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Improving efficiency of data augmentation algorithms using Peskun’s theorem

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  • Vivekananda Roy

    (Iowa State University)

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 60:607–612, 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 off-diagonal 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 83:681–682, 1996) modified sampler can be used to improve upon the DA algorithm. Two illustrative examples, namely the beta-binomial distribution, and a model for analyzing rank data are used to show the gains in efficiency by the proposed algorithms.

Suggested Citation

  • Vivekananda Roy, 2016. "Improving efficiency of data augmentation algorithms using Peskun’s theorem," Computational Statistics, Springer, vol. 31(2), pages 709-728, June.
    • Handle: RePEc:spr:compst:v:31:y:2016:i:2:d:10.1007_s00180-015-0632-4
    DOI: 10.1007/s00180-015-0632-4
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    References listed on IDEAS

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    1. D. Brook & G. J. G. Upton, 1974. "Biases in Local Government Elections Due to Position on the Ballot Paper," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 23(3), pages 414-419, November.
    2. Roy, Vivekananda, 2014. "Efficient estimation of the link function parameter in a robust Bayesian binary regression model," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 87-102.
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