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Allocation Variable-Based Probabilistic Algorithm to Deal with Label Switching Problem in Bayesian Mixture Models

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  • Jia-Chiun Pan
  • Chih-Min Liu
  • Hai-Gwo Hwu
  • Guan-Hua Huang

Abstract

The label switching problem occurs as a result of the nonidentifiability of posterior distribution over various permutations of component labels when using Bayesian approach to estimate parameters in mixture models. In the cases where the number of components is fixed and known, we propose a relabelling algorithm, an allocation variable-based (denoted by AVP) probabilistic relabelling approach, to deal with label switching problem. We establish a model for the posterior distribution of allocation variables with label switching phenomenon. The AVP algorithm stochastically relabel the posterior samples according to the posterior probabilities of the established model. Some existing deterministic and other probabilistic algorithms are compared with AVP algorithm in simulation studies, and the success of the proposed approach is demonstrated in simulation studies and a real dataset.

Suggested Citation

  • Jia-Chiun Pan & Chih-Min Liu & Hai-Gwo Hwu & Guan-Hua Huang, 2015. "Allocation Variable-Based Probabilistic Algorithm to Deal with Label Switching Problem in Bayesian Mixture Models," PLOS ONE, Public Library of Science, vol. 10(10), pages 1-23, October.
    • Handle: RePEc:plo:pone00:0138899
    DOI: 10.1371/journal.pone.0138899
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    References listed on IDEAS

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    1. 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.
    2. 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.
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