model
    {
    for(i in 1:s_total){
    y_s[i] ~ dnorm(nu + mu[y_s_region[i]] + w[i], inv_tausq[y_s_region[i]])
    y_s_ll[i] <- logdensity.norm(y_s[i],nu + mu[y_s_region[i]] + w[i], inv_tausq[y_s_region[i]])
    }
    
    nu ~ dnorm(0, 0.001) 
    inv_sigmasq ~ dgamma(2, 0.0006)
    sigmasq <- 1/inv_sigmasq
    inv_deltasq ~ dgamma(2, 0.1)
    deltasq <- 1/inv_deltasq
    phi ~ dunif(phi_a, phi_b)

    for(j in 1:N){
    inv_tausq[j] ~ dgamma(2, 0.001)
    mu[j] ~ dnorm(0,inv_deltasq)
    }

    for(i in 1:pop_total){
    for(j in 1:pop_total){
    bigsigma[i,j] <- sigmasq*exp(-phi*d[i,j])
    }
    }
    
    inv_bigsigma <- inverse(bigsigma)
    w ~ dmnorm(w.mu, inv_bigsigma)
 
    
    for(i in 1:ns_total){
    Y_ns[i] ~ dnorm(nu + mu[Y_ns_region[i]] + w[s_total+i], inv_tausq[Y_ns_region[i]])
    }
    
    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]
    }
    }