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.
"Multivariate Stein factors for a class of strongly log-concave distributions." Electron. Commun. Probab. 21 1 - 14, 2016. https://doi.org/10.1214/16-ECP15