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Safe testing
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DOI：10.1093/jrsssb/qkae011.png)
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摘要
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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 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.
Keyword:
Bayes factors
e-values
hypothesis testing
information projection
optional stopping
test martingales
期刊
J
IF:
3.6
论文数:
1.5K
被引数:
3.2W
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