Relative belief inferences from decision theory

TL;DR

This paper explores relative belief inferences, demonstrating their derivation from Bayesian principles, their invariance under reparameterizations, and their optimal properties as measures of statistical evidence.

Contribution

It introduces relative belief inferences as a direct, invariant, and optimal measure of statistical evidence derived from Bayesian rules.

Findings

Relative belief inferences are shown to arise from Bayes rules.

They are invariant under reparameterizations.

They possess several optimal properties.

Abstract

Relative belief inferences are shown to arise as Bayes rules or limiting Bayes rules. These inferences are invariant under reparameterizations and possess a number of optimal properties. In particular, relative belief inferences are based on a direct measure of statistical evidence.