Some topics on Gaussian and subGaussian SPRTs
Speaker: Hongjian Wang
Abstract: The sequential probability ratio test (SPRT), also known as the likelihood ratio test (LRT), was first developed by Wald in the 40s. In its modern incarnation it says that the probability ratio process dQ/dP(X1, ..., Xn) under the null P is a non-negative martingale, hence an e-process, which satisfies Ville's inequality. I will chiefly focus on the case when P and Q are both Gaussian, and cover the following very interconnected topics: (1) Growth and shrinkage (2) mixtures (proper and improper, which leads to interesting "non-integrable" martingales and maximal inequalities) (3) Confidence sequences (4) large, nonparametric, non-iid nulls. In particular, results from the following two papers will be mentioned: [1] Section 3.2 of https://arxiv.org/abs/2203.04485 [2] Sections 5-6 of https://arxiv.org/abs/2304.01163