The Posterior Distributions, the Marginal Distributions and the Normal Bayes Estimators of Three Hierarchical Normal Models
Ying-Ying Zhang *
Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China.
Wen-He Song
Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China.
Teng-Zhong Rong
Department of Statistics and Actuarial Science, College of Mathematics and Statistics, Chongqing University, Chongqing, China.
*Author to whom correspondence should be addressed.
Abstract
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.
Keywords: Posterior distribution, marginal distribution, normal Bayes estimator, hierarchical normal model, normal distribution