#############
#  Here is WinBUGS code for Poisson/gamma hierarchical model
#  (Carlin and Louis, 2008, Example 3.6)
#############

model
{
    for (i in 1:k) {
          theta[i] ~ dgamma(alpha,beta)
          lambda[i] <- theta[i]*t[i]
          Y[i] ~ dpois(lambda[i])
    }
    alpha ~ dexp(1.0)
    beta ~ dgamma(0.1, 1.0)
}

#  DATA:
list(k = 10, Y = c(5, 1, 5, 14, 3, 19, 1, 1, 4, 22),
  t = c(94.320, 15.72, 62.88, 125.76, 5.24, 31.44, 1.048,
        1.048, 2.096, 10.48))

#  INITIAL VALUES:
list(theta=c(1,1,1,1,1,1,1,1,1,1), alpha=1, beta=1)