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Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models.

Sperrin, Matthew and Jaki, Thomas and Wit, Ernst (2010) Probabilistic relabelling strategies for the label switching problem in Bayesian mixture models. Statistics and Computing, 20 (3). pp. 357-366. ISSN 0960-3174

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    Abstract

    The label switching problem is caused by the likelihood of a Bayesian mixture model being invariant to permutations of the labels. The permutation can change multiple times between Markov Chain Monte Carlo (MCMC) iterations making it difficult to infer component-specific parameters of the model. Various so-called ‘relabelling’ strategies exist with the goal to ‘undo’ the label switches that have occurred to enable estimation of functions that depend on component-specific parameters. Most existing approaches rely upon specifying a loss function, and relabelling by minimising its posterior expected loss. In this paper we develop probabilistic approaches to relabelling that allow estimation and incorporation of the uncertainty in the relabelling process. Variants of the probabilistic relabelling algorithm are introduced and compared to existing loss function based methods. We demonstrate that the idea of probabilistic relabelling can be expressed in a rigorous framework based on the EM algorithm.

    Item Type: Article
    Journal or Publication Title: Statistics and Computing
    Uncontrolled Keywords: Bayesian - Identifiability - Label switching - MCMC - Mixture model
    Subjects: Q Science > QA Mathematics
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 26391
    Deposited By: Mr Matthew Sperrin
    Deposited On: 08 May 2009 13:21
    Refereed?: Yes
    Published?: Published
    Last Modified: 09 Oct 2013 14:49
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/26391

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