Variance bounding Markov chains
Probability
2008-12-18 v1
Abstract
We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis--Hastings algorithms.
Cite
@article{arxiv.0806.2747,
title = {Variance bounding Markov chains},
author = {Gareth O. Roberts and Jeffrey S. Rosenthal},
journal= {arXiv preprint arXiv:0806.2747},
year = {2008}
}
Comments
Published in at http://dx.doi.org/10.1214/07-AAP486 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)