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October 2004 On the posterior distribution of the number of components in a finite mixture
Agostino Nobile
Ann. Statist. 32(5): 2044-2073 (October 2004). DOI: 10.1214/009053604000000788

Abstract

The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an “internal” consistency check of MCMC estimates of the posterior distribution of k and to provide improved estimates which are required to satisfy the constraints. Bounds on the posterior probability of k components are derived using the constraints. Implications on prior distribution specification and on the adequacy of the posterior distribution of k as a tool for selecting an adequate number of components in the mixture are also explored.

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Agostino Nobile. "On the posterior distribution of the number of components in a finite mixture." Ann. Statist. 32 (5) 2044 - 2073, October 2004. https://doi.org/10.1214/009053604000000788

Information

Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62037
MathSciNet: MR2102502
Digital Object Identifier: 10.1214/009053604000000788

Subjects:
Primary: 62F15

Keywords: Bayesian analysis , constrained estimation , finite mixture distribution , Markov chain Monte Carlo , prior distribution

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 5 • October 2004
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