Christine P. Chai's contribution to the Discussion of 'Safe testing' by Grünwald, De Heide, and Koolen
成果类型：
Editorial Material
署名作者：
Chai, Christine P.
署名单位：
Microsoft
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1093/jrsssb/qkae081
发表日期：
2024
关键词：
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 (GAO) as an analogue of power in an optional continuation context, and we show how to construct GAO e-variables for general testing problems with composite null and alternative, emphasizing models with nuisance parameters. GAO 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 2 x 2 contingency table. Sharing Fisherian, Neymanian, and Jeffreys-Bayesian interpretations, e-values may provide a methodology acceptable to adherents of all three schools.
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