Electronic Communications in Probability

Multivariate Stein factors for a class of strongly log-concave distributions

Lester Mackey and Jackson Gorham

Full-text: Open access

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.

Article information

Source
Electron. Commun. Probab., Volume 21 (2016), paper no. 56, 14 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1472830238

Digital Object Identifier
doi:10.1214/16-ECP15

Mathematical Reviews number (MathSciNet)
MR3548768

Zentralblatt MATH identifier
1348.60116

Subjects
Primary: 60J60: Diffusion processes [See also 58J65] 62E17: Approximations to distributions (nonasymptotic) 60E15: Inequalities; stochastic orderings

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

Mackey, Lester; Gorham, Jackson. Multivariate Stein factors for a class of strongly log-concave distributions. Electron. Commun. Probab. 21 (2016), paper no. 56, 14 pp. doi:10.1214/16-ECP15. https://projecteuclid.org/euclid.ecp/1472830238


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