A0359
Title: Extrapolation of tempered posteriors
Authors: Marina Riabiz - University of Cambridge (United Kingdom)
Mengxin Xi - Kings College London (United Kingdom) [presenting]
Chris Oates - Newcastle University (United Kingdom)
Zheyang Shen - Newcastle University (United Kingdom)
Nicolas Chopin - CREST-ENSAE (France)
Abstract: Accurately estimating quantities of interest from posterior distributions within a limited computational budget is essential across various fields. However, sampling from informative posterior distributions presents significant challenges. Tempering methods facilitate the construction of a path from the prior distribution to the complex posterior distribution. Instead of using samples from the posterior distribution to estimate posterior expectations, samples from intermediate tempered distributions and their corresponding tempered posterior expectations are used. The knowledge of the intermediate distributions enables posterior quantities of interest to be extrapolated. Specifically, weak sufficient conditions are established under which tempered expectations are not merely smooth as a function of t, but analytic, implying that knowledge of the tempered expectation in any open t interval fully determines the posterior expectation of interest.
