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Estimation of Finite Mixture Distributions through Bayesian Sampling

Jean Diebolt and Christian P. Robert
Journal of the Royal Statistical Society. Series B (Methodological)
Vol. 56, No. 2 (1994), pp. 363-375
Published by: Wiley for the Royal Statistical Society
Stable URL: http://www.jstor.org/stable/2345907
Page Count: 13
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Estimation of Finite Mixture Distributions through Bayesian Sampling
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Abstract

A formal Bayesian analysis of a mixture model usually leads to intractable calculations, since the posterior distribution takes into account all the partitions of the sample. We present approximation methods which evaluate the posterior distribution and Bayes estimators by Gibbs sampling, relying on the missing data structure of the mixture model. The data augmentation method is shown to converge geometrically, since a duality principle transfers properties from the discrete missing data chain to the parameters. The fully conditional Gibbs alternative is shown to be ergodic and geometric convergence is established in the normal case. We also consider non-informative approximations associated with improper priors, assuming that the sample corresponds exactly to a k-component mixture.

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