Dimension-free Relaxation Times of Informed MCMC Samplers on Discrete Spaces

arXiv:2404.03867v1 Announce Type: cross
Abstract: Convergence analysis of Markov chain Monte Carlo methods in high-dimensional statistical applications is increasingly recognized. In this paper, we develop general mixing time bounds for Metropolis-Hastings algorithms on discrete spaces by building upon and refining some recent theoretical advancements in Bayesian model selection problems. We establish sufficient conditions for a class of informed Metropolis-Hastings algorithms to attain relaxation times that are independent of the problem dimension. These conditions are grounded in high-dimensional statistical theory and …

abstract algorithms analysis applications arxiv bayesian building convergence free general markov math.pr mcmc metropolis model selection paper spaces stat.co statistical stat.ml type