Dirichlet process mixture models with shrinkage prior

Abstract

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.