Bayesian Decision Modeling in Watershed Management - Cross River Basin, Nigeria

Abstract

This paper aimed at examining simulation modeling in Bayesian Decision theory and its application in day to day decision making as well as planning in water resources and Environmental engineering. It also gives more insight in the validation of prior probability. The research objectives deals with the multi-objective value of water for its wide range of  purposes such as Power generation, water supply, Navigation, Irrigation, and Flood control, in the Cross River basin using Bayesian Modeling. In line with foregoing objectives, the research aim to achieve the following: (i) to lay bare the usefulness of the Bayesian theory that gives more than point estimation. It measures the magnitude of the difference between alternative actions and provides a variety of estimates for consideration, (ii) to present selected empirical results of a study employing decision-making theory as a framework for considering decision making under uncertainty. (iii) to evaluate the optimal policy or strategy or action that maximizes the expected benefit in the River Basin within the available limited resources and funds over the planning period of a course of action or alternatives. The multi-objectives arising from the development that were optimized include: Economic Efficiency, Regional Economic Distribution, State and Local Economic Redistribution, Youth Employment and Environmental Quality Improvement, which are primarily essential in Cross Rivers State and Nigeria. Methodology applied involving methods, experiments and data were collected for the River Basin Engineering Development, from Parastatals and Ministries. The conceptual framework on Bayesian Decision Model (BDM) as presented captured the iterative updates of prior probability toward achieving an optimum solution of a set problem. The analysis and presentation of results were based on simulation of Bayesian Models Iterations. Chi-square, Contingency and association and Pearson Product Moment Correlation were carried out as Interaction, reliability and Validity tests respectively. The study applied Bayesian Decision Model, where the following parameters were obtained:: (a)Posterior Probabilities of the States of Nature (b) Marginal Probability of the Courses of action, (c) Maximum Expected Monetary Value[EMV*] (d) Expected Profit in a Perfect Information[EPPI], (e) Expected Value of Perfect Information[EVPI], and (f) Expected Value of System Information[EVSI]. In the process of Iteration, and at some point the Prior becomes equal to the Posterior Probability, when this occurs an optimum solution is said to be achieved. However, the correlation of prior and posterior probability is equal to one (1) at the optimum solution. In conclusion, the efficiency of system information is 50%. Table 25 indicates monetary allocation to the multi-objectives which gave a clear indication that the life wire of the watershed/dam lies on it; and therefore should be comparatively considered; because without it, it will be difficult to maintain the watershed. The Basin Authority is expected to pay the researcher the Expected Value of System Information (EVSI) value of = ₦0.1billion for information generated using the Bayesian Decision theory model spreadsheet. The value of Economic efficiency optimized from 1^st iteration to 2^ndIteration with the EMV values of ₦2.54billion to ₦2.74billion respectively as in [ Table 4 & 15]

Keywords: Optimum Solution, Prior-posterior, Probability, River Basin.

DOI: 10.7176/CER/11-2-11

Publication date:March 31^st 2019