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Relabelling in Bayesian mixture models by pivotal units

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Abstract

Label switching is a well-known and fundamental problem in Bayesian estimation of finite mixture models. It arises when exploring complex posterior distributions by Markov Chain Monte Carlo (MCMC) algorithms, because the likelihood of the model is invariant to the relabelling of mixture components. If the MCMC sampler randomly switches labels, then it is unsuitable for exploring the posterior distributions for component-related parameters. In this paper, a new procedure based on the post-MCMC relabelling of the chains is proposed. The main idea of the method is to perform a clustering technique on the similarity matrix, obtained through the MCMC sample, whose elements are the probabilities that any two units in the observed sample are drawn from the same component. Although it cannot be generalized to any situation, it may be handy in many applications because of its simplicity and very low computational burden.

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Authors and Affiliations

  1. Dipartimento di Scienze Statistiche, Università degli Studi di Padova, Padua, Italy

    Leonardo Egidi

  2. Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche ‘Bruno de Finetti’, Università degli Studi di Trieste, Trieste, Italy

    Roberta Pappadà, Francesco Pauli & Nicola Torelli

Authors
  1. Leonardo Egidi
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  2. Roberta Pappadà
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  3. Francesco Pauli
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  4. Nicola Torelli
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Corresponding author

Correspondence to Leonardo Egidi.

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Egidi, L., Pappadà, R., Pauli, F. et al. Relabelling in Bayesian mixture models by pivotal units. Stat Comput 28, 957–969 (2018). https://doi.org/10.1007/s11222-017-9774-2

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  • DOI: https://doi.org/10.1007/s11222-017-9774-2

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