Markov chain comparison

@misc{citeulike:1189104, abstract = {This is an expository paper, focussing on the following scenario. We have two Markov chains, \$\mathcal {M}\$ and \$\mathcal {M}'\$. By some means, we have obtained a bound on the mixing time of \$\mathcal {M}'\$. We wish to compare \$\mathcal {M}\$ with \$\mathcal {M}'\$ in order to derive a corresponding bound on the mixing time of \$\mathcal {M}\$. We investigate the application of the comparison method of Diaconis and Saloff-Coste to this scenario, giving a number of theorems which characterize the applicability of the method. We focus particularly on the case in which the chains are not reversible. The purpose of the paper is to provide a catalogue of theorems which can be easily applied to bound mixing times.}, author = {Dyer, Martin and Goldberg, Leslie A. and Jerrum, Mark and Martin, Russell }, citeulike-article-id = {1189104}, eprint = {math.PR/0410331}, keywords = {algorithms, stochastic}, month = {May}, posted-at = {2007-03-27 11:46:36}, priority = {2}, title = {Markov chain comparison}, url = {http://arxiv.org/abs/math.PR/0410331}, year = {2006} }

TY - ELEC ID - citeulike:1189104 L3 - citeulike-article-id:1189104 TI - Markov chain comparison N2 - This is an expository paper, focussing on the following scenario. We have two Markov chains, $\mathcal {M}$ and $\mathcal {M}'$. By some means, we have obtained a bound on the mixing time of $\mathcal {M}'$. We wish to compare $\mathcal {M}$ with $\mathcal {M}'$ in order to derive a corresponding bound on the mixing time of $\mathcal {M}$. We investigate the application of the comparison method of Diaconis and Saloff-Coste to this scenario, giving a number of theorems which characterize the applicability of the method. We focus particularly on the case in which the chains are not reversible. The purpose of the paper is to provide a catalogue of theorems which can be easily applied to bound mixing times. KW - algorithms KW - stochastic AU - Dyer, Martin AU - Goldberg, Leslie AU - Jerrum, Mark AU - Martin, Russell PY - 2006/May/03/ UR - http://arxiv.org/abs/math.PR/0410331 ER -