Confidence and discoveries with e-values

TL;DR

This paper compares confidence regions based on p-values and e-values, introducing an e-value-based procedure that is computationally efficient and may outperform traditional p-value methods in controlling false discoveries.

Contribution

It introduces a new e-value-based procedure for multiple hypothesis testing that controls false discoveries under arbitrary dependence, with demonstrated efficiency and potential advantages over p-value methods.

Findings

E-value-based procedure is computationally efficient.

The new method controls false discoveries under arbitrary dependence.

Indications of better performance in some scenarios compared to p-value methods.

Abstract

We discuss systematically two versions of confidence regions: those based on p-values and those based on e-values, a recent alternative to p-values. Both versions can be applied to multiple hypothesis testing, and in this paper we are interested in procedures that control the number of false discoveries under arbitrary dependence between the base p- or e-values. We introduce a procedure that is based on e-values and show that it is efficient both computationally and statistically using simulated and real-world datasets. Comparison with the corresponding standard procedure based on p-values is not straightforward, but there are indications that the new one performs significantly better in some situations.