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

TL;DR

The paper introduces the fiducial-Bayes fusion, a comprehensive framework that integrates fiducial and Bayesian inference to enhance statistical analysis, supported by conceptual explanations and practical examples.

Contribution

It presents a unified theory combining fiducial and Bayesian inference, clarifying their relationship and application in statistical inference.

Findings

Provides a conceptual framework for fiducial-Bayes fusion

Includes practical example demonstrating the theory's application

Discusses the role and importance of Bayesian inference within the framework

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.