B1074
Title: Bayesian finite mixtures of regressions with random covariates
Authors: Konstantinos Perrakis - Durham University (United Kingdom) [presenting]
Panagiotis Papastamoulis - Athens University of Economics and Business (Greece)
Abstract: A class of Bayesian finite mixtures is introduced for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed approach aims to encompass potential heterogeneity in the distribution of the response variable as well as in the multivariate distribution of the covariates for detecting signals relevant to the underlying latent structure. Of particular interest are potential signals originating from: (i) the linear predictor structures of the regression models and (ii) the covariance structures of the covariates. The two components are modelled using a lasso shrinkage prior to the regression coefficients and a graphical lasso shrinkage prior to the covariance matrices. The case of unknown number of groups is handled by placing a sparse Dirichlet prior on the latent group probabilities. A novel Gibbs sampler is developed based on appropriate augmentation schemes. Some results from a simulation study are presented.
