An assessment of predictive performance of Zellner’s g-priors in Bayesian model averaging

Abstract

When making predictions and inferences, data analysts are often faced with the challenge of selecting the best model among competing models as a result of large number of regressors that cumulate into large model space. Bayesian model averaging (BMA) is a technique designed to help account for uncertainty inherent in model selection process. In Bayesian analysis, issues of the choice of prior distribution have been quite delicate in data analysis and posterior model probabilities (PMP) in the context of model uncertainty under model selection process are typically sensititve to the specification of prior distribution. This research identified a set of eleven candidate default priors (Zellner’s g-priors) prominent in literature and applicable in Bayesian model averaging. A new robust g-prior specification for regression coefficients in Bayesian Model Averaging is investigated and its predictive performance assessed along with other g-prior structures in literature. The predictive abilities of these g-prior structures are assessed using log predictive scores (LPS) and log maximum likelihood (LML). The sensitivity of posterior results to the choice of these g-prior structures was demonstrated using simulated data and real-life data. The simulated data obtained from multivariate normal distribution were first used to demonstrate the predictive performance of the g-prior structures and later contaminated for the same purpose. Similarly for the same purpose, the real life data were normalized before using the data as obtained. Empirical findings reveal that under different conditions, the new g-prior structure exhibited robust, equally competitive and consistent predictive ability when compared with identified g-prior structures from the literature. The new g-prior offers a sound, fully Bayesian approach that features the virtues of prior input and predictive gains that minimise the risk of misspecification.