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arXiv · 0904.1312

Curvature, concentration and error estimates for Markov chain Monte Carlo

Aldéric Joulin·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.

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Aldéric Joulin, Yann Ollivier. 2010-11-10. Curvature, concentration and error estimates for Markov chain Monte Carlo. https://doi.org/10.1214/10-aop541

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