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Title: Evidence and the optional continuation principle 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 such problem is its inability to deal with optional continuation (a weaker and, we argue, more urgent requirement than optional stopping) and its dependence on unknowable counterfactuals. The E-value is a notion of evidence which overcomes these issues. When both hypotheses are simple, the E-value is a likelihood ratio (LR) - nowadays the standard notion of probabilistic evidence in courts of law. When there is a null hypothesis and it is simple, the E-value coincides with the Bayes factor, the notion of evidence preferred by Bayesians. But while nonparametric hypotheses and/or lack of crisp alternatives pose difficulties for LRs and Bayes factors, one can still design useful E-values for them.