## MCMC and the label switching problem in Bayesian mixture models (2005)

Venue: | Statistical Science |

Citations: | 1 - 0 self |

### BibTeX

@ARTICLE{Jasra05mcmcand,

author = {A. Jasra and C. C. Holmes and D. A. Stephens},

title = {MCMC and the label switching problem in Bayesian mixture models},

journal = {Statistical Science},

year = {2005},

volume = {20},

pages = {50--67}

}

### OpenURL

### Abstract

Abstract. In the past ten years there has been a dramatic increase of interest in the Bayesian analysis of finite mixture models. This is primarily because of the emergence of Markov chain Monte Carlo (MCMC) methods. Whilst MCMC provides a convenient way to draw inference from complicated statistical models, there are many, perhaps under appreciated, problems associated with the MCMC analysis of mixtures. The problems are mainly caused by the nonidentifiability of the components under symmetric priors, which leads to so called label switching in the MCMC output. This will mean that ergodic averages of component specific quantities will be identical and thus useless for inference. We review the solutions to the label switching problem, such as artificial identifiability constraints (e.g. Diebolt & Robert (1994)), relabelling algorithms (Stephens 1997a) and label invariant loss functions (Celeux, Hurn & Robert 2000). We also review various MCMC sampling schemes that have been suggested for mixture models and discuss posterior sensitivity to prior specification.

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Citation Context ...n this subsection we discuss variable dimension samplers. Following Richardson & Green (1997) the standard way to simulate from a mixture with an unknown number of components is reversible jump MCMC (=-=Green 1995-=-) (for an up-to-date review see Green (2003)). Reversible jump is simply an extension of the Metropolis-Hastings method, with the measure theoretic construction necessary because of the lack of common... |

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Citation Context ...modal distributions. We emphasise that we can simulate from a mixture posterior using Metropolis-Hastings updates without completion (simulation of the missing class labels), and that tempering MCMC (=-=Neal 1996-=-) may be used. We also consider reparameterisations, as discussed by Celeux et al. (2000), and variable dimension samplers. Next, we examine the existing solutions to the label switching problem. We b... |

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Citation Context ...dentical and thus useless for inference. We review the solutions to the label switching problem, such as artificial identifiability constraints (e.g. Diebolt & Robert (1994)), relabelling algorithms (=-=Stephens 1997-=-a) and label invariant loss functions (Celeux, Hurn & Robert 2000). We also review various MCMC sampling schemes that have been suggested for mixture models and discuss posterior sensitivity to prior ... |

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Citation Context ... as biological sequence analysis (Boys & Henderson 2004), econometrics (Frühwirth-Schnatter 2001), (Hurn, Justel & Robert 2003), machine learning (Beal, Ghahramani & Rasmussen 2002) and epidemiology (=-=Green & Richardson 2002-=-). One of the main challenges of a Bayesian analysis using mixtures is the nonidentifiability of the components. That is, if exchangeable priors are placed upon the parameters of a mixture model, then... |

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Citation Context ...dentical and thus useless for inference. We review the solutions to the label switching problem, such as artificial identifiability constraints (e.g. Diebolt & Robert (1994)), relabelling algorithms (=-=Stephens 1997-=-a) and label invariant loss functions (Celeux, Hurn & Robert 2000). We also review various MCMC sampling schemes that have been suggested for mixture models and discuss posterior sensitivity to prior ... |

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Citation Context ...s (2000a) (Birth-andDeath MCMC). Due to the above developments, implementation of Bayesian mixtures has become increasingly popular in many academic disciplines, such as biological sequence analysis (=-=Boys & Henderson 2004-=-), econometrics (Frühwirth-Schnatter 2001), (Hurn, Justel & Robert 2003), machine learning (Beal, Ghahramani & Rasmussen 2002) and epidemiology (Green & Richardson 2002). One of the main challenges of... |

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