Abstract: The e-BH procedure is an e-value-based multiple testing procedure that provably controls the false discovery rate (FDR) under any dependence structure between the e-values. Despite this appealing theoretical FDR control guarantee, the e-BH procedure often suffers from low power in practice. In this paper, we propose a general framework that boosts the power of e-BH without sacrificing its FDR control under arbitrary dependence. This is achieved by the technique of conditional calibration, where we take as input the e-values and calibrate them to be a set of “boosted e-values” that are guaranteed to be no less—and are often more—powerful than the original ones. Our general framework is explicitly instantiated in three classes of multiple testing problems: (1) testing under parametric models, (2) conditional independence testing under the model-X setting, and (3) model-free conformalized selection. Extensive numerical results demonstrate that our proposed method significantly improves the power of the e-BH procedure while continuing to control the FDR.

Host: Robert Lunde