## Special Colloquium

### Friday, February 1st, 2019

**Time:** 2:30 p.m. **Place:** Jeffery Hall 234

**Speaker:** Yanglei Song (UIUC)

**Title:** Asymptotically optimal multiple testing with streaming data.

**Abstract: ** The problem of testing multiple hypotheses with streaming (sequential) data arises in diverse applications such as multi-channel signal processing, surveillance systems, multi-endpoint clinical trials, and online surveys. In this talk, we investigate the problem under two generalized error metrics. Under the first one, the probability of at least $k$ mistakes, of any kind, is controlled. Under the second, the probabilities of at least $k_1$ false positives and at least $k_2$ false negatives are simultaneously controlled. For each formulation, we characterize the optimal expected sample size to a first-order asymptotic approximation as the error probabilities vanish, and propose a novel procedure that is asymptotically efficient under every signal configuration. These results are established when the data streams for the various hypotheses are independent and each local log-likelihood ratio statistic satisfies a certain law of large numbers. Further, in the special case of iid observations, we quantify the asymptotic gains of sequential sampling over fixed-sample size schemes.

**Yanglei Song** is a Ph.D. Candidate in Statistics at the University of Illinois, Urbana-Champaign. His current research interests include multiple testing with streaming data, sequential change-point detection and high dimensional U-statistics.