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arXiv · 2603.24421

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

Ben Chugg·Aaditya Ramdas·Peter Grünwald
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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.

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Ben Chugg, Aaditya Ramdas, Peter Grünwald. 2026-08-27. E-values as statistical evidence: A comparison to Bayes factors, likelihoods, and p-values. https://arxiv.org/abs/2603.24421

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