Abstract
This paper analyzes the Gibbs sampler applied to a standard variance component model, and considers the question of how many iterations are required for convergence. It is proved that for $K$ location parameters, with $J$ observations each, the number of iterations required for convergence (for large $K$ and $J$) is a constant times $(1 + \log K/\log J)$. This is one of the first rigorous, a priori results about time to convergence for the Gibbs sampler. A quantitative version of the theory of Harris recurrence (for Markov chains) is developed and applied.
Citation
Jeffrey S. Rosenthal. "Rates of Convergence for Gibbs Sampling for Variance Component Models." Ann. Statist. 23 (3) 740 - 761, June, 1995. https://doi.org/10.1214/aos/1176324619
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