MCMC Sampler Convergence Rates for Hierarchical Normal Linear Models: A Simulation Approach

This paper presents a straightforward method of approximating theoretical bounds on burn-in time for MCMC samplers for hierarchical normal linear models. An extension and refinement of Cowles and Rosenthal's (1998) simulation approach, it exploits Hodges's (1998) reformulation of hierarchical normal linear models. The method is illustrated with three real datasets, involving a one-way variance components model, a growth-curve model, and a spatial model with a pairwise-differences prior. In all three cases, when the specified priors produce proper, unimodal posterior distributions, the method provides very reasonable upper bounds on burn-in time. In contrast, when the posterior distribution for the variance-components model can be shown to be improper or bimodal, the new method correctly identifies convergence failure while several other commonly-used diagnostics provide false assurance that convergence has occurred.

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