Application of Bayesian Decision Theory in Well Field Design

Abstract

Bayesian decision theory is a method for comparing expected utilities of alternative actions given various possible states of nature. The method treats uncertainty as to the true state of nature by determining the expected utility of each action in terms of the probabilities of the various possible states. The decision rule is to choose the action having the best expected utility. This paper illustrates an application of Bayesian decision theory in a well field design problem where a decision had to be made regarding capacity-density combination for wells located in an extensive uniform grid. The uncertainty lay in anticipating the frequencies of transmissivity values among the wells.