A note on e-values and multiple testing

We discover a connection between the Benjamini-Hochberg procedure and the e-Benjamini-Hochberg procedure (Wang & Ramdas, 2022) with a suitably defined set of e-values. This insight extends to Storey's procedure and generalized versions of the Benjamini-Hochberg procedure and the model-free multiple testing procedure of Barber & Cand & eacute;s (2015) with a general form of rejection rules. We further summarize these findings in a unified form. These connections open up new possibilities for designing multiple testing procedures in various contexts by aggregating e-values from different procedures or assembling e-values from different data subsets.