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

Synthese, vol. 208

Abstract

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.

Authors 3

1. Ben Chugg corresponding

   Carnegie Mellon University

   Affiliation as printed

   Carnegie Mellon University, Pittsburgh, USA

2. Aaditya Ramdas

   Carnegie Mellon University

   Affiliation as printed

   Carnegie Mellon University, Pittsburgh, USA

3. Peter Grünwald Aachen

   Leiden University · Centrum Wiskunde & Informatica

   Affiliation as printed

   Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

   Leiden University, Leiden, The Netherlands