On the Role of Decision Theory in Uncertainty Analysis

Abstract. Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in in-dustrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold standard for comparison. The main drawback of MLE is that it may fail to prop-erly account for the uncertainty on the physical process generating the data, especially when only a small amount of data are available. HPE offers an improvement in that it takes this uncertainty into ac-count. However, we show that this approach is actually equivalent to Bayes estimation for a particular cost function that is not explic-itly chosen by the decision maker. This may produce results that are suboptimal from a decisional perspective. These results plead for a systematic use of Bayes estimators based on carefully defined cost functions. Key words and phrases: Uncertainty analysis; decision theory; epis-temic uncertainty; Bayes estimation; maximum likelihood estima-tion; heuristic predictive estimation. 1 a