Mathematics - Scholarly Publications

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Browsing Mathematics - Scholarly Publications by Author "Adeleke, Ismaila"

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    Open Access
    An assessment of predictive performance of Zellner’s g-priors in Bayesian model averaging
    (IOS Press, Nieuwe Hemweg 6B 1013 BG Amsterdam The Netherlands., 2018) Ogundeji, Rotimi; Adeleke, Ismaila; Okafor, Ray
    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.
  • Item
    Open Access
    A New Zellner’s g-Prior for Bayesian Model Averaging in Regression Analysis
    (Faculty of Science, University of Lagos, Lagos, Nigeria., 2018) Ogundeji, Rotimi; Adeleke, Ismaila; Okafor, Ray
    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.