The Posterior Distributions, the Marginal Distributions and the Normal Bayes Estimators of Three Hierarchical Normal Models

We calculate the posterior distributions, the marginal distributions and the normal Bayes estimators of three hierarchical normal models in the same manner. The three models are displayed in increasing complexity. We find that the posterior distributions and the marginal distributions are all normal distributions. We also obtain the normal Bayes estimators under the squared error loss function.