Multivariate Stein Factors for a Class of Strongly Log-concave Distributions
Probability
2016-11-24 v6
Abstract
We establish uniform bounds on the low-order derivatives of Stein equation solutions for a broad class of multivariate, strongly log-concave target distributions. These "Stein factor" bounds deliver control over Wasserstein and related smooth function distances and are well-suited to analyzing the computable Stein discrepancy measures of Gorham and Mackey. Our arguments of proof are probabilistic and feature the synchronous coupling of multiple overdamped Langevin diffusions.
Keywords
Cite
@article{arxiv.1512.07392,
title = {Multivariate Stein Factors for a Class of Strongly Log-concave Distributions},
author = {Lester Mackey and Jackson Gorham},
journal= {arXiv preprint arXiv:1512.07392},
year = {2016}
}
Comments
14 pages. The strong continuity argument in an earlier version did not identify an appropriate Banach space; this version does so. arXiv admin note: substantial text overlap with arXiv:1506.03039