"tau\", \"y.new\")\n",
    "\n",
    "res.light1 <- coda.samples(light.deviations1, var=light.par1, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(res.light1)\n",
    "\n",
    "plot(res.light1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "whole-softball",
   "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: 26\n",
      "   Unobserved stochastic nodes: 2\n",
      "   Total graph size: 30\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",
       "fatal[27] 24.39 4.9889  0.09108        0.09108\n",
       "lambda    24.30 0.9559  0.01745        0.01802\n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "           2.5%   25%  50%   75% 97.5%\n",
       "fatal[27] 15.00 21.00 24.0 28.00 34.00\n",
       "lambda    22.44 23.65 24.3 24.95 26.18\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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NRch9aRtNTq60g26dHxKOO0eKRCBk+MirkfqSNR5ZHkG3U2+iXTXjySBT6ORBbM\nSLIL+loM+nOCUadxOvOrMNJ564hHMltoIJ1WR1oUQGquVsc5+qUxqjyShpEoSPS8vo5UpUi/\n9yBFJu+RZFiWD3wfJmS2ZkFGk4G+Be+RlGUNTVZtInVkwRsy3bKiLrgnBx4pJ/HPrCMtCyA1\n1+bjNFLWpL/JeSSbwVnIcXUk++jWKZjZi1h4MI/kZQnpakSX8OK71CxejlGyCsHMkLkZD7uC\nVFrXBQuht9DJYmM036ZZC06GcK+vnPp2AkjNtfU4sz+arcj6iLRfOh+qYhlZ4dTigjEqHsnq\nSLpATwa/K+qEqDefrAOaLaYNU3WkOFJHsi6FXjeTg0ca7w0gVanvzXUkmeZUsWOsjhTDCwDO\nkWmxJGjFyKaEHJ6cGyOyadt4HclP9Oz9mEeK3h9J3iScVEdaIYDUXPtA6v67BqSoHsmvT5Bp\nU05C+7mdxgOrvWrAGdSReh6pTqVxFJERXepId9HuU99SAKm5doKUpn81ZFhHKjkEnfeoR/K5\nhrqORFpHKrmKw0T2XT71SFQ8Umys3ae+pQBSc+3xSPxgVUSKWoh8Va3Hs9PLhxbKfZBL9iGg\njjTVG0CqdlgTkfxgy3J1JOGDDYWPOjoUi5EJJYQVc8Ur6yR8SYYveTJKisDSa5ph4K2ifNmI\nlzvoIUgFSlaY2z0mxj3Sdr1w6tvpSSBNz41vpUMLsrI+oAxRIyYz4OpIll3TpAPZ/bPG6kg6\n3At5zh7x7tIXaR2JLJFux6O5b5fm0DoSZ681UdKrI0Wbc07UkWxRUZTIlNc48VNHnvrVehJI\n8zvfRoeCJHUks0nOI0m+OYYyKGXsBRt8xVpN1JGiEuX+tudd6KGoNz7t15HUBAXzSGLXLEC5\nTwDXJwc0N5Oz3zlXU+e2kzoS/zrNkad+tQBScx0LUpkI+aSBI0dDlryon+BBl7f5iV0Z5cM6\nUpRqqi2LC1UdKY7WkRy6WkvVr0T5OpKLdNRbUpGfdyXaWN5iGK8jASSAtL3FEiF0TJX7eNvf\n4x5JV65OeaSoJil4j1RlD6xGFQceSX7yT8kRhIUh8VUuYTjtkXTRhs1ao8VDnfRxDdfoPvLU\nrxZAaq7DPZJzERaPwqCOVDxOHK8jDT1StJSFGRhnlHjD/NtIMq2LtrTO5n08Jestly037TeP\nJDnxso1FLrfMgvfN/1VDxF8VjPbdqvA2EWk+AwCQGrcoHmm4ErpazEbeI7k6UrJPfhnsPiYY\nmf2/7XnN+YlHYsvF39Mgm0Zy42V2Vu7f5Zpzk0mb7BU0BSG1XG6BrOAmc06+Weu7gPTCnwBp\nc4suRkiugHbbyNcAACAASURBVHTYlQ9xrtuG8sMOJOM2aTDS8Zzk1/Wi4mk/GZtHsFspVwDL\nI7nUW3Wxj9zkJAizQe6vUhYqFVcTzXiVb8/qW9LD0SkeGb/l9aBt5PcDkADS9hZ9hBADXoam\njsLUH3YKQNIUtj1Z0naJ7wYkYaCqI5HrVeZq5pF0vXnkfHSpI5F++1DmlqWO5GaU0aaMTJlm\nwm39uSXso4UkPTyZ2L3N1O6FPwHS5hbVI7lUlmbHqjpS94TdkEtGptaRQr41XowuC2fDU0an\nDXCZlnX/JI02+uubZOt9jF+bkhln/P82EeX7v2pHllLUHal8MChdHJ7sbg+9OhK9j0d64U+A\ntLlFnvHo9+QMgZ5HilWmmT/Uo7Gjm8eyqNrxJ+27mGe0FY+U/9EQxnGJNFno4JrwSHojyeCe\nK3WkEio57CVFUN+ZOaX8U+2Y2jXe+Ta6gUeSWVC0YKB1pL5HcpkyNUtRPA4HpbqOZGFEEg4a\nMdjMJPtmha8j2ZcE/dRMcbL9Y5mmjteRODBVlWJ4pEN2vo1O9EiGgoPDxvlkHWnCI7k6knik\nJKbJseBmb0EnXTL4U7kpUSHM1YvsTkeVR3IlWs3IVSEyDD0Slfw5PFL7nW+jY0FKOrcKVrWM\nMtHiOhL/glCyaZpgoTek13kW+d8EMyul36Mt6005xx1scWwKBbd864Qxj0R6M2Ul3P7HOUQq\nN3jVENndYCjKF8gtNOnDr1gXk1SQsvMjTnfkGAWQANL2FnmhXawKMQwCjzAe1Uk+6jVxTGwo\nZM7Hf2vMqQKArtQr8y+X1XC/OqEwd7fntjpS+RYrpYk6UtAoEmThrFsnyz9ZU27xwEjlt8E/\nHcBHxb9ypmuX3ueLfQCprxM8khr8Akt1c9JSR9L72nVDN5U6Uj18nUcy28PfICT5AQlNTJfp\nltw5X752wc0mKwlJqVTrSD7eRfsASPnoJKMQCz76YxeW+Ob4yul5b9TylgCp9c630QkeyWZo\n+lEfXXiScd7zSHnUaR3JvkQRSs30qxfOkOdXknqkJB6pxLKgd/EWE1TVkdQe6T24ooVGtVqk\n98cLjiB5T5F0kbq7nRdDHvUXaDnEWp6fwinfkKUNd3ra2cMLfwIk3mHp+1V9j+RvnBqcR8re\nxLn7oAGAP+jJeST5hWWdalnMEE9lNiX/GBN7pGQjW+5QLL/d7D2S5OE0lWceyRL13iNFX0dK\nyh9ZrtGIz4eeNL+fn9fCEp0DEuXLNNcFQGqurcdFgwczLdpP15UpknokCzD6QV9mQfnlqDfr\n1kz4tEdydSQNa2V0m0dKY3WkaGQPPZItWGePpEHNR1LvkSQIJrZPyWU/LL+Xmdx/6tfKRSOA\ndJo2HteKKX4FUrTxXnmkRDbceRZEUjWVX3fIQ1SSabIGLwVdHkd5YiYJuZwI56ldzL/mpYtg\ndd1cBiBx+NOMQJcQSLIoVtN6UX4oho+AfxZMCQicbzePFfn30/inMEneBfeVcqaOkrxYwu15\nHonKfwHSaToYpDIX0+hSvi6rQ8x/G10tlPwei82YSFBRV9M1nj1S0gDHHifKAgLuQ6d++X74\n2mw+jFTqSPLLsxwH1V2pR4oW8CQSapzr+mdWNJshIAUFSZ7oDi3qYtZT0t9u0gCQTtOhIOXf\nfiSXCeOfgPR1pCjORjZR99L9jKT8GkQe5V2ISno//hyI+PM9BMnR6W9Yyh0p5Qb4Kc+nBCRe\nwKfUJp0vEq8JDA4kTjZw0j1/ySLzZOG1ayzlOlKSOpLFwS4Hkkgz6vmQietIkkM/I2tXSAJI\np+kcjzSsI6lHkohkpoSLtApZqiNS0LxzlFqrWxA05pEkO6ARKWkdyVLmjEaSTDdFDS1yo24X\nPBP1IlKGTX7lPNpNw11ECgI0lTpSOin9vXiRAFJzHZq1W+GR8iyNPRJXavKLJVrVU7sk4109\nEvXqSGxsbIm2rCjvwkcUjzSsI5EUVqPcI0Xybn2PJHUk55H4UJOlHfKmOQwzSD6ZjjrSQTvf\nRu2Pa8Qj2bdk6zrSqEeKxSO5rLLzSDTikZIukKM5jyQgcehyHoknjzy1s2V79oOykx4pJ+k1\nfzfpkTSFcp5HWiGA1Fytjmvi7tYhTHokTqSR5IrVI3GqK68hkKkdZdMRzSNR8UilvsPfP+If\nTpFxHixJ3U3eFCTvkaS0y0k7AynZ1C4nybPdyZsmWwDEHkmqXWKopAnzSGq6uJDF32ZPdM4N\nIrfMGnb28MKfAIl32FA155JrCpo4DmW0J82+if/ggUiSUKZuFtfzSBzfoqaoc9osmkdKZrmK\nRyJ5JTJIkUGSFHVKEia+uopJKCCSdbQSkSjpNzaSAKPJ8JRk6Z48b3UkSX9ztkM+IvJTIZ+8\nM0Da5GNf7GLHnwBJt1//+0j8wy7shfIY5aWbeeEBs5GHcSYoD9NUgyTr2fIsKvH3y7tsGfGr\nnDTIM0jhrqoj6R3rMkjJIpLWkfgYFKQcjXLnUk8lBkJAkjqSmKmYXPqbn7dAV0BKpOkRASmc\nk2zYlll9uY/NfwKksjnN7DkEKc+IyFYpyPyLgk9/sxtxESnavU5KRIqcgIt5fUCsPFKS29qp\nR+LUXxATlGTxnq3V6Y4u6owtSVGYA0wdkSQqhjCMSFZHsmVQMTiQ+K3zVgbSqXUkgHSi9oHU\n/Xft1C7xgjvJDzMA8h8DiWdllL+4GrLHSFFvwap1pJS0QhRptI4UfR2JnU7KabQaJA0dHIfy\nVCsmMVod8ykpSF1BU4JkLDGzX0figqtEw+5pPn5XR0ry1EkeCSBdoZ0gpVVV8+KRaMojjUSk\ntM4jxaqOtMIj5TkpMSax8khkIE17JBpEJKkj8TIIXSOk6W/xSCly/gEe6aCdb6M9HokfvOqR\nIk/tukjD3wci8UjJeyT5wTGZ2iXJgalHYtNkHqlXRyKe5TEgmv5OWkfqg5RvJ6xRbOiRiOen\nbNYEpGDZQDZJ3Z8FpMjRLaaTPdJk1q7hb6MApL62Z+2W9qyGSh6pfDsFkvEuS6A12ZDHnmak\n2SNlAjkdQFxTkmQDAxly7qAb/5z2Y4/EX2yQOpKY/RS0oaQgaV48JalEMUg6tvh77ylPxdgj\nUbI7vjJI0p+kvyUiyWK6mCxW5zQeu7oOpCge6ZVT304AqbnaH1cPJP7sjvqzJ0lBykNXQeK7\nYyfyIEUJGVJH6trT7FneSVch5FmZhDitI1HeOHdg31ugfJsFboWzfeKROGsniTyeUTJI5pH4\n6xLCm8RGAUmiZOAv2nqQ8pFbzpDEIx166lcLIDXX8SCVOhLbBh+RaDYiRblTQolISfwIlTpS\nqjySGDHKC1H5xhBJ4k/+MkVMpY7EKbVQgcS+zEUkThiwmctE+4jEHxTBvmLbB8nVkdgdAaTW\nO99Gh4MU9Ct1xCvkBlO7lLSOpCmyAlJeu11AktXk2dSM15HyWoR89zjzSAaSRKRAro5UQJK5\nZN4gSZatgMSLx5N8TSqVrJ2AJHeLqEDShXgGUqiN5QlDAlm703QGSDy9IU4tb/BIUZITLiJN\neyT53t2YR8pVJ0l/p1JHKh4pJv3qauhHpJ5H8hFpWEca80iJQYJHOmbn2+hKjxTHPVKqPZLU\nkbr23NSO60g5qebrSMUjSV2o260GaeCRUhWROCtXe6TEdSQuB5lH4lJrlOxhirVHykdePJLW\nkQ499asFkJrrcJDE63DWTjxSfk2mOXlqR/kTPEek5EHKJVSZUbFHyoFIp3bEqeruaV33wB4p\nN8yzt6QRSQ+Ns9sytUtSIS0eSYq4RBzZdNVSYvolULJH0joSRb3dSQ8kjktJjyGdPrWbEkBq\nrnM8Ev/cSvIeybJ2SUHiUZvqiESRCkg0ACnWIOUqkXzsB3X3GpU4x6b3dU3mkfLGlrXjyJSP\nzoEUBCSSPCCDJDaI+Hg5uhWQEoe/AtJpHgmrv8/XGSCpt6nqSEOQNCKJR+rUA0n8jHkkkq8F\npsRJbA4cQlLQg+mD1K8jJT2aJCD5iBQFJEkkkI9IUkfKZV75NYpUQMpvhKPkySDR4MHkFi93\nseNPgLS5RRJTEA2kkTpSKiAlD5JEJPJ1pH5E4hUK0UckXuKTJCJ5TyIgTXikEpGSgVQ8EmcC\nGYRBHUlB6nuklJLApUSfAhKNPpza5OU+Nv8JkDa3KB7JRaRQR6Q0E5HEI9GUR7KAssojSV9R\nAPPpbw/StEdikCqPpHWkDNKIR0rOI8mbBUiNd76NTpza5ZnO5NRO60iDiBRnPJLVkZLUkVJI\nQ48kIDmPNAlSiGnCI3mQenUkAylWIHX/xuBAQkRqsXNPS0d6lk4BKTsbXfWmCTABKT81ARIH\nnbyDwMAtyUNKUmrlZiPXlvQIikeSka9TO83U2a52CA4kNTq8QV4+m3oRSWuupSE5ENk1bySv\nq0eaOFFt9Uke6XNA6v6bPVIujYYZkEidRBWRBCRpNShInC2TRIOPSJqmcx5pDKSgjUi73iMl\nRwO/bh6Jm3IglVyHe9P5P7yReqQzQfqkrN0HgRRkEYIDKb/mrrOCZN8fHdSRNoAUZPBP1ZG0\nId2N/yRjpo5ICtKYR8p1pAWQYigRKZ0F0qI2d92fUAGkvs6a2mWQ0kJEGqkjJU5/rwSJeI0P\nPzdRR1qMSKMgWdZupI4k7Zc3nVLydaR08tRuWdtBmv8bIG09EN587bRBQcqjLslwWuuROhWQ\n1nkkGvVIss0qj9QHSSZmNUi+jnRDj7QsgNRce0Aq/yy0uM0jCQJ11i5RBVIvInHWLvqINOKR\nku77ukei1K8jOR9Wg1Sydv4Axk/U2QJIzbUDJJrfswYp+aldDZLbzkekVNWR5G6LIyClEZCG\nHikN6kjaUBoDaZNHIqqmjqMgqUcaOWcAqf3O1+lgkJJ4JKo8km0X6h2tVGoRKfFcrQJJHiTz\nSDH54Vx5JA+SBQQXkewIHNehvA0jz+Z4ziPlFocgpQqkVIE0daLOFkBqrrNASr6OZNstgJQG\nIHlXLzbEZ+SixDNthx+MgTQ46i0ghQqkclgVSPq0z9rVXQ6fOksAqbm2gkSeg6UWyT6uh+nv\nMZCyxiOSvTgSkZKPSBN1pLQ+IrmjGQEp1SD1+nC7VhEpAaRTdr5O2w+EM3bT+9UgJT+1G4DU\n2zGUh+KRtoNk6e805pFML03tFKS+R/Ld9DwSQDpl5+vU/kBaeyTaAFJyIBWPlHSXHR7Jjk2z\neXMeyZ8BmfQBJIC0rZ3xn3XR7zRQVUeynudAkscC0jqPlEY9kv33dY9EaaNHivBIAKlFi5b3\nNZD8dmMeSR/qqDTXnuoHDFKdtUsOpCoaDbTokdxh996UB8k9WR+bBarJIwBIB+x8nY4GST7+\nJ0Dq7Rj8a81AGh3Ki1O7VA67OtjaI6WxiOSaUZCQ/j5n5+u08UBWfBOkF5E8SAMnMTa109d2\ngpROAKl4JIC0/U+AtG77CZBGZ3Kvg2RPDTxSOYTFQ04bQQprQKqOFh7pnJ2v08undGGDVh7J\nXhyJSP0RfZlHGvZgHgkgnbLzddp+IEt7HOORXgDpPI807MGmdgDplJ2v00nJhpG5z9qp3Wir\n+twoSNpzWohKPWvl93PH0evee6Slxif+GLR5ugBSc50K0tLUrgKpfjgF0qDbidCwQesj0nLj\n5pFGXgNI7Xe+ToeDpNrtkaZbXRmRpjUekaoeZj3SUuPzGwGk9jtfp2sjUm/HG07t9kekCiRE\npHN2vk5v55Fcz+kokNZ7JIB07s7X6TSQ8uP+dq+DNOgWHmmFAFJzneaROk1ZosETwzYWj3Ma\npJc02tx6NB/rkRZuaAqQ+ro2IvV2HMvaTT4zsUHTiDTSXG+y+K4R6ToWANJ4i2PfWRjv+ZYg\nLb26snGAdNTOd7kVOCLS/PaPjEgNbln8GJDmtz5P8EjzeqJHosGD7V3fhgWAJEJEmtrsqIs+\n+4G0tuvbsACQRGd7pKHag7S+cYB06c4n6tSp3dKOMyAd1+28Vi0E2ieAdPjOJ+pWIL3SxkUg\nvSB4pMN3PlG3AgkRqY0+OGt3WTZ8c1fH/RrcLUFa0i1BatD1U0Ga3/lAbe2qxbRhcscbgvTI\niLSn600/yQeQBtrYVRMju7/tdXu31BM90q5Zw1NYAEgr9MLH+1F6Iki7Zg1PYWHbzud5JoA0\nrweCtO8a3ZaFA3duqRt5JIDUvF2ANP93Q21u+ris3S319iCtyy7cloWNOx8302t/NRGRVuoe\nHomGTy3/+ViQ5v98ha9WV7MJ5jcE6UAdF7onrsToNRr4cehSkI5s8U2FE/VOAkiXCSfqnbQ1\n/b0cADE+Vgon6p20O/3drMWP1QknCtfiNG1Pfzdv8VOFE/VO2n41l/bA+FgpnKh3EpINlwkn\n6p0EkC7T6XUk6EAdABK0Us1PvV6BwQNcrk166aQfoZ2NY7eXtGKt3cjW91moc/nOAOl9d9vZ\nBUDaszVAet/ddnYBkPZsDZDed7d9fazySOPbXj+cr9sZIL3vbhs72WCaAdLgT4D0vrsdJ4A0\n+BMgve9uxwkgDf4ESO+723ECSIM/AdL77nacANLgT4D0vrsdJ4A0+PN+IEHQpwggQVADASQI\naiCABEENBJAgqIEAEgQ1EECCoAYCSBDUQAAJghoIIEFQAwEkCGoggARBDQSQIKiBABIENdCB\nIK2/057dX8B2GT4Y33Fq67ndZrZuvdvyHjtvR9hKa7qnwYPZ9npXsunWvd1Wbrzc9LY3Od9A\nc9Hq1m3LmQfjO9LS/lO90b7dNva2fHzrT9IhWtO9DcSVzK1/X/XWi8expe2tJ3jLm5zu8RCR\n+3flljMPJnak8vLa3Xb2tme35eNbf5IO0ZruycLqOjLWv68dWxcslg56w8Zp25uc6/IIbR0j\n54K0c7dNB6kvPRokO8j1Y2zb+6It759GHs1uDJDS8gVZMVBH95JZ8/be6kuzZrfng5QGR7um\n1a0gbTUya9oux7CCo81vcqK7A7RxjGweo7tB2kVE3nF7b58I0oZAoFuvGu0VbctsbEk2fDZI\ntsf23fYM63eMSGUYL2207pO9tFl2bL71to3XHHc1kh4O0isf9qeAtG+3u4OUP683jbPlFsuW\nK7bftrVttBrpNU3XDD0bJKr/XTVG7f7WAOk1rQJp7d3EafBvu623bboeJH1vr/zO2D1Aqj5n\ntgw0RKSXtK57GjxY3Hbl+9qytdtoA6DbQuPKbecbaC4LluuPoYqv9YO5PbftNrN1890Wj2/9\nSTpEq7rfMMaGV7LZ1lSds00brznBNwZp9eoXF1CxROhcbZitpRVjZexKttraNlo3/3qjJUIQ\n9EECSBDUQAAJghoIIEFQAwEkCGoggARBDQSQIKiBABIENRBAgqAGAkgQ1EAACYIaCCBBUAMB\nJAhqIIAEQQ0EkCCogQASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEENBJAgqIEAEgQ1\nEECCoAYCSBDUQAAJghoIIEFQA70HSEu/OXDxjz5A76/3GF5rQIKgA/UeQwwgQRfrPYYY2U/9\n2G+P25/6mvzol3vdfm7noqOG3kjvMYgGP9BG5bfy9BcQR16n9b8BB0Gzeo8xRMlP78g9SBVI\nw9ff4/1Dl+s9BtIEKPkPAkjQ8XqPgVRmbPL7ov4HRGdBgkeCmug9BlENSvKgLIHk/wtBe/Ue\nY2i/R6r+C0F79R5jaJiVs6eT90gTRL3HSYCu1HuMoVJBsjoRPy8FpJE6ktvtPc4BdKkwiCCo\ngQASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEENBJAgqIEAEgQ1EECCoAYCSBDUQAAJ\nghoIIEFQAwEkCGoggARBDQSQIKiBABIENRBAgqAGAkgQ1EAACYIaCCBBUAMBJAhqIIAEQQ0E\nkCCogQASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEENBJAgqIEAEgQ1EECCoAYCSBDU\nQAAJghoIIEFQAwEkCGoggARBDQSQIKiBABIENRBAgqAGAkgQ1EAACYIaCCBBUAMBJAhqIIAE\nQQ0EkCCogQASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEENBJAgqIEAEgQ1EECCoAa6\nL0hU9FpDf34j+lkaXex1xVOfLrkuP36t3777z8+l7R58se47RlqB9LNr4ZHX5r6yK/P999rt\nU/rn2/J5fO7Fuu8YaQXS1/7/+T8Wt17x1KerXJo/Nu20ZpuHXqx7j5EWp6Vq41HX5r7iU/L7\n19d//9m404ZtHnWx7j1G7LR0V+w7/Ujp3y74/+Cr9/cfX9OAf/PDr6n1tz/9NOOfH7JZHdP4\nYWnk67+/f9K3X+nfH/Tt7/LEn0mb/fm7vw9k1+WLpHym7PR3L3z98T2bp3/+ILlA3dNyIYi+\n5V2/uRH/DhfrOSB96+YR/8iMojtHf/LD7kJ9y4++FZLktb9Gr41rhNv9ajk/8Xd54ke39Q+S\nP6t9ILsu//GJKqe/O3P5jy+S/ledZr0Qf/I5/EcQ7PQWF+s5IH2drd/pO/0vX6GvP/7++vf3\n10X4evhXd85+5UvB+rd77fePTBkNZguuke4js2vp69+vJ75rRz/ySPiVe/jR3weqrkt1+kku\nSncqv3V+5x89q7qTEPRnGebvcbGeA9I/vaf/yGf+9x//5lOZn7UT9zNv/k9OAA2vjXtI2dza\nv9rRP3qF+DGN7P7RqkFyp19mCHoqf/ntZafveW73rQOB9R4X694Do75gWb9//fzhr4u8Wk8K\nZAKe5+Nj16bXiPuXdM/eY7cP1Lsu7vT7U5ZnYD/+9pt1j391s7K/C2RvcrHuPTCGIP3Rv2by\nag3SyBn2L/QbWXNt/uh18dHS8/CfzrDGQEq/vhNPvqrT+bsLPV9R6HevsYdfrHsPjAFIX1Pr\nH//7PQJSvd/8h9ygkRXXxu0D2Tn91Z+P1XEh/fdXThHVkHQQ+QLUe1ysew+MAUjuLP6RJ8Xq\nkf6r9pufdg8uRf0E7/mH9vDPYENIzsPf3/IZcqe/B1KOWdQD6e+cd/vbGnuPi3XvgTEAKV+5\nP/NfmrX7ntNGP+V8sv6ZTQS5RsauDSd/JO+TW6n3gcpkLk/c3On3IH3vTtm//axd4mz5t9LY\ne1ysew+MAUh/5auXE6tafujC0nd+uoQlee3PNHZtXCNj12a0NOE7hoyjvNbOnX4P0r9kFyj/\n3RVJ8zK67lz+5Vp7i4v1MJDSr65s/puvyN8/bGXDX1/X8qc/bd1rLmNUN1gaGbs2//20YuGf\nXav9fSAFyVZ/2+n3IKX/fn5zKxvSf3/InKE7o9UQf4eLdW+QoHfU73esawMk6Gz9zKbmzQSQ\noHOVrdXVB9FeAAk6V9/o2891Xwd8lAASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEEN\nBJAgqIEAEgQ1EECCoAYCSBDUQAAJghoIIEFQAwEkCGoggARBDQSQIKiBABIENRBAgqAGAkgQ\n1EAACYIaCCBBUAMBJAhqIIAEQQ0EkCCogQASBDUQQIKgBgJIENRAAAmCGqg9SAStVPNTj2vU\nXOtPafuL1LzFN9WVIF3X9bMEkB4ggHR/AaQH6OgTNdM+rtFKAaQHCCDdXwDpATrqRK3wyrhG\nKwWQHqDDThQtto9rtFIA6QE67kRxJAJIrwsgPUBHnqgOJYD0ut4UpPe6/se+G7otSJvqnBcL\nID1AB7+budF66aKK8u/9BZAeoE8syBpAD7mUAOkB+kCQXCB6xrUESA/QCe+m7mLPWsy2h0Pj\nj+8rgPQAfV5Eopm/7imA9AB9HEg0++ctBZAeoE8Dqd/pE64mQHqAjlzZsOCErjiRwz4fcDkB\n0gN09Fq7mR4A0koBpAfosNXfy11ccCLHurz/9QRIDxBAuv/1BEgP0EeBNNrj/a8nQHqAPsoj\njfd4+wsKkB6gj8raAaQD+75T0xfok+pIEx3e/oIeCFL+nLvo0+72532TANL9L+hxIFH3/zS3\nI0BaqQ8C6UZmbZsOA4nKPhdkhO5+2rcJIN3/igKkBwgg3f+KAqQH6HNAmunu5pcUHukBAkjz\nL91ByNo9QABp/qU7CHWkB+hjQJrt7d7X9HyQTrkfwL1P+lYBpMUXL9ehUzua3xMgrdSngLTQ\n2a0v6qHJhoVbSwOklQJIa16+Vsemv9Ns2g4grRRAWvPytToaJM6CN2lxT+/voQ8BaamvW1/U\nw0FK0/doB0grBZBWbnChjvVI/AAgvSiAtHKDC3Vk1m5pT4C0UgBp5QYXCgXZB+gzQFrR1Y0v\nK0B6gADS+k2uEkB6gADS+k2uEkB6gD4CpFU93fe6AqQHCCBt2ugSAaRztevAANKmjS4RQDpX\nAOmlnm57XQHSyQJIr3X0BhcWILUQQHqtoze4sACphQDSax29wYUFSC26A0gvdnRXkgDSJoVX\nuwNIL/YDkM5o8fCmAdLV/QCkM1o8vGmAdHU/AOmMFs9oerS7Y8fB+4O0oZubkgSQNmkqIq3p\nj+yfrQJI+zY9UwBpk0Lvv9pdv78x4G4L0vW/2Lepl3uSBJC2KJ4GUtXAYScqI0RzPQCklQJI\nW/aI+uA9QMoI0WwXAGmlANKWPeJpHuk0kBJAaqKPAylOPL8NpG0RKZQebuWR7gLSxk5uSRJA\nWtzD77wbJLpjRCoNX3HLtN2dAKTDW1zR9Gsg6YPNHmkGpNHp4jkgacvTU1OAtFIAaXEPv/O8\nR5pqYz4iXQnSos7oemsfAGlli1NjfUO7B4G0UEeiwXb211aQdhzbIbojSLckCSAtHEy98xEg\njQoRqeUOJwggLRzM+M4rQKo3oXDvqV3dxSm/qjjR9xE7nKCPA2lmp2Vt8Uihenh3kKZ0OsPH\n7HG87g7Snl4LSCN7nza1WwVSGLa199iO0S1BuiNJ7wlSvAFITtMeKYzvgIjUfJej9VYgGT4e\npB459/JIFpEuAmnRCQGklbojSLt7PR6kN/NINHgwucVh2jl5v5vuCNK2iOS2PhYk72e2RCRa\n45Fm7s1VawAAIABJREFUjdJR44ZGH57S9Ys93I+kZ4Lkh90YSGkGpAmSVoG0yyPRbT0SQGqn\n9wRpLiLF8UbXgTR2AGkxIqWbeiSA1E73AakMnSFIc5WljSB1f4d6+/J4ySrs8khzU7tqw8kn\n4ZGa7HSongnSixFpH0gbp3YP8Eh3yNrt6wAgTbeYjUR+agmkuAmknmJ5OhwKktt3m0eiQQcX\nDpubgnQ/ku4DUjoIpOmItAMk/ftIjwSQjtvtON0HpBKRlnqddEzHgpRO8kgA6bjdjtMdQdoS\nkWgYkeg4j3RKHWl4EG8M0t72AdJkiy1BSvMgVR4pukZf9khx5HV4pAPa/yCQ8uDalhFSkGI3\nrqPbZhEkHxGIwuqpXZACbVwCidQj8SYrQHIRKc5EpPDZHml3+3cj6UCQdJ8l4yEKG0DybWwE\nKa0BaWCFhJQYxt9NDVKPtXmPFD7bIwGkNZu74bzc4hCk3EQeUbHeMPYiUuyBtN4jeZDSAkjB\ngSQbWD+VR6KXPFIYni6A1HDHg3RHkJKCRF10kSfchnEJpLChjrQ0tQvS5maQ3CE6j9RDVOJR\nHID0IRHpheZvRtJ9QErjIOkTRcENu1iDxI83eaSRZAP5YRw4VH09N+KRVkak7JFoCqTQq4wB\npKN3PUJ39EidZiKS/4tH8isgjUSkCZDS0CNFCT5rPBJvM3IrSVfo7ZrrIlL8EJBeaf1jQNq6\njqtOf/dBcjiMRSTJTAhIVaTQPTXyTHikwjxVICUFSfxMTckUSCMeSSJSsWEk/0pEkg8eAanC\nHyA13vcAHQjSxhZrkPKwmgIpBnEuIyBlj5TmQZr3SDX6IYOnU7sRjzQFkvUoHmkCJPNIGsER\nkY7f9wCdD9LMPdNc1i70PJIHycYZgxSHIC1HJBmyY1O7OiJJHFrpkXLrGpEMJO+RyptWkHoR\nKQGkE3ZurmOndvN7TkYkD9IwInlLwSAlD9JXtyGUAU49kNJWkJY8Ut6vgBSVlVBHpL5HCvJu\nBSRJ9ic9doB07M7NdXCyYTbb0AMppn4daWJql+tIPP8bRqTY8TsDkotIabyONPBIFKbT3xyp\niLMaktsYRKQpj0RDj0Sf5JFea/xDQHLRaA1I5EDioBHjTB0pqJGqQUoMkp/aWSex/IeKG/ER\niRihgUeicY8UBaTUAyn0PRINPVIwkHjLaCDRB3kkgLRhc1oLUhoHSZ8oG/PQnotIbmoXJSLF\nkYjUryMVkPxqoQqk1ANJiHUgdc3GKiJ1f/uIJNNBAykUkIKsgIgjX/G4RgBppQ4HKdFKkFxE\nykngXh3JRZYokycGKXmQaBok3X3aIw1BijLjNI/kB7iCFCTyfW0YOdmQm3Qg1R6JZE2Q90gx\nGkg5IgWAdPjubXWsR+IHK0GiRG749kCKBaQQtUzTi0gkIIU0G5HC0CNFocV5JD2SyiOlYFMz\nedE8Up6ZZZBSjkhU3JAHKTBIZWoXq4hEClIESEfv3lbHgeRj0nKLHJHIhm/gMED68V2B1Hmk\nKZC6XfTTPiNgIMkDHrPeI0X+RyJSdBmSmLGd8UiRDzDn8jkiRZnakd1Bjz1SnADJeSTK7YSP\nmdq92vangLSpReJ8Nw/fr3EUYnIeKUT3Cf31Wt8jUQ8kGa4Mks7dCkh+ahfGQAoOpNxKmPBI\nxLFIQbL0dxeRok3txjxSHHqk7sNEPNJHTO0A0gF9UwjjIHFE8gu+UygLCqSOVINEBSQSkIKB\nZHUkWgQpaETSvIRFCmGTEyJhAFKGvIAUK4/UzfQijXkkBilzCJBO2L+p7glSN33T9DfJM7Zp\nriORBylHqFg8UiwRKfZBsohE4pFycMuTQ+5+BCRXRxKQtI4U80SygMRBK9YRqZuJloiUQcpT\nO7I6ErmIxAHtEzwSQDqg727q9DWydLB3MciBFGLZ+GtYduNZA04FUmKQuvEoHilym8EqrlL7\n5IjUuZVgESn0PJIDKdQeKRaPFDm/SB2wvGj264ngPJL8yc2GDBJ7PAbJeaSuKXikMxtoqNuA\nFJIHKRhIeXJXLfjmlBgvfRhEJI4R/LmvEYlSVI9EPiKFLpowSKkGST1S6IOUhiAlBSlpYpvJ\n0YgkmfygIGViJENRe6TInwBE8EgnNdBQ9wHJRaTsETT9XYPEi+KCJiekjpQJyht/DcnskYLN\n/TJIIdqiIu+RQuWRapC6FmqQ2EjlgS+TuAwSz0nzuqYgdaSQKpBCAYmPjT0SqUcK7JEYpHwU\nnwDS600DpGGLeQBZ+ju4OlII6pE4DHAdqQskwSJSKCCFMPBIDJKPSNTzSGN1JAYpOY8UOaLk\n+SCR1JGimLv8V/B1JLE5McNjHokhl6ldZrJ7MxyRkoH0CR4JIB3Rt3gkBcnVkXIdlD/6E4PU\neYweSIE02dAN1DxYc9RRc1KDlJcXjHikyGTp9x76HimaR1KQskeKAlLXjGTtKo+ULR1xAj8o\nSJFB4jcqIOWEA3HTiEintNBOtwGJPZJl7bxHopz+LgtX88hUj0TskTQi8eIAntoJSDwPC1VE\nigJSGAeJE3GRA1Y1teMsW+T+U05lOJCC1JFqjxQ5lVh5JNkpCM0MEnukHEGDX7UKkI5ropXu\nAxJ/bHePO45K1q57zCDp2Aqc/u7mTAySrARikIpHIqkj5YikIPGqnjjqkRgkntLNeqTMbd8j\nFZB6HqmbeSpI+dhyIBNUczfd3uaR8gECpJOaaKUbgRRl7GlAciDFAhKPbgoeJC47DTwSOY+U\n3NQu7xeIzVD2SGR1JE6pDUDS6aF5JHZV0XmkfBxaHnYRKfLUTixT4OPTqV0OoMxaVI8kcfHQ\nU79ax3XdomWANGhRCOBVopETWZzt6qZx3ViNOX0Qg/dI3QbskaIGpsoj5VjAIOX1BbnOxImA\nyiOFkrXLyC57pBKRhIkMEh+690jReSRSjxRrjyRvp4OKPxw+YtEqQDqkbwo2/YpWRwrikXhq\nJ4mIyPOj4pHybKxEJO+RokakGIPUfgYeSb5l7kDi5drqkQZ1pCCrs3VqJ0xwHcmBFBQkkluE\nkfdIid9b5ioJSMzcmR5p4+0AmnZ9kzYa6T4gBV3Oo4aJp1SCRQwWkfIym+KRsq2ppnbikbrs\nV6kjBU1XR+5q3CNl/yJreoo3C/L/ccYjBakjMUicmUsMkjScQdI6UsaVOMnYHV2UfOS5Hqlr\neMvtAFr3fY9GmuhWIAVZWZdHE/GSAfZIudDKXwjKSHmPFCY8EnFE0qkSb0c52unUTj0Sj3LK\n3HEyWkFi25KZ5qBRgcR1pOx0omU0uA8hJ/LETd6RryNx1AxRZnqcfMwbx7M8kotGAOlF3Qak\nWIGUJCIF8UjEMz2pyvBw88kGqyNR8UgS0wJJ1s5AyhUojmzskSTbFqJMIqN4JE5ykHkk+S5T\nUI/E6TdNGTDONrXrjq94pOA9khRkJTwleTv8RaZ8ZL27FR0MEtem5zc5rO87tNJCtwEpe6Q8\nZY+xeKRQeyTO2wVJj6ec2cupsuw0cjGzeCROMnC6LHskUpCyR4platcDKXBympnKkzye2uXu\nuNxjSTZiC8VLunnvwEt8on5pPORlRzGYRyLuIteRJOwxSOKR8vs/MSKltO52AMf0fYNWWuhW\nIBF/iEcZX/JRL16F09F54sOpu8gFmphXLwSejREVjxT56+tcR+L5YU4hiEdSkCg7nShTvqAT\nR+u3BolHvXkk4oXqFPR4BCSSuMggBdmgqiOxV+JO81NSkA38/k/zSPwAIL2o+4AkQ8rqSKGu\nI0UFKYTUB0mGsE3r8qd9kMorRyaeH+Y0tEAaXR2JJ2UczqKuMs3himu/gXPmnG7LASjXkfJ/\nxdxxYlBW9xgmvAyDPRJ/McrS35wQ4U+KIOsfbNIaT/FIVUxa2OCwnm/RzOu6DUixgERc9ok8\n0nJ1JSZJaPMHvOFU6kh5h8gg5aGbok828MQxr85jSDlu5AldFDcUzPdH/SZr5DRFsDpSTiqI\nR+IJqHTNw1+Z5SJrzpeYR+I45OpI6pGCvimKgrgk64879asFkFbqJiAFrSPl72FbQZbYI2mA\nkhJpoL5Hyk9wXVY4CnVE4lQGL3SQfmxqF3mpXhRkpRVJR0TO2gVZhc6rehQNOQr5MxkVPJ+T\ntD1HrNwym6NsjfiLR8I9e75C0yestWvV8F1IuhVInAJLli4IUl7lqMALAThfrDNBdvFR45l4\nFBnElLMKXDNlx0/cRe2RIs8cXRPSmdSRhExNuCumOT3ACXIBWeEKSnMUkBR9EuZKHUk8Ukk5\n8MLwszzSsg7Pc9ymoRd1H5Ak/R20jsRDr6ojBR5i0cYeg6Q2XxPjAgJJRKKo8y2lwnkkzuQJ\nnZzgkCmjjm4BNzEl6pEkscBHwhPRpGkEqyNxk4Jh1ESHTOnEIwWNREqzJTmOPPVz1yLxooul\nX7dq2d8dGnpRNwHJ6kjy/ThNb+VPc2L3IGjo1MnqSHl4knqM4pGIc86ljmRZtVJHsnyby9qF\noB6JnyzpAKkKB12GETSI5oOJkhThMJRRS5LbYMSCeiQJmIH8PDC3xtzKAvQDT/1qAaSVuglI\nnK8OUhVij1RCi4wy+QUxqyOReCQ28To1ch6JkwQ6twulSlQ8EvOi8SzaFiR1pKDpb0FXppcl\nJS8riCT4SOa655F0Oap6JN6aotaRKo+ks8lDT/1qHdR1u2YB0ghIvJTa6khBE9oSSCho3qFM\ngUgCE8+vtBprIEWSrzpIUk9yF8UjEdeRLGJpvqJ4pGQeqWQyZGonPLo6Uog6Q/UgBUkpqEca\n1JHMTpUnANL5Tb2i+4Akc66Qygc0ybSKB6k3/T2Q7BNdTT5n6PLCUf2s18SdAsIL+SSDpjls\n0kBWOpY6UtR0gM06dV2f7BzFYXH4EUzIIiSHUK1zSdJBPix04ni+R9r4O7/t+r1lU6/oJiAl\nyxNzXVIHW9BP6WzU7fPd5k/5dtuWs+OByhMrrhgJSFHilQQaLt8mNWFaEDKPxNNIklf00ISX\nUHmk8nRdRyKOWeqRxGAV2KPNQg00m1qeV0darMcCpLW6CUhBvkwQSONN1MSxzH94cAexOzrD\niyVYyYq1MvvSpLTUTnlwR80tSGiRghBPunStXQ5dpFk180jkaq2W6i6WqaojMS3JcnK5A/NI\nsrN+H6nvkTgVeOSpH7R78soGgHRQ3zK14k/iYBMg+y+V/7lpXjTf4QxOyYPlgc9rRNkz5e+x\nasjRLwhS1OUJ1oSareL89Y8SPixHZ3PHpFkR5+HsWILZoKDlX0bbPFIsHokj7pGnftDuuSA1\nbfUeJN0EJPnIj/IRHyQvbR/PFJxHMi+hbifakzaAdfVqVEOlSxpsXhU1oWBmR12OB4m0juS+\nLKSWStHjnUtRiutIUlJyM1SpI2kOxS1rkHmd80inpL8BUjvdBSQb4ZG/rq0jTfMGkRe6uU94\n3oHioI5kX/rhb/iFIMuPgk6gpI5kUW/okSTvYRxrdOG0tU49JU9BZXao3wAJmlT3HqnyeGTv\nxMVPrSOFs+pIV3kkgHRU3zIfklmb90ha0ZF7B5Fmo206pjMpX0fiLwRJHSmQ+5rqqEeScKU0\nyexL68GhTgaWPwp1QeeYUfMHZMaID4frSMnXkUJdR6LSajitjnRR1g4gHdW3zLfM9EQDiTQw\n6QjzdSR1RWXo6sblM17T47ZOlDElyQjYrVEKkTbhCsXYyIDve6Qg674tRDFT0gIZGdKuLvRW\nj2RhUPIYJ3ukFXoASPcg6SYgmUeyeFT7nrJcNNgKhVAluWwcaxyTGpF6JPm+kKsjqQ+r6kia\nllZ6ojJqBoaMWjsgV0eiqJUoIddA0ntAlrgTgh0yXeKRVuiQrhs3CpDcY/VIkmOoBhvxdw/M\n25exKN+os8/1UkciZS/pXlH5svyEeSQl1+crqrikHUbnrAohpUmZsplHyketAatE2WBthdE6\nUoj13U8A0pnN7dNNQBJ3pLO34DxSjFqy4a+9llhRALEdoqIYZOFOAan2SGUEU5lJRjU1vGDJ\nxTf9VyeEni2Fn6xRpc3uEKSHG4N8/UkOZLSOJP859NSvFkBaqbuA5IYiE0WaVAhu0Nd1JIlC\nfkxXdSS5N6Pxwt89kvaMU1tsWsiMdZywAykTTJnMkfdIkj30garnkZRbqyNVGYbuf6n0d+ip\nX60ngHQLkm4CkgwysyK9daCSzbYY5TySn1wVhvTOd0FvP6J1JNlNB7A1QRbikgfJyr1WR9JM\ngvdIXEeS+7xqUIsawfQgiQpMJRxalj8XmryOPPWrBZBW6iYg0T205JFKoqFi0E0p1ePZl2WL\nR1runstOqiNP/Wod0XXzNgGSSZ1K8LFAPrC1jsTf7rMpX9TUXrCQpPEilBvFyddZbSJnsctU\n5lpzhClL/ut4wha7t1WYcnLOKlf+MBywPEE89NSvFkBaqbuANKmSPdBJkU3RbBmBmyyRiyO5\nLGuLXPOiCRL/79J/lMwjKS+ptBFXcaJoGwp2FDbxHIPGZpd296OPqCMdm/+9SIeDNLObn9ox\nBSVXHfWuCGsUdVVE7YLy/YLLanFLUvRGsQx7y+R5kGJZq1Q1XTyWkKCRhGLJY4xQ4/KA3qFJ\nD66ORJjaXdrigYdwLEjMTDKPYY4+6IoEcpxomi76adsMZ1HLtSTc8fPkg4gBp/9ZriPF6UBD\nUk2y/ElVQ7IGy9fSJc+heUd64zoSQNrUsNNyi2LQU6gSzyU48dpQIvlVljDpkVxtyTzS0SLX\nqx681pFsFYR+m52iMFo+AmyJX9BG4jt7pGc0edwhbD1YWtxtUEeyG9nnD/5oYaCqI1GZokVd\nolZl28r47v52dSS5H0T0m+v3HlzMqOtIfv5mIUmmYZEc0PU97PoeqaJOv2phU0T5REgfUUd6\nRpA77gg2H+v8L1jVL8moS54HmxQ5kPRFrYHaUJUvLEV2OMG1Z8O71JHKh79gWvkVD1L5GRlL\nA0Q363TIajdaeYoWpaJ24HIYOj/U71lpCNXbjb2zRwJI2xun1SDZUAtllOpNDSLXKoceiW+M\nUL6PFEojcgc6c/hu3lfWc8cyuVrjkfyCVff0oI4UdCVS0DpS3ZQmB6tlGDk7Qvbh8MYeCSDt\nan7l1I56waQU/UkW1PB3hKh8FWHcI+lianfTEjeMo87KCqn67SCjhVMFZSlDCZNB7xZpvWod\nqe+RKEkgsm1swkpkGXjZiXT9g739d/ZIj1grceQR7DvWuXveDj1SMGukv2IZqIoAJEt4/ARQ\nnpeFblRtq14k75M4ekXHBsnSHl3MWmjSIW2J7Wir/IxGWwLrkoHm6ZxH8hNBWbCuXyWUaSlH\ntfQJdaQnfMPp0ANodaij2TxbOlDNjVJVGxLxT43rKC+j1Za7jnmkKAGvX0eSBefRJ960BXFG\nwmgsnDGh2msJT8GaCqQEsp/ywVEpl/eW7F1HvekQh8MDTv0OAaTmB7Aj2bCQuBurI9lQtbHM\nsaR4JLv9t+CUSjGnYMBE2e2Eg36lgnTBEE8Gpz2SjnMZ9d5kTXgk7lyQkYmn3slhxG7Z4bu2\nqzrSK6e+nZ4C0uUkHZv+Xv3T88HltENvUXRUj8T309L7cFvaWbfT2yTY38mWNbjpWrn5lnFR\n6ClrhDRH4OjIberUUcZ/8vM534QUjYZ1JKVX60j6s38xhPgJHumo9/K2ILlotAakEGK5V7H+\nyIp+/heDrx5JCjBUxr78v1s/TXw/cLJbj4zWkUjqSOV7FFXg8KuPQrkbg35xPbk6kuY5eguK\nQpWLEG+lHknngfyt+E+oIwGkfSClmQx4r46ktxIK+hltHslFAZnK+aFr8ysqXqXnkcw9OU6k\nGqQ/GuNXiEeLLSkq0mQeyX3HyIq9ZRZIJfDYJFF/o8+FPirTRAu/Vkei9/VIh72VtwdpJgNe\n1ZHYxBQ7H1zRkn9mRby4bsOWPN/+W5cB5QBkvwOWP+IFQFemyvdDCPLzR7GM72qWl7QLA0XX\nZrsvGDqGtfrkPZL+UHOM5YaqQWZzzuLp3iTHq3Wk/ae+pR4D0tUkHb5EaCYD7qd2egvHKIs9\ny8d8qSPxb8amys7bcA7BLdXTOtLAI+UdU9mj3PLHrec2jxSFQyszUf/7SPKz6/WTgetI5D8X\nLI0e+YcEg9yGNd+ur/xi09t7JIC0I2u3tGfPI0UdWPIrR7FfR+L4ofO9EkgUnxx69AuBJUsd\npTLaRbRU1ZEi13gXPZKmuuVx8UjyWxf6A528l8wldf1S8Uh2l//Iv8hMzKx6JP0JGp3IvnDq\n2wkgNe/+0EQo2YDj5DWpR7JJEX+qB/lh87k6kg5/55GS1pEcJLokIXukFC0fGFyGnW8FFn0d\niVxE81M/fShJBPm1GfVhUR2cxba8nDaW35vJMSjqx8K7eqQD3wlAyg/FmkT90C54BKsj8VhO\nBRXFSadUUT08B4sQzSNFMkBICrqyoEF+/CVPBIvbiVX/JRMfQvmlFp9xsINa45EkvOnvNwW9\nB1/ydSQaP1Fn6zkgXUzSTUAKehs5/UIcD1gevXJDBf5t4zjhkSS6uG9VaB1Js3USRDSiyOBO\nClJeM2EhKXK0kLglsSpFWX0QdWmD/vKSfgL4OpLO2Cg6j2S/z8y/VpHhkQy8gKQB89BTv1oA\nqXnvB4OUf4ZcRqN5pFgSxDxLi/ZjFTLxqhZBRK0jRfVISSjIAShZHcliVKSUR3Firx8dcRMe\nKalH6vZL6pFS0K5LHUnimNztJET1SPkGrPIVxeQ9UtJQydQeeepXCyA17/1wj2TFlYFHYpDk\ni6QpRwWe2pVKp7gQNSbqkSKP3zRYhRd8RMo/R2ZZdA10SRpIfB9IadN+KzoF+/otBV3szRm4\nfHx2KFGWN1miO/FbZXZTdwQ8H00p6sq7N/VIh74RgMQPNcFtH8pkk6X84T/mkagKQt3upHWk\nnKPjQi8PXENI9tTeclpQPZJmvS2sRb2RhNaRzCPp/SWKR8pfIpe61NAjRdsvFY8U1SPld9Yd\naQab3rSOdOwbuZSkm4CkP38UdOWMeKTIv7ec+HM7l5HMI7nbKcpULmkmWlILbDpSGfOx9khW\nR0rikbS1ZEsTGCSNVZR/l48Pjh9wXcl5JFkey3UkMXnMUe73K+hoHSnl8lFKEsUUJIX20FO/\nWgCpeedHeyT54JZP5DxRSsQDVT/Gc6xKPM4p+Z/DIwEpuTpSBkmy1Tx/q+pIpJY/jXkkoVhv\n4iVTQdKfjE052pU6knoknVymcY/EicYuSUl8V3KNSCTpBflJZ/Z3B5761Wra9cHvAyA5j0R1\nHSmpkwmSKSBeEmQgyexJb7udrDbKHilxi4mslZKWsExfv44UNbWQg0mSOpLkx5NGNHePIrL4\nGYkbSt4jMWhUqlpMfs5U8Jf5eD6aUlTs6S09EkDatuWOFkmLrSTfGeKxKguiOTYlnm0lzjoL\nSPwtBJJibLceianKvl1AGvNIuVIjHqmbWGUKk+YygvulomB1pIx17ZGSeiSuIUUGTj2SfvFX\nPJICKN+SiikWj8QHylO80L+H2WErpjfdMq1Bfy0bu6D9Nn2f45FIb2Rqgzp/THcg+TqSgiTz\nOAXJVuuI0ZGIVHkkknsVWfo7hy4qHimbKk27MUjys3/ZrgXJwAtIUT1S5FsXc0yV1UzB6kh6\n5PmtyHfg5cfEOJR2HxqJC7Q8uTv01K9uGCA17/twj5T4g5uoeKQYM0HdfI7DRBS6uo9Q/pYd\np8tjAUlmbtxkDl0CGyX+zlNMamEUpJT7Vo+keWr2QrrsQBMJPIkTj8R1JLkjC8lNjQpINtvj\nVImu/MsfCyR5+eKRkoAkHolGT9Rxl2DnBi07u30HTfo+eGqXM2BJct/mkTxIqYDUufWkdzIJ\nUTPkfv1oBVLtkZLOyAQkyiAl80ia65NcGuepc0gkqSOloUdSj5cbSlZH4jJS/hhIziMlTdDH\nUkdKXVQqHukUkBabBkjN+z68jpRI8wnskZJEpMQgFY/EvyohESnPt2Rqx5EliVXP8yYSj6Tf\nAcog5SQdSYNcR+rG+oxHygskMhuJw53zSFyZzS1GubeEgJSEyxGPRJVHYr75mLs327VyDkhL\nehRIzzhRx07tUtKpHRsk80jE25HWkfhDm4pHShaRQizfD8pfcUoCknikZB4paa1K7iWuxkVy\nfcM6EteSEskiO7ZfUkfKnHLg0YRjSmzvZBpI/BHBaRLuqnsjyepIHJv4PMjU7v1AOuFdPOJE\nHQ0SQ5BxIi5dBqEo14eSTJPEI5U6UgaJCkhRQQoGknxJlutIGaQkeTxZ8ZZHd9RVSEmy1jkq\naYUqKkiSMkiJU4PZ0pEcRIgKkgYgXmLEZippEao7LpKpHgfcPMXT8wCQbtzF610f7JESeyRZ\nOSCZhuhB4k/9XEdKVNLfJSIliUiS+DaPJGOUVwwpSFzaJV7xlgOf3nk8JU1s6FSSRzopSEmX\n8/TqSOKRmDI5hJycG9aRONnACf5EMt3LYQwg3b2PV3s+AyRJbVnlM8p26pGo55EkJ52qOlKS\nG2dnnKJEpCRTtiADnaT+qd8KYtyCJKSNI7f4KOX0O39xooAki5Qke8f/JG45JfuKBuX5W+WR\niHMpEpF4/pjz4TkKU99BHq26i+X60qs9HCSAlIddntoJSPnjOUbdLkckqSPFoUeKDiQerpyq\nYJB4xhQlbLAZ4YgUdbA7j5TUI6VSR3JTu8iNs21KUT0S8V33DCRSj5R4aierBPmjoUSkJB6J\n32UsU7uTQZpSs65Peg+Xnar7gJQTVuyREmcfBiBpRNI6kpHnQYoGUqoiEtugqCDlbvK47nuk\n5DxS6nukxCB1ilz5oVQ8Uh2RJA/vIhKnOfg9VVM7fscFpASQbt3NKx2fAVLSiMQMDEBKdR2J\n9GZ1DFKSqZ2sC3Ig5T6KR4oSkcQ80ZhHSlESbeaR2MWJ+0mcwkjyNQsDifzUTuaAqUzteAV4\nxmTMI+XD4exDcsu/AdLdunml46PrSPlf/ZpCkvKkA0nIii5rR6QeibxHSm7JZ7YbPEjL1C6i\nKm6mAAANk0lEQVTHIdIeuI406pGCGCKOSEki0gCkEEYjktSZK4/EWXkFKTqQ8ilQj5ROAmnR\nCbXq+rQBfhVJNwMpOJDGIpLGkxxeeIGoT39rRCIxRYljTSogxSoiRVnLnXuXxaRirwpISaaa\nMrWT4CQeqa4jGUhSRyKqPZIcVD8imUey9Hc6ByQaPJjcolVPRwsgJQHJe6TyogcpFpBCoD5I\ncQhSiUg9jyQgcTdB40wVkThceJD0uDIGHAD5IFIfJF2OutojnQzSChsGkJr3e3zWLpFU9otH\nsu0cSDyaBaQU+O4l3fN9j5Szdqn2SNFn7QQkBSPpzEsXNrAn02JpCtZ1mdrJDUxyxkMmSgYS\nr3qqQKo9UrrYI50H0onD+yKSbgaSrrzRqV21nfNIDFLxSCVrZ9mvxOhUESkjJhlo75H4GQ1K\nNUglIqlHSn5qx6smBCRecKcNp5yH5DdgEcl7pDThkWZOVFMBpCu6PR2kKtlQfFEFEt/TIX/F\ntQ9SKCAVj5QUJI1IKXmPZCgJsinVHikpSHL8vOIirx/v5nceJEvoyxtQjyRdaUSS91d7JN1s\n5ES11WkeCSDt2XJHiw6ksnQ7ukErUzUDKWlEyjvkW+vz3vIFuQokmzUxG/khOZC0A/MqgVdm\nZ1rLwFaQKu8WODM4FpF0cV4VkbxHUpD6Huk0kM7K2p06uK8h6X4gmUcaA0mSDVm88k7S30k9\nUlJ/MQBJp1IakVKJAvK6RaRg0y5etGMgpRokntpRmdol8lM78UgOJF4B3otINnO0Xt6tjgSQ\ndm25o0WrI41N7VSRYSEPUjCQggOpX0fi7X1EUo+UfNZO/9GIlIpH8kdRDqpM7STZkAYeSd5d\niUgKTbRD4Q76HumNQDr3+AGSgpRGQQoGkjxRPNIoSByR3M+cVSCFSZCKRyoguQ2SH+J9j2Qg\nSR3JIm0yUKK25CJSzyO9XUQ6+fgvOV33A4lsvlWFIwdSFZF4sPY8Ug+kkYjEP/cwBMl7pG6D\nnkfK7fjj4gniICIlTTYoSCH5iKTN1D2nNwXp7MP/ZJCSTzYk80he4yCloCAln2xIoyANPJKF\nh1S6k4GsIA08kj+sIAmHAhL1QNI3GvQfm9pRzyOVNgHSs/rb2OkJIKU5kOY8ErsQblNTBNJa\n91+LSKnnkfjRIC5UIA09kt+uD5KPSOVf3dJ7JOp5pP4xTJyok/VEkC45X/cDKXmQao+UBiAl\nAykG12ZJf5PvYuCRuOEhSMlyCkOPNA5S6nskKQ4NPJK1VN0mvwfSaenvRTXo+vyjB0gCUpoA\nqY5I3aYhqE2pQEo1SON1JGt4JiLlAFJ7pLjgkZIHKY1HpPykj0iu496h9E/UyXq963uP6gu6\nPAUkfnoqIo2A5DxSr80BSJVH8lO74ZGVp6JPivMzvfR33yPNgmTVqompnev/XTzSzR3L+T0e\nC1L1dKgilGkEJF23MxKRXB911k62WIhIadojjYGUBhEpljewyyO9CUh3r+qc3+PVIA3qSLrp\nBEiTHkm2qGKX+49t7kDqvdJ7D3KvEgVJXohVREoFJOmKfEvv65EA0v4tX2xx4unRqd0USGl0\naudBSnMRKW/OII3M/MZBCrMgWR/FI/m3NnivlR4M0lWHfuNM4WkeKbmIVD3JQ7sGyR6s90jy\n8pxHypvn3mjiVS8PEvVA0oOyx2Vq59/aiEeqOrhMAKl5h1eDlEZB6n+8V0c5XkeSPmzLOBeR\nhiDFwaFNRSR7X4OItATSoIPL9GLX1x352T0fCJKtzp/acwVI/TpS3m0dSP2p3qRHmgMprQdJ\nPJI7kF7uzfXRA2kyKpa2rtJrXT/2wI/sb+uRZfdQbPZCi4NVDIOngw7hKtkw+cCD5OpII/vO\ngzQ46oWI5Jr3INVTu/GWJ/XY8XjhgZ/d92EguWjUKiKlAUjLB9f3SKW5AtLUvuMNz4PkiZ4G\n6UMi0pUcvRtIPOvZ2OKER3oZpDALUj8iTTQ8A1JyIPXeAUA6Xef2fjhI1eBa2WJrkHRvP1zD\nYJeVII31Qf6f0e56za5sefumrfVK19dy9C4gOZI2g7T9QLaD5DyS/Pc1kNIwIk2A9DEe6WKQ\nzu3/yKzd0p5zHmlvXzt2mfBIr4I0oc8B6WqO3gakTS2eAlKTiDThkQBSsz2b6cxDOB+k8R+x\nehGkdToUpLm0ypjeHKSGP1G2Xycew5FTuy0F2VN0QkRa1KdEpDtwdCbNxyYb1hdkz9eSR+pt\nZQJIR+7XWG8AkotGDwFp5YRyDKS8O0BqsF9rnXYch9eRZobXTUBS7XZm5TNjFUhT/S92cIUa\nligu0fuANJPJuglIs1O7DS2tfTsfEJFukWlgnXUkx3okfgCQKn0CSI2P4hWddCxHZu2W9nwm\nSFMeCSC9ttNROik63qUge6HOBqneq/GmrbWn6xtN7DqdczgAaasQkdrvcrDOOCKAtFkAqfku\nR+uEQwJIm/VOIB3wi323vKrHT+8A0ut6rkdazAe9kGK6l+Y+LNp0cMCW17V4jR4LEo0+fKnr\n+17Tg1ECSK8LIO3d/GTNTmJfbfuALa9r8RS9T/q7OUj3v6LzjvCVhg/Y8roWT9H7gNTYI92s\nfjStI2ACSJvVCKQNekTW7jEYZTVnCSBt1juB1KrrI93HYWp6zABps6ZAOk43BqkKaZT/R/kf\nEjtC10kPQ44ocdSUP8gOvs2pAEgP0B1BKsO1dlqPAsneyEunYsWr+7a8rsU31ekrXMpg/L8F\ndVvYRpT/l5+h7v9J/71GehhyROVoSf/Ug16lhQ13nuoWAkgrdceIBNVCRHqAANL9BZAeIIB0\nfwGkB+gRdaQPF0B6gB6ysuGjBZAeoMestftgAaQHCCDdXwDpAQJI99elIEEr1fzU6xUYPMA1\n2qvtJ/0I7Wwcu72ozaNgXasX7n1t55d38Ygx+ojd7iCAdFkXjxijj9jtDgJIl3XxiDH6iN3u\nIIB0WRePGKOP2O0OAkiXdfGIMfqI3e4ggHRZF48Yo4/Y7Q4CSJd18Ygx+ojd7iCAdFkXjxij\nj9jtDgJIl3XxiDH6iN3uIIB0cRcQ9P4CSBDUQAAJghoIIEFQAwEkCGoggARBDQSQIKiBABIE\nNRBAgqAGAkgQ1EAACYIaCCBBUAMBJAhqIIAEQQ10IEjrb6xm92CzXYYPxnec2nput5mtW++2\nvEfzu88dIX99th+u22nPex0OjvP23tLRoS2va922nHkwviMt7T/VG+3bbWNvy8e3/iRdqNeO\n1u20i4Sq860NnHeiD2uc3L8rt5x5MLEjlZfX7raztz27LR/f+pN0oV47WrcT7XinjTo//kTf\nACTb/kSQdu626SD1paeDxKLBg8177wHJdn/hJAGk+UZWDNTRvWS2vL03+9/q3QCS2+kFGshd\nt92dH3ue7wLS5jG6G6RdROQdt/f2PiA1CUh732m+XLtRkJP81GTD4SDZHtt32xn/PjkiNQlI\nL4G0u3e7CJ8QkV75sD8FpH27vQ1IbTja+U7rs3ju3tu6Oa7hlc1T/e+qMWq/AQSQDtfrHL3w\nm000+Pe8vbf2c1jD65qn3i6rBxoi0ilqwNH+/fuD48y9t3d0UMubOOpNAeoHc3tu221m6+a7\nLR7f+pN0oZpxtKeB4eA4b+9dPR3Q9Mo47mI+lgjdUGUOvWdyVu20/b2ODY6z9t7W1aGtQ9CH\nCCBBUAMBJAhqIIAEQQ0EkCCogQASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEENBJAg\nqIEAEgQ1EECCoAYCSBDUQAAJghoIIEFQAwEkCGoggARBDQSQIKiBABIENRBAgqAGAkgQ1EAA\nCYIaCCBBUAMBJAhqIIAEQQ30HiAt/dbAI3704V6i3n+nN1n7ywAr7sFPE3/RqktYN259uacP\n/OWC9xhea0CCNmn5ByR0nOpGS79Vs+IXKWZ+U2cZpHqLsaPpH3FLvccQA0jNRe7HneY2sK2G\nDwY7pIlXBpuMPL84+utux47GHzFAGhVZJLffHrc/9bUqzlNyv5vzHuegsZZAovQSSHq56hlY\nPdSr591/Jg9o0O0oSLNva7feYxAN4jhV52/q9XowQF79czPyG7D7QKqiAvWvygAkvVrVVRs7\nokWQyL3a/oq/xxgi97/BxaS519/j/R+g+pRNbrIFpDLwZ3YiQYhGrthsjBx5sd6nXG0kG6Y0\nAUr+g2jydYA0rQNAqv5TLsxJINVvpvl1f4+BVOYG+nOn8jzVl2TkYsMjjUspaQ6SnvXJiMQX\nqgFI1fFR79XWF/09BtHg45Pqf2dA8v+FiqoBmFI7jzTFjz1YC9KSR6rHQP/4AdKYZkEBSHvU\nB2lqk+tAmjjgXnc0+GO2ld16jzFkZ3lATEreI00Q9R4noa106C2BNDy39dxg2GLqXRh3VepL\nVxpbA1KvWxp72vptf8nfYwzx2S7/lmHAGdWROpLb7T3OQWOtiNblJE89qDd3cyu7MKUhvUY9\nkNLwEk4eD9WXtVQKp464oTCIIKiBABIENRBAgqAGAkgQ1EAACYIaCCBBUAMBJAhqIIAEQQ0E\nkCCogQASBDUQQIKgBgJIENRAAAmCGgggQVADASQIaiCABEENBJAgqIEAEgQ1EECCoAYCSBDU\nQAAJghoIIEFQAwEkCGoggARBDQSQIKiB/h+XIfyYj2k6RwAAAABJRU5ErkJggg==",
      "text/plain": [
       "Plot with title \"Density of lambda\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 3)\n",
    "\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    " # likelihood\n",
    " for (i in 1:I){\n",
    " fatal[i] ~ dpois(lambda)\n",
    " \n",
    " }\n",
    " \n",
    "  # prior\n",
    " lambda ~ dgamma(0.1, 0.1)\n",
    " \n",
    "\n",
    "}\",\n",
    "    \n",
    "    file = \"airline.jag\"\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "airline.fatalities <- read.table(file = \"airline.txt\", header=T, sep=\"\") \n",
    "\n",
    "air.data <- list(fatal=c(airline.fatalities$fatal, NA), I=27)\n",
    "\n",
    "air.inits <- list(list(lambda=15), list(lambda=23), list(lambda=30))\n",
    "\n",
    "fatalities.model <- jags.model(file = \"airline.jag\", data = air.data, n.chains = 3, inits = air.inits, n.adapt = 2000)\n",
    "\n",
    "air.par <- c(\"lambda\", \"fatal[27]\") # predict the next observation\n",
    "\n",
    "res.air <- coda.samples(model = fatalities.model, var=air.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(res.air)\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",
    "# fatal[27] 24.21 5.0880  0.09289        0.08617\n",
    "# lambda    24.30 0.9592  0.01751        0.01780\n",
    "# \n",
    "# 2. Quantiles for each variable:\n",
    "#   \n",
    "#           2.5%   25%   50%   75% 97.5%\n",
    "# fatal[27] 15.0 21.00 24.00 27.00 35.00\n",
    "# lambda    22.4 23.64 24.27 24.95 26.23\n",
    "\n",
    "plot(res.air)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "aggressive-pressing",
   "metadata": {},
   "outputs": [],
   "source": [
    "# 4\n",
    "\n",
    "cat(\"model{\n",
    "\n",
    " # likelihood\n",
    " for (i in 1:N){\n",
    "  b.mass[i] ~ dnorm(mu[i], psi)\n",
    "  mu[i] <- beta0 + beta1*gen[i] + beta2*b.length[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",
    " psi ~ dunif(0, 100)\n",
    " sigma <- 1.0/sqrt(psi) # standard deviation\n",
    " \n",
    "\n",
    "}\",\n",
    "    \n",
    "    file = \"snake.jag\"\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fancy-tsunami",
   "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: 50\n",
      "   Unobserved stochastic nodes: 4\n",
      "   Total graph size: 263\n",
      "\n",
      "Initializing model\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "\n",
       "Iterations = 2010:12000\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",
       "beta1 5.315 1.4333 0.026168        0.02605\n",
       "beta2 7.384 0.6149 0.011226        0.01086\n",
       "sigma 4.962 0.5114 0.009338        0.00934\n",
       "\n",
       "2. Quantiles for each variable:\n",
       "\n",
       "       2.5%   25%   50%   75% 97.5%\n",
       "beta1 2.400 4.378 5.337 6.271 8.079\n",
       "beta2 6.152 6.981 7.398 7.779 8.636\n",
       "sigma 4.114 4.608 4.909 5.271 6.139\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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GEXrOujk9Q6PXysjgZJQwYDSKwGEmbw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",
      "text/plain": [
       "Plot with title \"Density of sigma\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a)\n",
    "\n",
    "snake.inits <- list(list(beta0=2, beta1=1, beta2=2, psi=1), list(beta0=2, beta1=5, beta2=2, psi=0.5), list(beta0=2, beta1=1, beta2=1, psi=0.05))\n",
    "\n",
    "snake <- read.table(file = \"snake.txt\", header=T, sep=\"\")\n",
    "\n",
    "snake.data <- list(b.mass=snake$b_mass, b.length=snake$b_length, gen=snake$gen, N=length(snake$b_mass))\n",
    "\n",
    "snake.model <- jags.model(file = \"snake.jag\", data = snake.data, inits = snake.inits, n.chains = 3, n.adapt = 2000)\n",
    "\n",
    "snake.par <- c(\"beta1\", \"beta2\", \"sigma\")\n",
    "\n",
    "res.snake <- coda.samples(model = snake.model, variable.names = snake.par, n.iter = 10000, thin = 10)\n",
    "\n",
    "summary(res.snake)\n",
    "\n",
    "\n",
    "\n",
    "plot(res.snake)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "fifty-excellence",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"dataframe\">\n",
       "<caption>A matrix: 5 × 3 of type dbl</caption>\n",
       "<thead>\n",
       "\t<tr><th></th><th scope=col>beta1</th><th scope=col>beta2</th><th scope=col>sigma</th></tr>\n",
       "</thead>\n",
       "<tbody>\n",
       "\t<tr><th scope=row>Lag 0</th><td> 1.00000000</td><td> 1.000000000</td><td> 1.000000000</td></tr>\n",
       "\t<tr><th scope=row>Lag 10</th><td> 0.03118653</td><td>-0.037889269</td><td> 0.032665921</td></tr>\n",
       "\t<tr><th scope=row>Lag 50</th><td> 0.02807971</td><td>-0.010912926</td><td>-0.009250506</td></tr>\n",
       "\t<tr><th scope=row>Lag 100</th><td>-0.02831578</td><td> 0.004258111</td><td> 0.015774471</td></tr>\n",
       "\t<tr><th scope=row>Lag 500</th><td> 0.01902215</td><td>-0.038483185</td><td> 0.019976780</td></tr>\n",
       "</tbody>\n",
       "</table>\n"
      ],
      "text/latex": [
       "A matrix: 5 × 3 of type dbl\n",
       "\\begin{tabular}{r|lll}\n",
       "  & beta1 & beta2 & sigma\\\\\n",
       "\\hline\n",
       "\tLag 0 &  1.00000000 &  1.000000000 &  1.000000000\\\\\n",
       "\tLag 10 &  0.03118653 & -0.037889269 &  0.032665921\\\\\n",
       "\tLag 50 &  0.02807971 & -0.010912926 & -0.009250506\\\\\n",
       "\tLag 100 & -0.02831578 &  0.004258111 &  0.015774471\\\\\n",
       "\tLag 500 &  0.01902215 & -0.038483185 &  0.019976780\\\\\n",
       "\\end{tabular}\n"
      ],
      "text/markdown": [
       "\n",
       "A matrix: 5 × 3 of type dbl\n",
       "\n",
       "| <!--/--> | beta1 | beta2 | sigma |\n",
       "|---|---|---|---|\n",
       "| Lag 0 |  1.00000000 |  1.000000000 |  1.000000000 |\n",
       "| Lag 10 |  0.03118653 | -0.037889269 |  0.032665921 |\n",
       "| Lag 50 |  0.02807971 | -0.010912926 | -0.009250506 |\n",
       "| Lag 100 | -0.02831578 |  0.004258111 |  0.015774471 |\n",
       "| Lag 500 |  0.01902215 | -0.038483185 |  0.019976780 |\n",
       "\n"
      ],
      "text/plain": [
       "        beta1       beta2        sigma       \n",
       "Lag 0    1.00000000  1.000000000  1.000000000\n",
       "Lag 10   0.03118653 -0.037889269  0.032665921\n",
       "Lag 50   0.02807971 -0.010912926 -0.009250506\n",
       "Lag 100 -0.02831578  0.004258111  0.015774471\n",
       "Lag 500  0.01902215 -0.038483185  0.019976780"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
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MvYjz1uGtozrJw+CB82ABmtHHbhCfQ6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",
      "text/plain": [
       "Plot with title \"beta1\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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AGKBBigSIABigQYoEiAAYoEGKBIgAGKBBigSIABigQYcCxSyX9e7zLiNKhgbPqx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",
      "text/plain": [
       "Plot with title \"beta2\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Potential scale reduction factors:\n",
       "\n",
       "      Point est. Upper C.I.\n",
       "beta1          1       1.00\n",
       "beta2          1       1.01\n",
       "sigma          1       1.00\n",
       "\n",
       "Multivariate psrf\n",
       "\n",
       "1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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QKEBAFCggAhQYCQIEBIECAkCBASBAgJ\nAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAh\nQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAg\nJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkC\nhAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFB\ngJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAk\nCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKE\nBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGA\nkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQI\nEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQE\nAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQ\nIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQ\nEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQB\nQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBASBAgJAoQEAUKCACFBgJAg\nQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFCggAhQYCQIEBIECAkCBAS\nBAgJAoQEAUKCACFBgJAgQEgQICQIEBIECAkChAQBQoIAIUGAkCBASBAgJAgQEgQICQKEBAFC\nggAhQYCQIEBIECAkCBASBPwfsArox7qSpgYAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"sigma\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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MPp8GaKdAgigWK2w99lBhu6xV9E6hHJFjZFakI6RLLEZSItvha29DkSIsHFXHWO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\nAIgEIMD/rfR3byXMUgoAAAAASUVORK5CYII=",
      "text/plain": [
       "Plot with title \"sigma\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 420,
       "width": 420
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# b) autocorrelation of samples\n",
    "\n",
    "autocorr.diag(res.snake)\n",
    "\n",
    "#           beta1         beta2        sigma\n",
    "# Lag 0    1.000000000  1.0000000000  1.000000000\n",
    "# Lag 10  -0.042364897  0.0154337160 -0.017003074\n",
    "# Lag 50  -0.031771650 -0.0020843421 -0.009945504\n",
    "# Lag 100 -0.025130144  0.0000523702  0.011555804\n",
    "# Lag 500 -0.001193404  0.0031277665 -0.014275575\n",
    "\n",
    "autocorr.plot(res.snake)\n",
    "\n",
    "# The autocorrelation of all the parameters approach zero as the lag increases\n",
    "# which indicate convergence of the sample mean towards true mean\n",
    "\n",
    "gelman.diag(res.snake)\n",
    "\n",
    "gelman.plot(res.snake)\n",
    "\n",
    "# Potential scale reduction factors:\n",
    "#   \n",
    "#           Point est. Upper C.I.\n",
    "# beta1          1       1.01\n",
    "# beta2          1       1.00\n",
    "# sigma          1       1.00\n",
    "# \n",
    "# Multivariate psrf\n",
    "# \n",
    "# 1\n",
    "\n",
    "# There is no evidence of non-convergence since:\n",
    "\n",
    "# i) the scale redution factors are all below 1.1 which means that between chain variance and within chain variance are equal\n",
    "\n",
    "# ii) the 97.5% quantiles for all the parameters are all below 1.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "uniform-great",
   "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
}