Open Access
November 2023 Game-Theoretic Statistics and Safe Anytime-Valid Inference
Aaditya Ramdas, Peter Grünwald, Vladimir Vovk, Glenn Shafer
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Statist. Sci. 38(4): 576-601 (November 2023). DOI: 10.1214/23-STS894


Safe anytime-valid inference (SAVI) provides measures of statistical evidence and certainty—e-processes for testing and confidence sequences for estimation—that remain valid at all stopping times, accommodating continuous monitoring and analysis of accumulating data and optional stopping or continuation for any reason. These measures crucially rely on test martingales, which are nonnegative martingales starting at one. Since a test martingale is the wealth process of a player in a betting game, SAVI centrally employs game-theoretic intuition, language and mathematics. We summarize the SAVI goals and philosophy, and report recent advances in testing composite hypotheses and estimating functionals in nonparametric settings.


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Aaditya Ramdas. Peter Grünwald. Vladimir Vovk. Glenn Shafer. "Game-Theoretic Statistics and Safe Anytime-Valid Inference." Statist. Sci. 38 (4) 576 - 601, November 2023.


Published: November 2023
First available in Project Euclid: 6 November 2023

Digital Object Identifier: 10.1214/23-STS894

Keywords: Confidence sequence , e-process , nonparametric composite hypothesis testing , optional stopping , reverse information projection , Test martingales , universal inference , Ville’s Inequality

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.38 • No. 4 • November 2023
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