Estimation of Finite Mixture Distributions Through Bayesian Sampling

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ID: 301436
1994
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Ranked #122 of 145 articles by views in Journal of the Royal Statistical Society Series B (Statistical Methodology)

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Abstract
SUMMARY 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.
Reference Key
openalex_W130037070 Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Jean Diebolt, Christian P. Robert
Journal Journal of the Royal Statistical Society Series B (Statistical Methodology)
Year 1994
DOI
10.1111/j.2517-6161.1994.tb01985.x
URL
https://doi.org/10.1111/j.2517-6161.1994.tb01985.x
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