ch2.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0</li>\n",
       "\t<li>0.15</li>\n",
       "\t<li>0.4</li>\n",
       "\t<li>0.45</li>\n",
       "\t<li>0</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0\n",
       "\\item 0.15\n",
       "\\item 0.4\n",
       "\\item 0.45\n",
       "\\item 0\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0\n",
       "2. 0.15\n",
       "3. 0.4\n",
       "4. 0.45\n",
       "5. 0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.00 0.15 0.40 0.45 0.00"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 2.1\n",
    "ways <- c( 0 , 3 , 8 , 9 , 0 )\n",
    "ways/sum(ways)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "0.1640625"
      ],
      "text/latex": [
       "0.1640625"
      ],
      "text/markdown": [
       "0.1640625"
      ],
      "text/plain": [
       "[1] 0.1640625"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 2.2\n",
    "dbinom( 6 , size=9 , prob=0.5 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 2.3\n",
    "# define grid\n",
    "p_grid <- seq( from=0 , to=1 , length.out=20 )\n",
    "\n",
    "# define prior\n",
    "prior <- rep( 1 , 20 )\n",
    "\n",
    "# compute likelihood at each value in grid\n",
    "likelihood <- dbinom( 6 , size=9 , prob=p_grid )\n",
    "\n",
    "# compute product of likelihood and prior\n",
    "unstd.posterior <- likelihood * prior\n",
    "\n",
    "# standardize the posterior, so it sums to 1\n",
    "posterior <- unstd.posterior / sum(unstd.posterior)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "## R code 2.4\n",
    "plot( p_grid , posterior , type=\"b\" ,\n",
    "    xlab=\"probability of water\" , ylab=\"posterior probability\" )\n",
    "mtext( \"20 points\" )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 2.5\n",
    "prior <- ifelse( p_grid < 0.5 , 0 , 1 )\n",
    "prior <- exp( -5*abs( p_grid - 0.5 ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Loading required package: rstan\n",
      "Loading required package: ggplot2\n",
      "rstan (Version 2.9.0, packaged: 2016-01-05 16:17:47 UTC, GitRev: 05c3d0058b6a)\n",
      "For execution on a local, multicore CPU with excess RAM we recommend calling\n",
      "rstan_options(auto_write = TRUE)\n",
      "options(mc.cores = parallel::detectCores())\n",
      "Loading required package: parallel\n",
      "rethinking (Version 1.58)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "  Mean StdDev 5.5% 94.5%\n",
       "p 0.67   0.16 0.42  0.92"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 2.6\n",
    "library(rethinking)\n",
    "globe.qa <- map(\n",
    "    alist(\n",
    "        w ~ dbinom(9,p) ,  # binomial likelihood\n",
    "        p ~ dunif(0,1)     # uniform prior\n",
    "    ) ,\n",
    "    data=list(w=6) )\n",
    "\n",
    "# display summary of quadratic approximation\n",
    "precis( globe.qa )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "text/plain": [
       "plot without title"
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   ],
   "source": [
    "## R code 2.7\n",
    "# analytical calculation\n",
    "w <- 6\n",
    "n <- 9\n",
    "curve( dbeta( x , w+1 , n-w+1 ) , from=0 , to=1 )\n",
    "# quadratic approximation\n",
    "curve( dnorm( x , 0.67 , 0.16 ) , lty=2 , add=TRUE )"
   ]
  }
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