Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician

Abstract

A common reaction among applied statisticians is that the Bayesian statistician's energies in an applied problem must be directed at the a priori elicitation of one model specification from which an optimal design and all inferences follow automatically by applying Bayes's theorem to calculate conditional distributions of unknowns given knowns. I feel, however, that the applied Bayesian statistician's tool-kit should be more extensive and include tools that may be usefully labeled frequency calculations. Three types of Bayesianly justifiable and relevant frequency calculations are presented using examples to convey their use for the applied statistician.