
  model {
    # Likelihood
    for (i in 1:N) {
      post[i] ~ dnorm(mu[i], tau)
      mu[i] <- beta0
    }

    # Priors
    beta0 ~ dnorm(0, 0.0001) # Overall intercept
    tau ~ dgamma(0.001, 0.001) # Precision for within-cluster variation (residual variance)
    sigma <- 1 / sqrt(tau) # Within-cluster standard deviation (Residual SD)

  }
