The e-value and the Full Bayesian Significance Test: Logical Properties and Philosophical Consequences

TL;DR

This paper reviews the e-value and the Full Bayesian Significance Test, emphasizing their logical coherence, philosophical implications, and how they integrate mathematical and foundational principles for hypothesis testing.

Contribution

It provides a conceptual analysis of the e-value and FBST, highlighting their logical properties and philosophical significance in hypothesis testing.

Findings

The e-value offers a logically coherent measure of evidence.

FBST allows testing of sharp hypotheses within a Bayesian framework.

The approach bridges mathematical statistics and logical foundations.

Abstract

This article gives a conceptual review of the e-value, ev(H|X) -- the epistemic value of hypothesis H given observations X. This statistical significance measure was developed in order to allow logically coherent and consistent tests of hypotheses, including sharp or precise hypotheses, via the Full Bayesian Significance Test (FBST). Arguments of analysis allow a full characterization of this statistical test by its logical or compositional properties, showing a mutual complementarity between results of mathematical statistics and the logical desiderata lying at the foundations of this theory.