The fiducial-Bayes fusion: A general theory of statistical inference

Abstract

An overview is presented of a general theory of statistical inference that is referred to as the fiducial-Bayes fusion. This theory combines organic fiducial inference and Bayesian inference. The aim is that the reader is given a clear summary of the conceptual framework of the fiducial-Bayes fusion as well as pointers to further reading about its more technical aspects. Particular attention is paid to the issue of how much importance should be attached to the role of Bayesian inference within this framework. The appendix contains a substantive example of the application of the theory of the fiducial-Bayes fusion, which supplements various other examples of the application of this theory that are referenced in the paper.