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Activity Number: 67 - Believable Big Bayes: Large-Scale Bayesian Inference with Finite-Data Guarantees
Type: Topic Contributed
Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
Sponsor: SSC
Abstract #307040
Title: Diffusion-Stein Sample Quality Measures for Distributions in Finite and Infinite Dimensions
Author(s): Andrew Duncan*
Companies: Imperial College London
Keywords: finite data guarantees; stein method; sampling; big bayes

In many applications one often wishes to quantify the discrepancy between a finite-size sample and a probability distribution. We introduce a quality measure based on Stein’s method which quantifies the maximum discrepancy between sample and target expectations over a large class of test functions. This discrepancy is able to provide relatively tight, deterministic upper and lower bounds to the Wasserstein metric for a large class of target distributions including multimodal and heavy-tailed densities.

The key ingredient is a careful construction of the Stein operator from the infinitesimal generator of a diffusion process which converges sufficiently quickly to a unique invariant distribution defined by the target density. Through a similar construction, we introduce an analogous discrepancy measure for distributions on a Hilbert space which are absolutely continuous with respect to a Gaussian reference measure, demonstrating similar control over the Wasserstein metric. Applications to path sampling and Bayesian inverse problems are discussed.

Authors who are presenting talks have a * after their name.

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