Bayesian Modeling via Goodness-of-fit

TL;DR

This paper introduces a 'Bayes via goodness of fit' framework to improve Bayesian prior selection and unify Bayesian and frequentist data analysis, applicable to a wide range of models.

Contribution

It proposes a novel general framework for Bayesian modeling that enhances prior calibration and integrates Bayesian and frequentist methods.

Findings

Illustrative examples demonstrate practical benefits.

Framework unifies Bayesian and frequentist approaches.

Applicable to most probability models.

Abstract

The two key issues of modern Bayesian statistics are: (i) establishing principled approach for distilling statistical prior that is consistent with the given data from an initial believable scientific prior; and (ii) development of a Bayes-frequentist consolidated data analysis workflow that is more effective than either of the two separately. In this paper, we propose the idea of "Bayes via goodness of fit" as a framework for exploring these fundamental questions, in a way that is general enough to embrace almost all of the familiar probability models. Several illustrative examples show the benefit of this new point of view as a practical data analysis tool. Relationship with other Bayesian cultures is also discussed.