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Friday, August 21, 2020

Friday, August 21, 2020 — 10:30 to 11:30 AM to 11:30 AM EDT

Optimal supermartingales for anytime-valid sequential testing

Statistical testing is`anytime-valid’ if the decision to stop or continue an experiment can depend on anything that has been observed so far, without compromising statistical error guarantees. For instance, suppose that a promising but inconclusive study receives funding to gather additional data. Then standard p-value analysis is invalidated, but anytime-valid testing is not. A recent approach to anytime-valid testing views a test statistic as a bet against the null hypothesis. These bets are constrained to be supermartingales - hence unprofitable - under the null, but designed to be profitable under the relevant alternative hypotheses. This perspective opens the door to using tools from financial mathematics. In this talk I will explain how notions such as supermartingale measures, fork-convexity, the optional decomposition theorem, and universal portfolios can be used to design optimal supermartingales for anytime-valid sequential testing. (This talk is based on ongoing work with Aaditya Ramdas (CMU) and Johannes Ruf (LSE).) 

Please Note: This talk will be given through Webex. To join, please click here: Department seminar by Martin Larsson

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