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Journal of Classification

, Volume 24, Issue 2, pp 155–181 | Cite as

Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering

  • Chris Fraley
  • Adrian E. Raftery
Article

Abstract

Normal mixture models are widely used for statistical modeling of data, including cluster analysis. However maximum likelihood estimation (MLE) for normal mixtures using the EM algorithm may fail as the result of singularities or degeneracies. To avoid this, we propose replacing the MLE by a maximum a posteriori (MAP) estimator, also found by the EM algorithm. For choosing the number of components and the model parameterization, we propose a modified version of BIC, where the likelihood is evaluated at the MAP instead of the MLE. We use a highly dispersed proper conjugate prior, containing a small fraction of one observation's worth of information. The resulting method avoids degeneracies and singularities, but when these are not present it gives similar results to the standard method using MLE, EM and BIC.

Keywords

Bayesian Information Criterion American Statistical Association Normal Mixture Finite Mixture Model Posterior Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science + Business Media Inc. 2007

Authors and Affiliations

  • Chris Fraley
    • 1
  • Adrian E. Raftery
    • 1
  1. 1.University of WashingtonSeattleUSA

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