Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering

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. This revision includes a corrected version of Table 2, for which the published version (Fraley and Raftery 2007) contains errors. Key words: BIC; EM algorithm; mixture models; m...

• Type: Journal
• Year: 2007
• Where: CLASSIFICATION
• Authors: Chris Fraley, Adrian E. Raftery
• Keywords: CLASSIFICATION 2007, Mixture Models, Normal Mixture Models, Normal Mixtures