ch9.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 9.1\n",
    "p <- list()\n",
    "p$A <- c(0,0,10,0,0)\n",
    "p$B <- c(0,1,8,1,0)\n",
    "p$C <- c(0,2,6,2,0)\n",
    "p$D <- c(1,2,4,2,1)\n",
    "p$E <- c(2,2,2,2,2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 9.2\n",
    "p_norm <- lapply( p , function(q) q/sum(q))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl class=dl-horizontal>\n",
       "\t<dt>A</dt>\n",
       "\t\t<dd>0</dd>\n",
       "\t<dt>B</dt>\n",
       "\t\t<dd>0.639031859650177</dd>\n",
       "\t<dt>C</dt>\n",
       "\t\t<dd>0.950270539233235</dd>\n",
       "\t<dt>D</dt>\n",
       "\t\t<dd>1.47080847632211</dd>\n",
       "\t<dt>E</dt>\n",
       "\t\t<dd>1.6094379124341</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description*}\n",
       "\\item[A] 0\n",
       "\\item[B] 0.639031859650177\n",
       "\\item[C] 0.950270539233235\n",
       "\\item[D] 1.47080847632211\n",
       "\\item[E] 1.6094379124341\n",
       "\\end{description*}\n"
      ],
      "text/markdown": [
       "A\n",
       ":   0B\n",
       ":   0.639031859650177C\n",
       ":   0.950270539233235D\n",
       ":   1.47080847632211E\n",
       ":   1.6094379124341\n",
       "\n"
      ],
      "text/plain": [
       "        A         B         C         D         E \n",
       "0.0000000 0.6390319 0.9502705 1.4708085 1.6094379 "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 9.3\n",
    "( H <- sapply( p_norm , function(q) -sum(ifelse(q==0,0,q*log(q))) ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 9.4\n",
    "ways <- c(1,90,1260,37800,113400)\n",
    "logwayspp <- log(ways)/10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "## R code 9.5\n",
    "# build list of the candidate distributions\n",
    "p <- list()\n",
    "p[[1]] <- c(1/4,1/4,1/4,1/4)\n",
    "p[[2]] <- c(2/6,1/6,1/6,2/6)\n",
    "p[[3]] <- c(1/6,2/6,2/6,1/6)\n",
    "p[[4]] <- c(1/8,4/8,2/8,1/8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "\t<li>1</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\item 1\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1\n",
       "2. 1\n",
       "3. 1\n",
       "4. 1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1 1 1 1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# compute expected value of each\n",
    "sapply( p , function(p) sum(p*c(0,1,1,2)) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>1.38629436111989</li>\n",
       "\t<li>1.32966134885476</li>\n",
       "\t<li>1.32966134885476</li>\n",
       "\t<li>1.2130075659799</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 1.38629436111989\n",
       "\\item 1.32966134885476\n",
       "\\item 1.32966134885476\n",
       "\\item 1.2130075659799\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 1.38629436111989\n",
       "2. 1.32966134885476\n",
       "3. 1.32966134885476\n",
       "4. 1.2130075659799\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 1.386294 1.329661 1.329661 1.213008"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 9.6\n",
    "# compute entropy of each distribution\n",
    "sapply( p , function(p) -sum( p*log(p) ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>0.09</li>\n",
       "\t<li>0.21</li>\n",
       "\t<li>0.21</li>\n",
       "\t<li>0.49</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 0.09\n",
       "\\item 0.21\n",
       "\\item 0.21\n",
       "\\item 0.49\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 0.09\n",
       "2. 0.21\n",
       "3. 0.21\n",
       "4. 0.49\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "[1] 0.09 0.21 0.21 0.49"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 9.7\n",
    "p <- 0.7\n",
    "( A <- c( (1-p)^2 , p*(1-p) , (1-p)*p , p^2 ) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "1.22172860410979"
      ],
      "text/latex": [
       "1.22172860410979"
      ],
      "text/markdown": [
       "1.22172860410979"
      ],
      "text/plain": [
       "[1] 1.221729"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## R code 9.8\n",
    "-sum( A*log(A) )\n",
    "\n",
    "## R code 9.9\n",
    "sim.p <- function(G=1.4) {\n",
    "    x123 <- runif(3)\n",
    "    x4 <- ( (G)*sum(x123)-x123[2]-x123[3] )/(2-G)\n",
    "    z <- sum( c(x123,x4) )\n",
    "    p <- c( x123 , x4 )/z\n",
    "    list( H=-sum( p*log(p) ) , p=p )\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": {
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       "</svg>\n"
      ],
      "text/plain": [
       "Plot with title “”"
      ]
     },
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     },
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    }
   ],
   "source": [
    "## R code 9.10\n",
    "library('rethinking')\n",
    "H <- replicate( 1e5 , sim.p(1.4) )\n",
    "dens( as.numeric(H[1,]) , adj=0.1 )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "## R code 9.11\n",
    "entropies <- as.numeric(H[1,])\n",
    "distributions <- H[2,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
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     },
     "execution_count": 13,
     "metadata": {},
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   ],
   "source": [
    "## R code 9.12\n",
    "max(entropies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "1. 1. 0.0900834964541867\n",
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   ],
   "source": [
    "## R code 9.13\n",
    "distributions[ which.max(entropies) ]"
   ]
  }
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