E-values as statistical evidence: A comparison to Bayes factors, likelihoods, and p-values

TL;DR

This paper evaluates e-values and e-processes as measures of statistical evidence, highlighting their advantages over traditional methods like p-values, likelihood ratios, and Bayes factors, especially in combining evidence and handling optional stopping.

Contribution

It introduces e-values and e-processes as promising evidence measures, comparing their properties to existing methods and demonstrating their practical and theoretical benefits.

Findings

E-values naturally combine evidence across studies.

E-processes handle optional stopping and continuation.

E-values and e-processes possess desirable evidential properties.

Abstract

A recurring debate in the philosophy of statistics concerns what, exactly, should count as a measure of evidence for or against a given hypothesis. P-values, likelihood ratios, and Bayes factors all have their defenders. In this paper we add two additional candidates to this list: the e-value and its sequential analogue, the e-process. E-values enjoy several desirable properties as measures of evidence: they combine naturally across studies, handle composite hypotheses, provide long-run error rates, and admit a useful interpretation as the wealth accrued by a bettor in a game against the null distribution. E-processes additionally handle optional stopping and optional continuation. This work examines the extent to which e-values and e-processes satisfy the evidential desiderata of different statistical traditions, concluding that they combine attractive features of p-values, likelihood ratios, and Bayes factors, and merit serious consideration as interpretable and intuitive measures of statistical evidence.