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

Jia-Chiun Pan,Guan-Hua Huang,Chih-Min Liu,Hai-Gwo Hwu,Cathy W.S Chen

doi:10.1371/journal.pone.0138899

Jia-Chiun Pan, Guan-Hua Huang + Show 3 more

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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.

Highlights

Finite mixture models provide a flexible way to model heterogeneous data, and have been applied to a wide variety of data in social, medical and physical science
In the Bayesian setting, if the prior information does not distinguish the components of the mixture model, the resulting posterior distributions will be invariant to all permutations of component labels
A odds ratios (ORs): odds ratio b CI: 95% credible interval of OR * Asterisk is added if value is significantly different from 1, judged by CI not covering 1

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Finite mixture models provide a flexible way to model heterogeneous data, and have been applied to a wide variety of data in social, medical and physical science. In the Bayesian setting, if the prior information does not distinguish the components of the mixture model, the resulting posterior distributions will be invariant to all permutations of component labels. An allocation variable based probabilistic relabelling approach (AVP algorithm) is proposed to find the labelling functions.

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