Locally Simultaneous Inference
Speaker: Tijana Zrnic (Berkeley)
Abstract: I will begin the talk with an overview of selective inference, which is the problem of giving valid answers to statistical questions chosen in a data-driven manner. I will describe a standard solution to selective inference called simultaneous inference, which delivers valid answers to the set of all questions that could possibly have been asked. Then, I will describe a less conservative solution that we call locally simultaneous inference, which only answers those questions that could plausibly have been asked in light of the observed data, all the while preserving rigorous type I error guarantees. For example, if the objective is to construct a confidence interval for the “winning” treatment effect in a clinical trial with multiple treatments, and it is obvious in hindsight that only one treatment had a chance to win, then locally simultaneous inference will return an interval that is nearly the same as the uncorrected, standard interval. Based on joint work with Will Fithian. No prior knowledge of selective inference will be assumed. Link to paper: https://arxiv.org/pdf/2212.09009.pdf