Bayes inference for a multi-choice poll

Igor — May 31, 2015, 12:52 PM

# This script does Bayesian analysis of the typical
# multi-choice poll (survey), in which people are given
# several choices from which they must choose one

## for more info, see book "Bayesian Computation with R"
## by Jim Albert

library("LearnBayes")

poll <- 1600*0.01*c(29, 36, 19, 7, 9)

n=length(poll)

N.samples <-10000
theta <- rdirichlet(N.samples,poll)


boxplot(theta,col=rainbow(10),horizontal=TRUE)

library(vioplot)

Loading required package: sm
Package 'sm', version 2.2-5.4: type help(sm) for summary information

plot(1,1,ylim=c(0.4,n+0.6),xlim=c(min(theta),max(theta)),type="n",
     xlab="posterior values",ylab="answer")

for(i in 1:n)
{
vioplot(theta[,i],
        at=i,
        add=TRUE,
        col="gold", horizontal=TRUE)
}

densities <- list()
ymax <-0
for(i in 1:n)
{
  densities[[i]] <- density(theta[,i])
  ymax <- max(ymax, max(densities[[i]]$y))
}  


## make an empty plot (type ="n") with axis
## limits to contain elements of the figure

plot(NA,NA,type='n',
     xlab="theta",ylab="pdf",
     xlim=c(min(theta),max(theta)),
     ylim=c(0,ymax))

for(i in 1:n)
{
  color <- sample(rainbow(8, alpha = .5),1)
  polygon(densities[[i]],col=color)
  ## lines(densities[[i]]$x,densities[[i]]$y,
  ##       type="l",lwd=4,col="red")
}