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Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler

G. O. Roberts and S. K. Sahu
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 59, No. 2 (1997), pp. 291-317
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2346048
Page Count: 27
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Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler
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Abstract

In this paper many convergence issues concerning the implementation of the Gibbs sampler are investigated. Exact computable rates of convergence for Gaussian target distributions are obtained. Different random and non-random updating strategies and blocking combinations are compared using the rates. The effect of dimensionality and correlation structure on the convergence rates are studied. Some examples are considered to demonstrate the results. For a Gaussian image analysis problem several updating strategies are described and compared. For problems in Bayesian linear models several possible parameterizations are analysed in terms of their convergence rates characterizing the optimal choice.

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