The application of game-theoretic probability to statistical tasks, often yielding different—and sometimes superior—procedures to traditional methods. See, for instance, game-theoretic hypothesis testing. Modern approaches to safe, anytime-valid inference (SAVI) tend to use the toolbox of game-theoretic statistics. Much of the recent work on confidence sequences, e-values, and e-processes is motivated by, or based on, game-theoretic statistics.
While game-theoretic statistics was originally formulated in terms of game-theoretic probability, and the results can be stated in that language, they are often stated measure theoretically for practical purposes (and to convince other statisticians and practitioners of the value of the methodology).
Game-theoretic statistics might be considered a third perspective on the foundations of statistics, alongside Bayesian statistics and frequentist statistics.
Refs
- A 2023 review paper by Ramdas, Grünwald, Vovk, and Shafer.
- How to invent game-theoretic statistics yourself, in 16 mostly easy steps.