# This is the WinBUGS version of the DUGONGS  model, without discretization
# of the variable gamma (This was done due to a technical limitation of
# classic BUGS: it could only sample from log concave distributions)
#
var
   x[N],Y[N],mu[N],alpha,beta,gamma,tau,sigma,p[M],U1,U2,U3;
model {
   for (i in 1:N) {
      mu[i] <- alpha - beta * gamma^x[i]
      Y[i] ~ dnorm(mu[i], tau)
   }
   alpha ~ dnorm(0.0, 1.0E-6) 
   beta ~ dnorm(0.0, 1.0E-6) 
   gamma ~ dunif(0.5, 1)
   tau ~ dgamma(1.0E-3, 1.0E-3)
   sigma <- 1.0/sqrt(tau)
   U3 <- logit(gamma)
}