This is the public, feature-limited version of the conference webpage. After Registration and login please visit the full version.

Confidence sequences for sampling without replacement

Ian Waudby-Smith, Aaditya Ramdas

Spotlight presentation: Orals & Spotlights Track 25: Probabilistic Models/Statistics
on 2020-12-10T08:10:00-08:00 - 2020-12-10T08:20:00-08:00
Poster Session 6 (more posters)
on 2020-12-10T09:00:00-08:00 - 2020-12-10T11:00:00-08:00
Abstract: Many practical tasks involve sampling sequentially without replacement (WoR) from a finite population of size $N$, in an attempt to estimate some parameter $\theta^\star$. Accurately quantifying uncertainty throughout this process is a nontrivial task, but is necessary because it often determines when we stop collecting samples and confidently report a result. We present a suite of tools for designing \textit{confidence sequences} (CS) for $\theta^\star$. A CS is a sequence of confidence sets $(C_n)_{n=1}^N$, that shrink in size, and all contain $\theta^\star$ simultaneously with high probability. We first exploit a relationship between Bayesian posteriors and martingales to construct a (frequentist) CS for the parameters of a hypergeometric distribution. We then present Hoeffding- and empirical-Bernstein-type time-uniform CSs and fixed-time confidence intervals for sampling WoR which improve on previous bounds in the literature.

Preview Video and Chat

To see video, interact with the author and ask questions please use registration and login.