E-values: Calibration, combination, and applications

TL;DR

This paper advocates replacing p-values with e-values in multiple hypothesis testing, demonstrating their mathematical advantages and proposing new procedures for more efficient testing.

Contribution

It introduces e-values as a superior alternative to p-values for multiple testing, with simple averaging for merging and enhanced mathematical tractability.

Findings

E-values can be merged by averaging, simplifying multiple testing procedures.

E-values are mathematically more tractable than p-values.

Proposed methods improve efficiency in multiple hypothesis testing.

Abstract

Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values. In this paper we replace p-values with their natural competitor, e-values, which are closely related to betting, Bayes factors, and likelihood ratios. We demonstrate that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e-values can be merged simply by averaging them. This allows us to develop efficient procedures using e-values for testing multiple hypotheses.