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Abstract
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 out-
comes. 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.
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 out-
comes. 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.
| Original language | English |
|---|---|
| Publisher | arXiv |
| Pages | 1-47 |
| Number of pages | 47 |
| DOIs | |
| Publication status | Published - 10 Mar 2023 |
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Safe testing
Grünwald, P., de Heide, R. & Koolen, W., Nov 2024, In: Journal of the Royal Statistical Society. Series B: Statistical Methodology. 86, 5, p. 1091-1128 38 p.Research output: Contribution to Journal › Article › Academic › peer-review
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Safe Testing
Grunwald, P., De Heide, R. & Koolen, W. M., 2020, 2020 Information Theory and Applications Workshop (ITA) : [Proceedings]. IEEE, 47 p. 9244948Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review