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Title: E is the new P: Optional continuation and evidence Authors:  Peter Grunwald - CWI and Leiden University (Netherlands) [presenting]
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. One central problem is its inability to deal with optional stopping, combining evidence of separate studies and its dependence on unknowable counterfactuals. We present the E-value, a recently popularized notion of evidence which overcomes these issues. If the null hypothesis is simple and there is an alternative, the E-value coincides with the Bayes factor, the notion of evidence preferred by Bayesians. But if the null is composite or nonparametric, or an alternative cannot be explicitly formulated, E-values and Bayes factors become distinct. Unlike the Bayes factor, E-values allow for tests with strict Type-I error control. They are also the basic building blocks of anytime-valid confidence intervals that remain valid under optional stopping.