E-values have gained attention as potential alternatives to p-values as measures of uncertainty, significance and evidence. In brief, e-values are realized by random variables with expectation at most one under the null; examples include betting scores, (point null) Bayes factors, likelihood ratios and stopped supermartingales. We design a natural analog of the Benjamini-Hochberg (BH) procedure for false discovery rate (FDR) control that utilizes e-values, called the e-BH procedure, and compare it with the standard procedure for p-values. One of our central results is that, unlike the usual BH procedure, the e-BH procedure controls the FDR at the desired level -- with no correction -- for any dependence structure between the e-values. We illustrate that the new procedure is convenient in various settings of complicated dependence, structured and post-selection hypotheses, and multi-armed bandit problems. Moreover, the BH procedure is a special case of the e-BH procedure through calibration between p-values and e-values. Overall, the e-BH procedure is a novel, powerful and general tool for multiple testing under dependence, that is complementary to the BH procedure, each being an appropriate choice in different applications.

翻译：电子价值作为不确定性、意义和证据的衡量标准,作为P值的潜在替代物,得到了人们的注意。简言之,电子价值是通过随机变量实现的,预期多数在无效值下;例子包括赌注分数、(点空)贝斯系数、概率比率和停止超离值。我们设计了一个Benjani-Hochberg(BH)程序天然模拟程序,用于假发现率(FDR)控制,该程序使用电子价值,称为e-BH程序,并与P-价值标准程序进行比较。我们的核心结果之一是,与通常的BH程序不同,e-BH程序在理想水平上控制FDR(没有纠正)电子价值之间任何依赖性结构。我们指出,新程序在各种复杂依赖性、结构化和选后假设以及多臂强的土匪问题的环境中是方便的。此外,BH程序是电子-BH程序的一个特殊案例,通过校准P-价值和电子价值之间的标准程序。总的来说,e-BH程序是一种新颖的、强大的和通用工具,在B-H程序下对多种依赖性进行适当的测试是一种新的、强大的和通用工具。