require(R2jags)
model <- function() {
  ## Prior
  H ~ dbern(0.5)
  theta1 ~ dunif(0,1)
  theta <- H*theta1 + (1-H)*0.5
  
  ## Likelihood
  y ~ dbin(theta, n)
}
Data <- list(y=13, n=17)
binom.test(13,17)
fit <- jags(Data, model=model, param=c("H","theta"), n.chain=1, n.iter=10000, n.thin=1, n.burn=0, DIC=FALSE)
attach.jags(fit)
1-mean(H)

source("http://web.as.uky.edu/statistics/users/pbreheny/701/S13/notes/fun.R")
dnplot(theta, xlab=expression(theta), bw="ucv")