The Annals of Probability

Curvature, concentration and error estimates for Markov chain Monte Carlo

Aldéric Joulin and Yann Ollivier

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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.

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

First available in Project Euclid: 24 September 2010

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Zentralblatt MATH identifier

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

Markov chain Monte Carlo concentration of measure Ricci curvature Wasserstein distance


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.

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