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August 2000 Antithetic coupling of two Gibbs sampler chains
Arnoldo Frigessi, Jørund Gåsemyr, Håvard Rue
Ann. Statist. 28(4): 1128-1149 (August 2000). DOI: 10.1214/aos/1015956710


Two coupled Gibbs sampler chains, both with invariant probability density $p$, are run in parallel so that the chains are negatively correlated.We define an asymptotically unbiased estimator of the $\pi$-expectation $E(f(\mathbf(X))$ which achieves significant variance reduction with respect to the usual Gibbs sampler at comparable computational cost. The variance of the estimator based on the new algorithm is always smaller than the variance of a single Gibbs sampler chain, if $\pi$ is attractive and $f$ is monotone nondecreasing in all components of $\mathbf{X}$. For nonattractive targets $\pi$, our results are not complete: The new antithetic algorithm outperforms the standard Gibbs sampler when $\pi$ is a multivariate normal density or the Ising model. More generally, nonrigorous arguments and numerical experiments support the usefulness of the antithetically coupled Gibbs samplers also for other nonattractive models. In our experiments the variance is reduced to at least a third and the efficiency also improves significantly.


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Arnoldo Frigessi. Jørund Gåsemyr. Håvard Rue. "Antithetic coupling of two Gibbs sampler chains." Ann. Statist. 28 (4) 1128 - 1149, August 2000.


Published: August 2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.65303
MathSciNet: MR1810922
Digital Object Identifier: 10.1214/aos/1015956710

Primary: 62M05
Secondary: 62C05 , 62M10

Keywords: Antithetic Monte Carlo , associated random variables , attractive models , decay of cross-autocorrelations , Markov chain Monte Carlo , variance reduction

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.28 • No. 4 • August 2000
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