E is the new P

Abstract

How much evidence do the data give us about one hypothesis versus another? The standard way to measure evidence is still the p-value, despite a myriad of problems surrounding it. In this talk I will provide a gentle introduction to the e-value (wikipedia), a recently popularized notion of evidence which overcomes some of these issues. In particular, they effortlessly deal with optional continuation: with e-value based tests and the corresponding anytime valid (AV) confidence intervals, one can always gather additional data, while keeping statistically valid conclusions. Until 2019, publications on e-values were few and far between: the concept did not even have a name. Then, in the course of a few months, four papers by different research groups appeared on arXiv that firmly established them as an important statistical concept. The first of these was Safe Testing (see below) ; another one was Shafer's testing by betting (Shafer's "bets" are the same as e-values). By now, there are 100s of papers and there have been three international workshops on e-values. Allowing for optional continuation is just one way in which e-values provide more flexibility than p-values – they also allow to set a type of significance/confidence level alpha after seeing the data, which - despite being unconsciously done all the time - is a mortal sin in classical testing. In this talk I will introduce e-values, e-processes and AV confidence intervals, and discuss in detail the relation to Bayesian approaches, which are in some ways related and in others completely different.

Main Literature:

G., De Heide, Koolen. Safe Testing. Journal of the Royal Statistical Society Series B, 2024 (first version appeared on arXiv 2019).

G. Beyond Neyman-Pearson: e-values enable hypothesis testing with a data-driven alpha. Proceedings National Academy of Sciences of the USA (PNAS), 2024.

G. The E-Posterior. Phil. Trans. Roy. Soc. London Series A, 2023.