A0682
Title: Multivariate strong invariance principle and uncertainty assessment for time in-homogeneous cyclic MCMC samplers
Authors: Haoxiang Li - University of Minnesota, Twin Cities (United States) [presenting]
Qian Qin - University of Minnesota (United States)
Abstract: Time in-homogeneous cyclic Markov chain Monte Carlo (MCMC) samplers, including deterministic scan Gibbs samplers and Metropolis within Gibbs samplers, are extensively used for sampling from multi-dimensional distributions. A multivariate strong invariance principle (SIP) is established for Markov chains associated with these samplers. The rate of this SIP essentially aligns with the tightest rate available for time-homogeneous Markov chains. The SIP implies the strong law of large numbers (SLLN) and the central limit theorem (CLT) and plays an essential role in uncertainty assessments. Using the SIP, conditions are given under which the multivariate batch means estimator for estimating the covariance matrix in the multivariate CLT is strongly consistent. Additionally, conditions are provided for a multivariate fixed volume sequential termination rule, which is associated with the concept of effective sample size (ESS), to be asymptotically valid. The uncertainty assessment tools are demonstrated through various numerical experiments.
