Hierarchical Bayes and Empirical Bayes. Mlii Method. 1.1 Hierarchical Bayesian Analysis

Hierarchical Bayes and Empirical Bayes are related by their goals, but quite different by the methods of how these goals are achieved. The attribute hierarchical refers mostly to the modeling strategy, while empirical is referring to the methodology. Both methods are concerned in specifying the distribution at prior level, hierarchical via Bayes inference involving additional degrees of hierarchy (hyperpriors and hyperparameters), while empirical Bayes is using data more directly. In expanding Bayesian models and inference to more complex problems, going beyond the simple likelihood-prior-posterior scheme, a hierarchy of models may be needed. The parameter(s) of interest considered are entering the model via their “realizations” which are modeled similarly as they were “measurements.” The common name parameter population distribution is indicative of the nature of the approach.