Curvature, concentration and error estimates for Markov chain Monte Carlo

Details Curvature, concentration and error estimates for Markov chain Monte Carlo Curvature, concentration and error estimates for Markov chain Monte Carlo

2009-04-08

arxiv.org/abs/0904.1312v2

Annals of Probability 2010, Vol. 38, No. 6, 2418-2442

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/10-AOP541 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of

Scientific paper

10.1214/10-AOP541

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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