ZELLNER’S G-PRIORS IN BAYESIAN MODEL AVERAGING OF LARGE MODEL SPACE USING MARKOV CHAIN MONTE CARLO MODEL COMPOSITION APPLICABLE UNDER BAYESIAN MODEL SAMPLING

Abstract

Applied researchers are frequently faced with the issue of model uncertainty in situations where
many possible models exist. For large model space in regression analysis, the challenge has
always been how to select a single model among competing large model space when making
inferences. Bayesian Model Averaging (BMA) is a technique designed to help account for the
uncertainty inherent in the model selection process. Informative prior distributions related to a
natural conjugate prior specification are investigated 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 study focuses on situations with extremely large model space made
up of large set of regressors generated by a small number of observations, when estimating
model parameters. A set of g-prior structures in literature are considered with a view to identify
an improved g-prior specification for regression coefficients in Bayesian Model Averaging. The
study demonstrates the sensitivity of posterior results to the choice of g-prior on simulated data
and real-life data. Markov Chain Monte Carlo (MCMC) are used to generate a process which
moves through large model space to adequately identify the high posterior probability models
using the Markov Chain Monte Carlo Model Composition (MC3), a method applicable under
Bayesian Model Sampling (BMS). To assess the sensitivity and predictive ability of the g-priors,
predictive criteria like Log Predictive Score (LPS) and Log Marginal Likelihood (LML) are
employed. The results reveal a g-prior structure that exhibited equally competitive and
consistent predictive ability among considered g-prior structures in literature.