Game-theoretic statistics and anytime-valid inference using e-values, martingales and betting

Date
Thu January 11th 2024, 4:30pm
Location
Pigott 113
Speaker
Aaditya Ramdas, Carnegie Mellon University

This talk will describe an approach towards testing hypotheses and estimating functionals that is based on games. In short, to test a (possibly composite, nonparametric) hypothesis, we set up a game in which no betting strategy can make money under the null (the wealth is an "e-process" under the null). But if the null is false, then smart betting strategies will have exponentially increasing wealth. Thus, hypotheses are rewritten as constraints in games, the statistician is a gambler, test statistics are betting strategies, and the wealth obtained is directly a measure of evidence which is valid at any data-dependent stopping time (an e-value). The optimal betting strategies are typically Bayesian, but the guarantees are frequentist. This "game perspective" provides new statistically and computationally efficient solutions to many problems, like nonparametric independence or two-sample testing by betting, estimating means of bounded random variables, testing exchangeability, and so forth. The talk will summarize some past work and present some future directions.

These ideas were summarized in a recent survey paper in Statistical Science.

Zoom Recording [SUNet/SSO authentication required]