Geometric Ergodicity of Trans-Dimensional Markov Chain Monte Carlo Algorithms

• 成果类型: Article; Early Access
• 署名作者: Qin, Qian
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2024.2427432
• 发表日期: 2024
• 关键词: bayesian model selection; OUTPUT ANALYSIS; CONVERGENCE; distributions; gibbs; mcmc

摘要

This article studies the convergence properties of trans-dimensional MCMC algorithms when the total number of models is finite. It is shown that, for reversible and some nonreversible trans-dimensional Markov chains, under mild conditions, geometric convergence is guaranteed if the Markov chains associated with the within-model moves are geometrically ergodic. This result is proved in an L2 framework using the technique of Markov chain decomposition. While the technique was previously developed for reversible chains, this work extends it to the point that it can be applied to some commonly used nonreversible chains. The theory herein is applied to reversible jump algorithms for three Bayesian models: a probit regression with variable selection, a Gaussian mixture model with unknown number of components, and an autoregression with Laplace errors and unknown model order. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.