The Annals of Probability

Curvature, concentration and error estimates for Markov chain Monte Carlo

Aldéric Joulin and Yann Ollivier

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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.

Article information

Source
Ann. Probab., Volume 38, Number 6 (2010), 2418-2442.

Dates
First available in Project Euclid: 24 September 2010

Permanent link to this document
https://projecteuclid.org/euclid.aop/1285334210

Digital Object Identifier
doi:10.1214/10-AOP541

Mathematical Reviews number (MathSciNet)
MR2683634

Zentralblatt MATH identifier
1207.65006

Subjects
Primary: 65C05: Monte Carlo methods 60J22: Computational methods in Markov chains [See also 65C40] 62E17: Approximations to distributions (nonasymptotic)

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

Citation

Joulin, Aldéric; Ollivier, Yann. Curvature, concentration and error estimates for Markov chain Monte Carlo. Ann. Probab. 38 (2010), no. 6, 2418--2442. doi:10.1214/10-AOP541. https://projecteuclid.org/euclid.aop/1285334210


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