## code to accompany the CBS presidential poll example
## lecture 8 of PSTAT 215A, Bayesian Inference, UCSB
##
## Robert B. Gramacy adapted from Peter Hoff

## rdirichlet
##
## sample from a dirichlet distribution

rdirichlet <- function(n, alpha)
  {
    m <- length(alpha)
    x <- matrix(rgamma(n*m, alpha), ncol=m, byrow=TRUE)
    return(x/apply(x, 1, sum))
  }

## sample fromt he posterior in the poll example
theta <- rdirichlet(10000, alpha=c(728,584,138))

## create a histogram of the evidence in favor of Bush
## over Dukakis
hist(theta[,1] - theta[,2], bty="n", main=NULL,
     xlab="theta1 - theta2")