Bayesian Influence and Frequentist Interface

Abstract

Under the Bayesian paradigm to statistical inference the posterior probability distribution contains in principle all relevant information. All statistical inference can be deduced from the posterior distribution by reporting appropriate summaries. This coherent nature of Bayesian inference can give rise to problems when the implied posterior summaries are unduly sensitive to some detail choices of the model. This chapter discusses summaries and diagnostics that highlight such sensitivity and ways to choose a prior probability model to match some desired (frequentist) summaries of the implied posterior inference.