Game-Theoretic Statistics and Safe Anytime-Valid Inference

Statistical Science, vol. 38

Abstract

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.

Authors 4

1. Aaditya Ramdas

   Carnegie Mellon University

   Affiliation as printed

   Aaditya Ramdas is Assistant Professor, Statistics and Data Science, and Machine Learning, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

2. Peter Grünwald Aachen Peter Grünwald is Head Machine Learning Group

   Leiden University · Centrum Wiskunde & Informatica

   Affiliation as printed

   Peter Grünwald is Head, Machine Learning Group, Centrum Wiskunde & Informatica, Amsterdam, The Netherlands, and Professor of Statistics at Leiden University, The Netherlands

3. Vladimir Vovk

   Royal Holloway University of London

   Affiliation as printed

   Vladimir Vovk is Professor, Computer Science, Royal Holloway, University of London, UK

4. Glenn R. Shafer

   Rutgers, The State University of New Jersey

   Affiliation as printed

   Glenn Shafer is University Professor, Rutgers University, Piscataway, New Jersey 08854-8019, USA