A0547
Title: Geometric ergodicity of trans-dimensional Markov chain Monte Carlo algorithms
Authors: Qian Qin - University of Minnesota (United States) [presenting]
Abstract: The convergence properties of trans-dimensional MCMC algorithms are studied(e.g., the reversible jump algorithm) 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 is extended to the point that it can be applied to some commonly used non-reversible chains. Under geometric convergence, a central limit theorem holds for ergodic averages, even in the absence of Harris ergodicity. This allows for the construction of simultaneous confidence intervals for features of the target distribution.
