Reconciling Bayesian and Non-Bayesian Analysis

. This paper is an attempt to reconcile Bayesian and non-Bayesian approaches to statistical inference, by casting both in terms of a broader formalism. In particular, this paper is an attempt to show that when one extends conventional Bayesian analysis to distinguish the truth from one's guess for the truth, one gains a broader perspective which allows the inclusion of non-Bayesian formalisms. This perspective shows how it is possible for non-Bayesian techniques to perform well, despite their handicaps. It also highlights some difficulties with the "degree of belief" interpretation of probability. 1. Introduction Why should one want to reconcile Bayesian and non-Bayesian analysis? Why be bothered with non-Bayesian techniques? Bayesian analysis forces one to makes one's assumptions explicit; it ensures self-consistency; it provides a single unified approach to all inference problems; if one is very sure of the prior (e.g., as an extreme, you constructed the datagenerating mechanism you..