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‘Safe Testing’
We develop the theory of hypothesis testing based on the e-value, a notion of evidence that, unlike the p-value, allows for effortlessly combining results from several studies in the common scenario where the decision to perform a new study may depend on previous outcomes. Tests based on e-values are safe, i.e. they preserve Type-I error guarantees, under such optional continuation. We define growth rate optimality (GRO) as an analogue of power in an optional continuation context, and we show how to construct GRO e-variables for general testing problems with composite null and alternative, emphasizing models with nuisance parameters. GRO e-values take the form of Bayes factors with special priors. We illustrate the theory using several classic examples including a one-sample safe t-test and the 2 × 2 contingency table. Sharing Fisherian, Neymanian and Jeffreys-Bayesian interpretations, e-values may provide a methodology acceptable to adherents of all three schools. |
Paper: ‘Safe Testing’
Authors:
Peter Grünwald, CWI and Leiden University, Netherlands, Rianne de Heide, Vrije Universiteit Amsterdam, Netherlands, Wouter Koolen, CWI and University of Twente, Netherlands.