Bayesian probability

Bayes factor

Mathematics

Statistical hypothesis testing

Statistics

Calibration

Econometrics

Bayes' theorem

Multiple comparisons problem

The Annals of Statistics

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.

E-values: Calibration, combination and applications