Bayesian Structural Variable Selection in Linear Regression Models

• Activity Number: 130
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Min Wang*+ and Xiaoqian Sun and Tao Lu
• Companies: Michigan Technological University and Clemson University and State University of New York
• Keywords: Variable selection ; interactions ; generalized singular g-prior ; beta-prime prior ; posterior probability ; consistency

Abstract

We consider the Bayesian variable selection in linear regression models with related predictors. The commonly used Zellner's g-prior depends on the inverse of empirical covariance matrix of the predictors. However, this matrix may be rank deficient or almost when the number of predictors is almost equal to the sample size, or some predictors are highly correlated each other. In addition, the integral representation is often involved in the expression of the posterior probability density. To overcome these potential difficulties, we adopt a generalized singular g-prior distribution for the unknown model parameters and choose a particular prior for g, which results in a closed-form expression of the marginal posterior distribution without integral representation. A special prior on the model space is then advocated to maintain the hierarchical or structural relationships among predictors. It is shown that under some nominal assumptions, the proposed approach is consistent in terms of model selection and prediction. Finally, Monte Carlo simulations and a real data application are conducted to investigate the performance of the proposed and previous approaches in the literature.