Applications and Limitations of Robust Bayesian Bounds and Type II MLE

Three applications of robust Bayesian analysis and three examples of its limitations are given. The applications that are reviewed are the development of an automatic Ockham’s Razor, outlier detection, and analysis of weighted distributions. Limitations of robust Bayesian bounds are highlighted through examples that include analysis of a paranormal experiment and a hierarchical model. This last example shows a disturbing difference between actual hierarchical Bayesian analysis and robust Bayesian bounds, a difference which also arises if, instead, a Type II MLE or empirical Bayes analysis is performed.