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On the Convergence Rate of Random Permutation Sampler and ECR Algorithm in Missing Data Models

Author

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  • Panagiotis Papastamoulis

    (University of Piraeus)

  • George Iliopoulos

    (University of Piraeus)

Abstract

Label switching is a well-known phenomenon that occurs in MCMC outputs targeting the parameters’ posterior distribution of many latent variable models. Although its appearence is necessary for the convergence of the simulated Markov chain, it turns out to be a problem in the estimation procedure. In a recent paper, Papastamoulis and Iliopoulos (J Comput Graph Stat 19:313–331, 2010) introduced the Equivalence Classes Representatives (ECR) algorithm as a solution of this problem in the context of finite mixtures of distributions. In this paper, label switching is considered under a general missing data model framework that includes as special cases finite mixtures, hidden Markov models, and Markov random fields. The use of ECR algorithm is extended to this general framework and is shown that the relabelled sequence which it produces converges to its target distribution at the same rate as the Random Permutation Sampler of Frühwirth-Schnatter (2001) and that both converge at least as fast as the Markov chain generated by the original MCMC output.

Suggested Citation

  • Panagiotis Papastamoulis & George Iliopoulos, 2013. "On the Convergence Rate of Random Permutation Sampler and ECR Algorithm in Missing Data Models," Methodology and Computing in Applied Probability, Springer, vol. 15(2), pages 293-304, June.
    • Handle: RePEc:spr:metcap:v:15:y:2013:i:2:d:10.1007_s11009-011-9238-7
    DOI: 10.1007/s11009-011-9238-7
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    References listed on IDEAS

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    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. C. P. Robert & T. Rydén & D. M. Titterington, 2000. "Bayesian inference in hidden Markov models through the reversible jump Markov chain Monte Carlo method," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 57-75.
    3. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    4. repec:dau:papers:123456789/6069 is not listed on IDEAS
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    Cited by:

    1. Papastamoulis, Panagiotis, 2018. "Overfitting Bayesian mixtures of factor analyzers with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 220-234.

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