We study composite quantile regression (CQReg) with composite group bridge penalty for model selection and estimation. Compared to conventional mean regression, composite quantile regression (CQR) is an efficient and robust estimation approach. A simple and efficient algorithm was developed for posterior inference using a pseudo composite asymmetric Laplace distribution which can be formulated as a location-scale mixture of normals. The composite group bridge priors were formulated as a scale mixture of multivariate uniforms. We assess the performance of the proposed method using simulation studies, and demonstrate it with an air pollution data. Results indicated that our approach performs very well compared to the existing approaches

Bayesian Inference, Composite Quantile Regression, Gibbs Sampler, Group Bridge, Hierarchical Model