Dirichlet process mixture models with shrinkage prior

We propose Dirichlet process mixture (DPM) models for prediction and cluster-wise variable selection. based on two choices of shrinkage baseline prior distributions for the linear regression coefficients, namely, the Horseshoe prior and the Normal-Gamma prior. We show in a simulation study that each of the two 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. A real data set is analysed to illustrate the proposed modelling methodology, where both proposed DPM models again attained better predictive accuracy.