Deviance information criteria for mixtures of distributions

Abstract

As a Bayesian criterion for model comparison, Spiegelhalter et al. proposed the deviance information criterion (DIC) which consists of two parts: a classical estimate of fit and an effective number of parameters. This model comparison method is based on generalized linear models, and it may be inappropriate to be used for comparison in the case of mixture of distributions mainly due to the label switching and multimodality issues. For this purpose, Celeux et al. proposed several modified DIC constructions and assessed their behaviors under a mixture of distributions, however they did not fully explore the properties of alternative DICs. Here, we study and provide the properties of DIC3, one of the variations Celeux et al. proposed, and propose our modified DIC to lessen the issue raised by using the dataset twice. We compare our proposed criterion to other model selection criteria based on two numerical examples, the Galaxy dataset and the simulated dataset.