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.

翻译：统计学哲学中的一个反复争论点涉及什么确切应被视为支持或反对某一假设的证据度量。p值、似然比和贝叶斯因子均有各自的拥护者。本文在两个候选度量中加入新增的两项：e-value及其序贯版本e-process。e-values作为证据度量具有若干理想性质：它们能自然地跨研究整合、处理复合假设、提供长期错误率，并允许一种有用的解释，即作为博弈中赌徒对抗零假设分布所累积的财富。e-processes额外允许可选停止与可选继续。本研究考察了e-values和e-processes在多大程度上满足不同统计传统的证据性需求，结论认为它们融合了p值、似然比和贝叶斯因子的吸引人特征，值得作为可解释且直观的统计证据度量予以认真考虑。