On a Modified g-Parameter Prior in Bayesian Model Averaging

A special technique that measures the uncertainties embedded in model selection processes is Bayesian Model Averaging (BMA) which depend on the appropriate choices of model and parameter priors. As important as parameter priors’ specification in BMA, the existing parameter priors based on fast increasing sample sizes compared to the number of regressors in a model give low Posterior Model Probability (PMP). Therefore, this research aimed at eliciting a modified g-parameter priors to improve the performance of the PMP and predictive ability of the model. From the functional form of the g-priors used; g_j = / where and are functions of regressors per model j and sample size n with , the tools of BMA like Bayes Theorem, Bayes Factor (BF), Posterior Model Probability (PMP), Prior Inclusion Probability (PIP) and Shrinkage Factor (SF) through the modified g-parameter priors g_j = established the superiority of the consistency’s conditions and asymptotic properties of the prior(s) using the Fernandez, Ley and Steel (FLS) models (1 & 2); and  respectively with as sample sizes. The result from the analysis revealed that the performance of PMP was reliable with the least standard deviations (0.1994 SD 0.0411) and (0.1086SD0.000) for model 1 and model 2 respectively; and it was convergent with the highest means (0.5378Mean0.9577) and (0.8342Mean1.000) for model 1 and model 2 respectively. For the three modified g-parameter priors, the best reliability occurred when n = 100; 000 for Model 1 and Model 2 with (0.0631, 0.0521 and 0.0411) and (0.00, 0.00 and 0.00) respectively; also, the best convergence occurred with (0.9343, 0.9460 and 0.9577) and (1.00, 1.00 and 1.00) for Model 1 and Model 2 respectively when n = 100; 000. The predictive performance affirmed the goodness of the elicited g-parameter priors when n = 50 for Point prediction with (2.302, 2.357, 2.357); and when n = 100; 000 for Overall prediction with (2.332, 2.334, 2.335) which were all closed to the LPS threshold 2.335 according to BMA specification.

Keywords: Dissolved Solids (DS), Log-Predictive Score (LPS), Model Uncertainty (MU), Posterior Inclusion Probability (PIP)