model {
r <- 15; n <- 20 # data
######################################
r ~ dbin(p, n) # likelihood
p <- theta[pick]
pick ~ dcat(q[])
q[1] <- 0.9
q[2] <- 0.1
theta[1] <- 0.5 # if unbiased
theta[2] ~ dunif(0, 1) # if biased
biased <- pick - 1 # 1 if biased, 0 otherwise
}

node mean sd MC error 2.5% median 97.5% start sample
biased 0.2619 0.4397 0.002027 0.0 0.0 1.0 1 100000
theta[2] 0.5594 0.272 9.727E-4 0.03284 0.6247 0.9664 1 100000