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

arXiv: https://arxiv.org/abs/2603.24421 · HTML: https://mlsanity.com/paper/2603.24421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Mar 2026.

## Built on by (most cited first, 1 of 1)

- [Optimal Rates for Differentially Private Hypothesis Testing with E-values](https://mlsanity.com/paper/2605.28952/) (2026)

## Abstract (arXiv)

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.