model
    {
    for(i in 1:s_total){
      y_s[i] ~ dnorm(nu + mu[y_s_region[i]],inv_sigmasq[y_s_region[i]])
      y_s_pred[i] ~ dnorm(nu + mu[y_s_region[i]],inv_sigmasq[y_s_region[i]])
      y_s_ll[i] <- logdensity.norm(y_s[i],nu + mu[y_s_region[i]],inv_sigmasq[y_s_region[i]])
    }
    
    nu ~ dnorm(0,0.00001)
    inv_deltasq ~ dgamma(2, 0.1)
    deltasq <- 1/inv_deltasq

    for(l in 1:N){
      inv_sigmasq[l] ~ dgamma(2, 0.000625)
      mu[l] ~ dnorm(0,inv_deltasq)
    }

    for(j in 1:ns_total){
      Y_ns[j] ~ dnorm(nu + mu[Y_ns_region[j]], inv_sigmasq[Y_ns_region[j]])
    }

    grand_mean = (y_s_total + sum(Y_ns))/pop_total

    for(k in 1:N){
      mu_pred[k] = (sum(Y_ns[(site_ends[k]+1):site_ends[k+1]]) + sum_samp[k])/region_total[k]
    }
    }