## Bayesian finite mixtures with an unknown number of components: the allocation sampler (2005)

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Venue: | University of Glasgow |

Citations: | 12 - 1 self |

### BibTeX

@TECHREPORT{Nobile05bayesianfinite,

author = {Agostino Nobile and Alastair Fearnside},

title = {Bayesian finite mixtures with an unknown number of components: the allocation sampler},

institution = {University of Glasgow},

year = {2005}

}

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### Abstract

A new Markov chain Monte Carlo method for the Bayesian analysis of finite mixture distributions with an unknown number of components is presented. The sampler is characterized by a state space consisting only of the number of components and the latent allocation variables. Its main advantage is that it can be used, with minimal changes, for mixtures of components from any parametric family, under the assumption that the component parameters can be integrated out of the model analytically. Artificial and real data sets are used to illustrate the method and mixtures of univariate and of multivariate normals are explicitly considered. The problem of label switching, when parameter inference is of interest, is addressed in a post-processing stage.

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Citation Context ...of running a sampler on a composite model, so that the posterior of k can be estimated by the relative frequency with which each model is visited during the simulation. Some other authors (Carlin and =-=Chib 1995-=-, Chib 1995, Raftery 1996) preferred to avoid placing a prior distribution on k, instead, they estimated the marginal likelihoods of k components and possibly used Bayes factors to test k vs. k + 1 co... |

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Citation Context ...s the idea of running a sampler on a composite model, so that the posterior of k can be estimated by the relative frequency with which each model is visited during the simulation. Some other authors (=-=Carlin and Chib 1995-=-, Chib 1995, Raftery 1996) preferred to avoid placing a prior distribution on k, instead, they estimated the marginal likelihoods of k components and possibly used Bayes factors to test k vs. k + 1 co... |

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Citation Context ...ters, including the number k of components. Beside Richardson and Green (1997), other researchers have studied methods to estimate the posterior distribution of k. Some of them (Nobile 1994 and 2005, =-=Roeder and Wasserman 1997-=-) have provided estimates of the marginal likelihoods of k components, then used Bayes theorem to obtain the posterior of k. Others (Phillips and Smith 1996, Stephens 2000a) have derived MCMC methods ... |

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Citation Context ...e 1994 and 2005, Roeder and Wasserman 1997) have provided estimates of the marginal likelihoods of k components, then used Bayes theorem to obtain the posterior of k. Others (Phillips and Smith 1996, =-=Stephens 2000-=-a) have derived MCMC methods that share with Richardson and Green’s the idea of running a sampler on a composite model, so that the posterior of k can be estimated by the relative frequency with which... |

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Citation Context ...of k. Some of them (Nobile 1994 and 2005, Roeder and Wasserman 1997) have provided estimates of the marginal likelihoods of k components, then used Bayes theorem to obtain the posterior of k. Others (=-=Phillips and Smith 1996-=-, Stephens 2000a) have derived MCMC methods that share with Richardson and Green’s the idea of running a sampler on a composite model, so that the posterior of k can be estimated by the relative frequ... |

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Citation Context ...n a composite model, so that the posterior of k can be estimated by the relative frequency with which each model is visited during the simulation. Some other authors (Carlin and Chib 1995, Chib 1995, =-=Raftery 1996-=-) preferred to avoid placing a prior distribution on k, instead, they estimated the marginal likelihoods of k components and possibly used Bayes factors to test k vs. k + 1 components. Mengersen and R... |

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Citation Context ...tion of all the parameters, including the number k of components. Beside Richardson and Green (1997), other researchers have studied methods to estimate the posterior distribution of k. Some of them (=-=Nobile 1994-=- and 2005, Roeder and Wasserman 1997) have provided estimates of the marginal likelihoods of k components, then used Bayes theorem to obtain the posterior of k. Others (Phillips and Smith 1996, Stephe... |

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