Open Access
Translator Disclaimer
November 2010 Curvature, concentration and error estimates for Markov chain Monte Carlo
Aldéric Joulin, Yann Ollivier
Ann. Probab. 38(6): 2418-2442 (November 2010). DOI: 10.1214/10-AOP541

Abstract

We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a “positive curvature” assumption expressing a kind of metric ergodicity, which generalizes the Ricci curvature from differential geometry and, on finite graphs, amounts to contraction under path coupling.

Citation

Download Citation

Aldéric Joulin. Yann Ollivier. "Curvature, concentration and error estimates for Markov chain Monte Carlo." Ann. Probab. 38 (6) 2418 - 2442, November 2010. https://doi.org/10.1214/10-AOP541

Information

Published: November 2010
First available in Project Euclid: 24 September 2010

zbMATH: 1207.65006
MathSciNet: MR2683634
Digital Object Identifier: 10.1214/10-AOP541

Subjects:
Primary: 60J22 , 62E17 , 65C05

Keywords: concentration of measure , Markov chain Monte Carlo , Ricci curvature , Wasserstein distance

Rights: Copyright © 2010 Institute of Mathematical Statistics

JOURNAL ARTICLE
25 PAGES


SHARE
Vol.38 • No. 6 • November 2010
Back to Top