Statistics and Computing

, Volume 28, Issue 4, pp 957–969 | Cite as

Relabelling in Bayesian mixture models by pivotal units

  • Leonardo EgidiEmail author
  • Roberta Pappadà
  • Francesco Pauli
  • Nicola Torelli


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.


Label switching Complex posterior distributions MCMC Finite mixture model 

Supplementary material

11222_2017_9774_MOESM1_ESM.pdf (566 kb)
Supplementary material 1 (pdf 565 KB)


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Leonardo Egidi
    • 1
    Email author
  • Roberta Pappadà
    • 2
  • Francesco Pauli
    • 2
  • Nicola Torelli
    • 2
  1. 1.Dipartimento di Scienze StatisticheUniversità degli Studi di PadovaPaduaItaly
  2. 2.Dipartimento di Scienze Economiche, Aziendali, Matematiche e Statistiche ‘Bruno de Finetti’Università degli Studi di TriesteTriesteItaly

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