European Journal of Statistics and Probability Vol.8, No.1, pp, 43-59, April 2020 Published by ECRTD-UK Print ISSN: 2055-0154(Print), Online ISSN 2055-0162(Online) 43 APPLICATION OF A MODIFIED G -PARAMETER PRIOR   5 j k n IN BAYESIAN MODEL AVERAGING TO WATER POLLUTION IN IBADAN O. B. Akanbi 1 & S. A. Afolabi 2 Department of Statistics,University of Ibadan, Ibadan, Nigeria. 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 gj =   j a k n , 3, 4, 5 a   established the consistency conditions and asymptotic properties using the models in the literature. The results show that the PMP with the best prior (gj= 5 / j k n ) 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 INTRODUCTION Over the years in Nigeria, environmental problem is a great issue especially in the Southern part of the country where oil is spilled into water to cause water pollution. The people of the area are adversely affected with one environmental issue or the other. Previous researches on environment in Nigeria involve the classical approach. To this end, there is prior knowledge about challenges facing the community. I am now motivated to apply Bayesian Analysis through prior elicitation so as to form likelihood in such a way to give a compromise and update of knowledge in pattern of the Posterior using Bayesian Model Averaging (BMA). Bayesian Model Averaging (BMA) is a method that measures the uncertainties embedded in the model selection processes which depends on the appropriate choices of model and parameter priors. By averaging over many different competing models, BMA incorporates model uncertainty into conclusions about parameters and prediction. BMA approach allows the assessment of the predictive skill of a model. Akanbi, (2016) contributed that a composite inference that takes account of model uncertainty can be made in a simple and formally justifiable way. BMA is the method that has been proposed for handling some applications that are very large numbers of