Bayesian Variable Selection for the Seemingly Unrelated Regression Models with a Large Number of Predictors

Computationally efficient methods for Bayesian analysis of Seemingly Unrelated Regression (SUR) models with a large number of predictors are developed. One of the most crucial problems in Bayesian modeling of SUR models is how to determine the optimal combination of predictors. In this paper, under a Bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis functions, the regression coefficients, the variance matrix of the errors, and a set of predictors to be included in the model are estimated simultaneously. Usually the Bayesian model estimation problem is solved using Markov Chain Monte Carlo (MCMC) techniques. Herein we show how a direct Monte Carlo (DMC) technique can be employed to solve the variable selection and model parameter estimation problems more efficiently.