Statistics and Data Science Seminar: A Martingale Theory of Evidence

Abstract: 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 modern 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 future directions. These ideas were summarized in, for example, a recent survey paper in Statistical Science (arXiv:2210.01948) and a JRSSB discussion paper (https://arxiv.org/abs/2010.09686).

Bio: Aaditya Ramdas is an Associate Professor in the Department of Statistics and Data Science and the Machine Learning Department at Carnegie Mellon University, as well as a visiting academic at Amazon Research. Aaditya received the Sloan fellowship in mathematics, the IMS Peter Gavin Hall Early Career Prize, the inaugural COPSS Emerging Leader Award, the Bernoulli New Researcher Award, the NSF CAREER Award, faculty research awards from Google and Adobe, and the Umesh K. Gavasker thesis award for his PhD. His research in mathematical statistics and learning focuses on designing algorithms that both have strong theoretical guarantees and also work well in practice. Key areas of interest include post-selection inference, game-theoretic statistics and predictive uncertainty quantification.

Host: Robert Lunde