False Discovery Rate Control with E-values

Abstract E-values have gained attention as potential alternatives to p-values 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 stopped supermartingales. We design a natural analogue Benjamini-Hochberg (BH) procedure for false discovery rate (FDR) control that utilizes e-values, called e-BH procedure, compare it standard p-values. One our central results is that, unlike usual BH controls FDR desired level—with no correction—for any dependence structure between e-values. illustrate new convenient in various settings complicated dependence, structured post-selection hypotheses, multi-armed bandit problems. Moreover, special case through calibration Overall, novel, powerful general tool multiple testing complementary each being an appropriate choice different applications.