Two-stage decision-making under uncertainty and stochasticity: Bayesian Programming

Abstract

This paper develops a new method for decision-making under uncertainty. The method, Bayesian Programming (BP), addresses a class of two-stage decision problems with features that are common in environmental and water resources. BP is applicable to two-stage combinatorial problems characterized by uncertainty in unobservable parameters, only some of which is resolved upon observation of the outcome of the first-stage decision. The framework also naturally accommodates stochastic behavior, which has the effect of impeding uncertainty resolution. With the incorporation of systematic methods for decision search and Monte Carlo methods for Bayesian analysis, BP addresses limitations of other decision-analytic approaches for this class of problems, including conventional decision tree analysis and stochastic programming. The methodology is demonstrated with an illustrative problem of water quality pollution control. Its effectiveness for this problem is compared to alternative approaches, including a single-stage model in which expected costs are minimized and a deterministic model in which uncertain parameters are replaced by their mean values. A new term, the expected value of including uncertainty resolution, or EVIUR, is introduced and evaluated for the illustrative problem. It is a measure of the worth of incorporating the experimental value of decisions into an optimal decision-making framework. For the illustrative problem, the two-stage adaptive management framework extracted up to approximately 50% of the gains of perfect information. The strength and limitations of the method are discussed and conclusions are presented.