A New Zellner’s g-Prior for Bayesian Model Averaging in Regression Analysis

Abstract

In regression analysis, one of the main challenges is selecting a single model among competing models when making inferences. Likewise, the issue of the choice of prior distribution has been delicate in data analysis. Informative prior distributions related to a natural conjugate prior specification are investigated under a limited choice of a single scalar hyperparameter called g-prior, which corresponds to the degree of prior uncertainty on regression coefficients. This research identified a set of 11 candidate default priors (Zellners g-priors) prominent in the Literature and applicable in Bayesian model averaging. Some new sets of g-prior structures were investigated with a view to proposing an improved g-prior specification for regression coefficients in Bayesian Model Averaging (BMA) and the predictive performance of these g-priors were compared. Results obtained include the respective prior distributions, posterior distributions and sampling properties of the regression parameters, based on the new set of g-prior structures investigated. Also, empirical findings revealed that the proposed g-prior structure exhibited equally competitive and consistent predictive ability when compared with identified g-prior structures from the Literature.