False discovery rate control with e-values
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E-values have gained recent attention as potential alternatives to p-values as measures of uncertainty, significance and evidence. In brief, e-values are random variables with expectation at most one under the null; examples include betting scores, inverse Bayes factors, likelihood ratios and stopped supermartingales. We design a natural analog of the Benjamini-Hochberg (BH) procedure for false discovery control (FDR) control that utilizes e-values (e-BH) 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 show that the e-BH procedure includes the BH procedure as a special case through calibration between p-values and e-values. Several illustrative examples and results of independent interest are provided.
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