Curvature, concentration and error estimates for Markov chain Monte Carlo
Probability
2010-11-11 v2
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.
Cite
@article{arxiv.0904.1312,
title = {Curvature, concentration and error estimates for Markov chain Monte Carlo},
author = {Aldéric Joulin and Yann Ollivier},
journal= {arXiv preprint arXiv:0904.1312},
year = {2010}
}
Comments
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)