Application of a Modified g -Parameter Prior in Bayesian Model Averaging to Water Pollution in Ibadan

Abstract

A special technique that measures the uncertainties embedded in model selection processes is Bayesian Model Averaging (BMA) which depends on the appropriate choices of model and parameter priors. Inspite the importance of the parameter priors' specification in BMA, the existing parameter priors give exitremely low Posterior Model Probability (PMP). Therefore, this paper elicits modified g-parameter priors to improve the performance of the PMP and predictive ability of the model with an application to the Water Pollution of Asejire in Ibadan.  The modified g-parameter priors g_j = , established the consistency conditions and asymptotic properties using the models in the literature. The results show that the PMP with the best prior (g_j= ) had the least standard deviations (0.0411 at n=100,000 and 0:000 at n=1000) for models 1 & 2 respectively; and had the highest posterior means (0.9577 at n=100,000 and 1.000 at n=1000) for models 1 & 2 respectively. The point and overall predictive performances for the best prior were 2.357 at n=50 and 2.335 at n=100,000 when compared with the BMA Log Predictive Score threshold of 2.335. Applying this best g-parameter prior in modeling the Asejire river, it indicates that the dissolved solids (mg/l) and total solids (mg/l) are the most important pollutants in the river model with their PIP of 6.14% and 6.1% respectively.

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

DOI: 10.7176/JEES/9-11-06

Publication date: November 30^th 2019