Robust Bayesianism and Likelihoodism

TL;DR

This paper introduces Robust Bayesianism, a new theory of statistical evidence that supports key principles like the likelihood and sufficiency principles, extending results to qualitative judgments.

Contribution

It develops Robust Bayesianism, linking it to established principles and extending results to qualitative, non-numerical likelihood comparisons.

Findings

RB entails the law of likelihood and likelihood principle

Extends results to qualitative judgments of likelihood

Supports widely-accepted statistical principles

Abstract

We defend a new theory of statistical evidence, which we call Robust Bayesianism (RB). We prove that, under widely accepted assumptions, RB entails the law of likelihood [Royall, 1997], the likelihood principle [Berger and Wolpert, 1988], and a variety of other widely-accepted "statistical principles", e.g., the sufficiency principle [Birnbaum, 1962, 1972] and stopping-rule principle [Berger and Wolpert, 1988]. The main technical contribution of this paper is to extend some of those results to a qualitative framework in which experimenters are justified only in making comparative, non-numerical judgments of the form "A given B is more likely than C given D."