The present paper is the revised text of a special invited IMS lecture presented at the joint meeting of the IMS and ASA, August 21, 1982, Cincinnati, Ohio, by the author. It consists of an introduction and six sections. In the introduction the meaning of the terms used in the title of the paper is described.
Section 2 presents several reasons why the applied statistician should care about Bayesian methods of inference. Section 3 describes simple frequency calculations that are useful in practice for understanding and communicating Bayesian statements, as well as frequency calculations that calibrate Bayesian statements by tying them to frequencies of real-world events.
Section 4 discusses the use of frequency calculations to examine the operating characteristics of Bayesian inferences in order to guide the choice of models on which to base inferences. Section 5 describes the use of posterior predictive frequency distributions of test statistics to monitor the adequacy of specific model specifications with fixed data sets. Finally, Section 6 concludes with a few summary comments.