Abstract

In Bayesian analysis, posterior distribution summarises what we know about uncertain quantities. It is a combination of the prior distribution and the likelihood function. Inference proceeds from the posterior distribution where all required posterior quantities were generated analytically. Informative prior distributions related to a natural conjugate prior specification are studied under a limited choice of a single scalar hyper parameter called g-prior which corresponds to the degree of prior uncertainty on regression coefficients. This research identified a set of nine candidate default priors (called Zellner’s g-priors) prominent in literature and applicable in Bayesian model averaging (BMA). The methods adopted are theoretical and literature based and can be applied to derive the prior and posterior distributions of the regression parameters of multiple regression models. Results obtained include the respective prior distributions and posterior distributions based on the set of g-prior structures prominent in Bayesian Model Averaging (BMA).