Comparison of evidence theory and Bayesian theory for uncertainty modeling

This paper compares Evidence Theory (ET) and Bayesian Theory (BT) for uncertainty modeling and decision under uncertainty, when the evidence about uncertainty is imprecise. The basic concepts of ET and BT are introduced and the ways these theories model uncertainties, propagate them through systems and assess the safety of these systems are presented. ET and BT approaches are demonstrated and compared on challenge problems involving an algebraic function whose input variables are uncertain. The evidence about the input variables consists of intervals provided by experts. It is recommended that a decision-maker compute both the Bayesian probabilities of the outcomes of alternative actions and their plausibility and belief measures when evidence about uncertainty is imprecise, because this helps assess the importance of imprecision and the value of additional information. Finally, the paper presents and demonstrates a method for testing approaches for decision under uncertainty in terms of their effectiveness in making decisions. 1 Corresponding author Introduction The information in many problems of design under uncertainty, especially those involving reducible (epistemic) uncertainty, is imprecise. Reducible uncertainty is uncertainty due to lack of knowledge, as opposed to random (aleatory) uncertainty, which is due to inherent variability in a physical phenomenon. It is called reducible, because it can be reduced or eliminated if one collects information. The uncertainty in the probability of getting heads in one flip of a bent coin is reducible, because it is due to lack of knowledge. It can be reduced if we conduct experiments. On the other hand there is aleatory uncertainty when flipping a coin even if we know the probability of events; heads and tails. This type of uncertainty cannot be reduced even if we conduct n experiments, where n is a very large number. For example, we know the probability of heads and tails in a fair coin is 0.5. But each time you flip it, you are uncertain about the output. So this uncertainty is also called irreducible uncertainty. Oberkampf et al. [1] explained these two types of uncertainty and presented examples in which aleatory and epistemic uncertainty are encountered in engineering problems. There is no consensus about what the best theory is for modeling epistemic uncertainty. Oberkampf et al. [1] studied the differences and similarities of epistemic and random uncertainty. In their study, they used a hybrid approach in which random uncertainty was modeled using probability and epistemic uncertainty was modeled using intervals bounding variables in which there was epistemic uncertainty. Theories for modeling epistemic uncertainty, include Coherent Upper and Lower Previsions [2-4], Possibility Theory [5-8], Evidence Theory [9-10], the Transferable Belief Model [11] and Bayesian Theory [12-13]. Information gap-Decision Theory is another alternative for decision making under uncertainty when information about uncertainty is scarce [14].