Curvature, concentration and error estimates for Markov chain Monte Carlo
arXiv:0904.1312 · 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.
Published in at http://dx.doi.org/10.1214/10-AOP541 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)
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