  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 Normal-Gamma prior. We show in a simulation study that each
of the two proposed DPM models tend 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 analyzed to illustrate the proposed modeling methodology, where
both proposed DPM models again attained better predictive accuracy.
