Semiparametric Local Multivariate Priors for Bayesian Model Averaging

• Activity Number: 579
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yingbo Li*+
• Companies: Duke University
• Keywords: Bayesian statistics ; shrinkage prior ; Bayesian model averaging ; Dirichlet process ; lasso ; ridge regression

Abstract

Ridge regression may outperform lasso when regression coefficients are small or covariates are highly correlated. Unlike lasso, which depends on the choice of coordinate system used to represent the model, ridge regression is invariant under orthogonal rotation of the explanatory variables. Inspired by the rotation invariant property of ridge regression, we propose a Bayes approach that has a local rotation invariant structure, which is induced by Dirichlet Process (DP) prior on variance parameters in normal prior distributions for the regression coefficients. Due to the natural grouping structure induced by DP, our shrinkage prior acts like multivariate Cauchy prior within a group. Point masses at zero in DP base measure can achieve sparse solutions like lasso or Bayesian variable selection priors. Compared with pure shrinkage methods, it has the advantage of valid built-in variable selection. Meanwhile, the Cauchy tails of the prior lead to bounded influence, which preserves large effects. Both simulation and real-world examples show that our method achieves high accuracy in parameter estimation and prediction.