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February 2000 Bayesian analysis of mixture models with an unknown number of components—an alternative to reversible jump methods
Matthew Stephens
Ann. Statist. 28(1): 40-74 (February 2000). DOI: 10.1214/aos/1016120364

Abstract

Richardson and Green present a method of performing a Bayesian analysis of data from a finite mixture distribution with an unknown number of components. Their method is a Markov Chain Monte Carlo (MCMC) approach, which makes use of the “reversible jump” methodology described by Green. We describe an alternative MCMC method which views the parameters of the model as a (marked) point process, extending methods suggested by Ripley to create a Markov birth-death process with an appropriate stationary distribution. Our method is easy to implement, even in the case of data in more than one dimension, and we illustrate it on both univariate and bivariate data. There appears to be considerable potential for applying these ideas to other contexts, as an alternative to more general reversible jump methods, and we conclude with a brief discussion of how this might be achieved.

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Matthew Stephens. "Bayesian analysis of mixture models with an unknown number of components—an alternative to reversible jump methods." Ann. Statist. 28 (1) 40 - 74, February 2000. https://doi.org/10.1214/aos/1016120364

Information

Published: February 2000
First available in Project Euclid: 14 March 2002

zbMATH: 1106.62316
MathSciNet: MR1762903
Digital Object Identifier: 10.1214/aos/1016120364

Subjects:
Primary: 62F15

Keywords: Bayesian analysis , birth-death process , Markov process , MCMC , mixture model , model choice , Reversible jump , spatial point process

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 1 • February 2000
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