Computation of Failure Probability Subject to Epistemic Uncertainty

• Published in: SIAM journal on scientific computing Vol. 34; no. 6; pp. A2946 - A2964
• Main Authors: Li, Jing, Xiu, Dongbin
• Format: Journal Article
• Language: English
• Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2012
• Subjects: Algorithms; Applied mathematics; Approximation; Complex systems; Computation; Entropy; Epistemology; Failure; Lower bounds; Mathematical models; Optimization; Probability distribution; Random variables; Tasks; Uncertainty
• ISSN: 1064-8275; 1095-7197
• DOI: 10.1137/120864155

Computing failure probability is a fundamental task in many important practical problems. The computation, its numerical challenges aside, naturally requires knowledge of the probability distribution of the underlying random inputs. On the other hand, for many complex systems it is often not possible to have complete information about the probability distributions. In such cases the uncertainty is often referred to as epistemic uncertainty, and straightforward computation of the failure probability is not available. In this paper we develop a method to estimate both the upper bound and the lower bound of the failure probability subject to epistemic uncertainty. The bounds are rigorously derived using the variational formulas for relative entropy. We examine in detail the properties of the bounds and present numerical algorithms to efficiently compute them. [PUBLICATION ABSTRACT]