Open Access
2016 Multivariate Stein factors for a class of strongly log-concave distributions
Lester Mackey, Jackson Gorham
Electron. Commun. Probab. 21: 1-14 (2016). DOI: 10.1214/16-ECP15


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.


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Lester Mackey. Jackson Gorham. "Multivariate Stein factors for a class of strongly log-concave distributions." Electron. Commun. Probab. 21 1 - 14, 2016.


Received: 4 April 2016; Accepted: 8 August 2016; Published: 2016
First available in Project Euclid: 2 September 2016

zbMATH: 1348.60116
MathSciNet: MR3548768
Digital Object Identifier: 10.1214/16-ECP15

Primary: 60E15 , 60J60 , 62E17

Keywords: generator method , multivariate log-concave distribution , overdamped Langevin diffusion , Stein discrepancy , Stein factors , Stein’s method , synchronous coupling

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