Game-Theoretic Statistics and Safe Anytime-Valid Inference
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.
November 2023 Game-Theoretic Statistics and Safe Anytime-Valid Inference Aaditya Ramdas, Peter Grünwald, Vladimir Vovk, Glenn Shafer Statist. Sci. 38(4): 576-601 (November 2023). DOI: 10.1214/23-STS894 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…
saved by
related reading
- A statistical approach to model evaluations \ Anthropicanthropic.com
- An optimization perspective on log-concave sampling and beyond | Sinho Chewichewisinho.github.io
- Background Risk and Small-Stakes Risk Aversiontamuz.caltech.edu
- 2012.00174arxiv.org
- [2605.01172] A Theory of Generalization in Deep Learningarxiv.org
- 2312.06942arxiv.org
- survey.dvimath.uchicago.edu
- Robust Regression for Safe Exploration in Controlarxiv.org
- Performative Predictionarxiv.org
- [2602.12316] GT-HarmBench: Benchmarking AI Safety Risks Through the Lens of Game Theoryarxiv.org
- [2411.00640] Adding Error Bars to Evals: A Statistical Approach to Language Model Evaluationsarxiv.org
- Gneiting2007jasa.pdfsites.stat.washington.edu