%0 Report %1 fraley200501 %A Fraley, Chris %A Raftery, Adrian E. %D 2005 %K BIC EM algorithm bayesian clustering conjugate finite mclust mixture mode model-based posterior prior %N 486 %T Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering %U http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA454825&Location=U2&doc=GetTRDoc.pdf %X 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.

@techreport{fraley200501, 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.}, added-at = {2009-08-24T15:08:53.000+0200}, author = {Fraley, Chris and Raftery, Adrian E.}, biburl = {https://www.bibsonomy.org/bibtex/20b6f6ac2b1ef3299b5175b7fd83ef551/neongod}, institution = {Department of Statistics}, interhash = {2cc93c63423663cb1ebf10fd46d03454}, intrahash = {0b6f6ac2b1ef3299b5175b7fd83ef551}, keywords = {BIC EM algorithm bayesian clustering conjugate finite mclust mixture mode model-based posterior prior}, number = 486, timestamp = {2009-08-24T15:08:53.000+0200}, title = {Bayesian Regularization for Normal Mixture Estimation and Model-Based Clustering}, type = {Technical Report}, url = {http://www.dtic.mil/cgi-bin/GetTRDoc?AD=ADA454825&Location=U2&doc=GetTRDoc.pdf}, year = 2005 }