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

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Ogundeji, Rotimi
Adeleke, Ismaila
Okafor, Ray
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Faculty of Science, University of Lagos, Lagos, Nigeria.
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 (Zellner’s 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.
Bayesian Regression , Model Uncertainty , Normal Linear Model , Predictive Performance , Prior Elicitation , Zellner’s g-Priors
Ogundeji, R. (2018). A New Zellner’s g-Prior for Bayesian Model Averaging in Regression Analysis. Journal of Scientific Research and Development, 18(1), 51-60.