Dirichlet Process Mixture Models with Shrinkage Prior

We propose Dirichlet process mixture (DPM) models for prediction and cluster-wise variable selection, based on three choices of shrinkage baseline prior distributions for the linear regression coefficients, namely, conditional Laplace prior, Horseshoe prior and Normal-Gamma prior. We show in a simulation study that each of the three proposed DPM models tends to outperform the standard DPM model based on the non-shrinkage normal prior, in terms of predictive, variable selection, and clustering accuracy. This is especially true for the Horseshoe model and when the number of covariates exceeds the within-cluster sample size. Real data sets are analyzed to illustrate the proposed modeling methodology, where all proposed DPM models again attained better predictive accuracy.