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

[example-5_4_1-biased-coin0][example-5_4_1-biased-coin1]