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Abstract:
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Over the last 25 years, techniques based on drift and minorization (d&m) have been mainstays in the convergence analysis of MCMC algorithms. Recent results suggest that d&m may be less useful in the emerging area of convergence complexity analysis, which is the study of how Monte Carlo Markov chain convergence behavior scales with sample size, $n$, and/or number of covariates, $p$. Alternative methods of constructing convergence rate bounds (with respect to total variation distance) will be presented. These new methods, which are based on Wasserstein distance and random mappings, have been used to analyze Albert and Chib's (1995, JASA) data augmentation algorithm for the Bayesian probit model, and the results will be described. (This is joint work with Qian Qin.)
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