Download or read book Bayesian Variable Selection and Estimation written by Xiaofan Xu and published by . This book was released on 2014 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: The paper considers the classical Bayesian variable selection problem and an important subproblem in which grouping information of predictors is available. We propose the Half Thresholding (HT) estimator for simultaneous variable selection and estimation with shrinkage priors. Under orthogonal design matrix, variable selection consistency and asymptotic distribution of HT estimators are investigated and the oracle property is established with Three Parameter Beta Mixture of Normals (TPBN) priors. We then revisit Bayesian group lasso and use spike and slab priors for variable selection at the group level. In the process, the connection of our model with penalized regression is demonstrated, and the role of posterior median for thresholding is pointed out. We show that the posterior median estimator has the oracle property for group variable selection and estimation under orthogonal design while the group lasso has suboptimal asymptotic estimation rate when variable selection consistency is achieved. Next we consider Bayesian sparse group lasso again with spike and slab priors to select variables both at the group level and also within the group, and develop the necessary algorithm for its implementation. We demonstrate via simulation that the posterior median estimator of our spike and slab models has excellent performance for both variable selection and estimation.