Principle of detailed balance and convergence assessment of Markov Chain Monte Carlo methods and simulated annealing

Simple item page
dc.creatorCosma, Ioana A.
dc.creatorAsgharian, Masoud
dc.date2008-07-20
dc.date.accessioned2026-07-07T09:51:45Z
dc.date.available2026-07-07T09:51:45Z
dc.descriptionMarkov Chain Monte Carlo (MCMC) methods are employed to sample from a given distribution of interest, whenever either the distribution does not exist in closed form, or, if it does, no efficient method to simulate an independent sample from it is available. Although a wealth of diagnostic tools for convergence assessment of MCMC methods have been proposed in the last two decades, the search for a dependable and easy to implement tool is ongoing. We present in this article a criterion based on the principle of detailed balance which provides a qualitative assessment of the convergence of a given chain. The criterion is based on the behaviour of a one-dimensional statistic, whose asymptotic distribution under the assumption of stationarity is derived; our results apply under weak conditions and have the advantage of being completely intuitive. We implement this criterion as a stopping rule for simulated annealing in the problem of finding maximum likelihood estimators for parameters of a 20-component mixture model. We also apply it to the problem of sampling from a 10-dimensional funnel distribution via slice sampling and the Metropolis-Hastings algorithm. Furthermore, based on this convergence criterion we define a measure of efficiency of one algorithm versus another.
dc.description29 pages, 5 figures
dc.identifierhttps://arxiv.org/abs/0807.3151
dc.identifierhttp://arxiv.org/abs/0807.3151
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/165355
dc.subjectComputation
dc.subjectMethodology
dc.titlePrinciple of detailed balance and convergence assessment of Markov Chain Monte Carlo methods and simulated annealing
dc.typetext

Files

Collections

arXiv