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June, 1995 Rates of Convergence for Gibbs Sampling for Variance Component Models
Jeffrey S. Rosenthal
Ann. Statist. 23(3): 740-761 (June, 1995). DOI: 10.1214/aos/1176324619


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.


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Jeffrey S. Rosenthal. "Rates of Convergence for Gibbs Sampling for Variance Component Models." Ann. Statist. 23 (3) 740 - 761, June, 1995.


Published: June, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0841.62074
MathSciNet: MR1345197
Digital Object Identifier: 10.1214/aos/1176324619

Primary: 62M05
Secondary: 60J05

Keywords: Gibbs sampler , Harris recurrence , Markov chain Monte Carlo , rate of convergence , variance component model

Rights: Copyright © 1995 Institute of Mathematical Statistics


Vol.23 • No. 3 • June, 1995
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