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Rates of convergence for Gibbs sampling for variance component models. (English) Zbl 0841.62074
Summary: This paper analyzes the Gibbs sampler applied to a standard variance components 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.

##### MSC:
 62M05 Markov processes: estimation; hidden Markov models 60J05 Discrete-time Markov processes on general state spaces
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