E-values as statistical evidence: A comparison to Bayes factors, likelihoods, and p-values
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| Format: | Preprint |
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2026
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| _version_ | 1866908913370136576 |
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| author | Chugg, Ben Ramdas, Aaditya Grünwald, Peter |
| author_facet | Chugg, Ben Ramdas, Aaditya Grünwald, Peter |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_24421 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | E-values as statistical evidence: A comparison to Bayes factors, likelihoods, and p-values Chugg, Ben Ramdas, Aaditya Grünwald, Peter Methodology Statistics Theory Other Statistics 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. |
| title | E-values as statistical evidence: A comparison to Bayes factors, likelihoods, and p-values |
| topic | Methodology Statistics Theory Other Statistics |
| url | https://arxiv.org/abs/2603.24421 |