标题： 跨维度马尔可夫链蒙特卡洛算法的几何遍历性 显示英文标题

标题： Geometric ergodicity of trans-dimensional Markov chain Monte Carlo algorithms

摘要： 本文研究了当模型总数有限时，跨维度MCMC算法的收敛性质。 结果表明，对于可逆和某些非可逆的跨维度马尔可夫链，在温和条件下，如果与模型内移动相关的马尔可夫链是几何遍历的，则保证几何收敛性。 此结果在一个$L^2$框架中通过马尔可夫链分解技术得到证明。 虽然该技术之前已开发用于可逆链，但这项工作将其扩展到可以应用于一些常用非可逆链的程度。 文中理论被应用于三个贝叶斯模型的可逆跳跃算法：具有变量选择的probit回归、具有未知成分数量的高斯混合模型，以及具有拉普拉斯误差和未知模型阶数的自回归模型。 显示英文摘要

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 non-reversible 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 $L^2$ 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 non-reversible 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.