Wenkai Xu's contribution to the Discussion of 'Safe testing' by Grünwald, De Heide and Koolen

• 成果类型: Article
• 署名作者: Xu, Wenkai
• 署名单位: Eberhard Karls University of Tubingen
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkae087
• 发表日期: 2024
• 关键词: information; divergence; RISK

摘要

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 1-sample safe t-test and the 2x2 contingency table. Sharing Fisherian, Neymanian, and Jeffreys-Bayesian interpretations, e-values may provide a methodology acceptable to adherents of all three schools.