Multivariate Stein Factors for a Class of Strongly Log-concave Distributions

Understand

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.