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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.

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