model{   
      for( i in 1 : N ) {
         S[i] ~ dcat(pi[])
          mu[i] <- theta[S[i]]
          x[i] ~ dpois(mu[i])   
         for (j in 1 : C) {
            SC[i, j] <- equals(j, S[i])
         }
      }
   # Precision Parameter       
      alpha <- 1
   # alpha~ dgamma(0.1,0.1)
   # Constructive DPP
       p[1] <- r[1]
      for (j in 2 : C) {
         p[j] <- r[j] * (1 - r[j - 1]) * p[j -1 ] / r[j - 1]
      }
       p.sum <- sum(p[])      
      for (j in 1:C){ 
         theta[j] ~ dgamma(A, B)
         r[j] ~ dbeta(1, alpha)         
   # scaling to ensure sum to 1 
         pi[j] <- p[j] / p.sum 
      }
    # hierarchical prior on theta[i] or preset parameters
      A ~ dexp(0.1) B ~dgamma(0.1, 0.1)
   #   A <- 1 B <- 1
   # total clusters         
      K <- sum(cl[])
      for (j in 1 : C) {
         sumSC[j] <- sum(SC[ , j])
         cl[j] <- step(sumSC[j] -1)
      }
   }