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On Bayesian Analysis of Mixtures with an Unknown Number of Components

Sylvia Richardson and Peter J. Green
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 59, No. 4 (1997), pp. 731-792
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2985194
Page Count: 62
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On Bayesian Analysis of Mixtures with an Unknown Number of Components
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Abstract

New methodology for fully Bayesian mixture analysis is developed, making use of reversible jump Markov chain Monte Carlo methods that are capable of jumping between the parameter subspaces corresponding to different numbers of components in the mixture. A sample from the full joint distribution of all unknown variables is thereby generated, and this can be used as a basis for a thorough presentation of many aspects of the posterior distribution. The methodology is applied here to the analysis of univariate normal mixtures, using a hierarchical prior model that offers an approach to dealing with weak prior information while avoiding the mathematical pitfalls of using improper priors in the mixture context.

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