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Eindhoven SPOR seminar
Nov 22, 2022, 15:45 - 16:45
Peter Grunwald (CWI/LEI) – E is the New P
Tuesday, the 22nd of November, 15:45 – 16:45, MetaForum MF14
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. We present the e-value, a recently popularized notion of evidence which overcomes some of these issues. While e-values have lain dormant until 2019, interest in them has recently exploded with papers in the Annals of Statistics, Journal of the Royal Statistical Society and the like – in June 2022 we held a first workshop on e-values at EURANDOM in Eindhoven with attendees from probability theory, theoretical statistics, clinical trial design and meta-analysis but also from some of the large tech companies interested in A/B testing.
E-values are also the basic building blocks of anytime-valid confidence intervals that remain valid under optional stopping. In simple cases, e-values coincide with a classical Bayesian notion of evidence. But if the null is composite or nonparametric, or an alternative cannot be explicitly formulated, e-values and Bayes factors become distinct and e-processes can be seen as a generalization of nonnegative supermartingales. Unlike the Bayes factor, E-values allow for tests with strict ‘ classical’ Type-I error control under optional continuation and combination of data from different sources. They are also easier to interpret than p-values, having a straightforward interpretation in terms of betting.