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Title of Journal: Comput Stat

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Abbravation: Computational Statistics

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Springer Berlin Heidelberg

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DOI

10.1016/0006-8993(94)90048-5

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1613-9658

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Improving efficiency of data augmentation algorith

Authors: Vivekananda Roy
Publish Date: 2015/11/19
Volume: 31, Issue: 2, Pages: 709-728
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Abstract

Data augmentation DA algorithm is a widely used Markov chain Monte Carlo algorithm In this paper an alternative to DA algorithm is proposed It is shown that the modified Markov chain is always more efficient than DA in the sense that the asymptotic variance in the central limit theorem under the alternative chain is no larger than that under DA The modification is based on Peskun’s Biometrika 60607–612 1973 result which shows that asymptotic variance of time average estimators based on a finite state space reversible Markov chain does not increase if the Markov chain is altered by increasing all offdiagonal probabilities In the special case when the state space or the augmentation space of the DA chain is finite it is shown that Liu’s Biometrika 83681–682 1996 modified sampler can be used to improve upon the DA algorithm Two illustrative examples namely the betabinomial distribution and a model for analyzing rank data are used to show the gains in efficiency by the proposed algorithms

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