## The Annals of Statistics

### On the posterior distribution of the number of components in a finite mixture

Agostino Nobile

#### 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.

#### Article information

Source
Ann. Statist., Volume 32, Number 5 (2004), 2044-2073.

Dates
First available in Project Euclid: 27 October 2004

https://projecteuclid.org/euclid.aos/1098883781

Digital Object Identifier
doi:10.1214/009053604000000788

Mathematical Reviews number (MathSciNet)
MR2102502

Zentralblatt MATH identifier
1056.62037

Subjects
Primary: 62F15: Bayesian inference

#### Citation

Nobile, Agostino. On the posterior distribution of the number of components in a finite mixture. Ann. Statist. 32 (2004), no. 5, 2044--2073. doi:10.1214/009053604000000788. https://projecteuclid.org/euclid.aos/1098883781

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