Tail uncertainty analysis in complex systems

Abstract

The paper presents an efficient computational method for estimating the tails of a target variable Z which is related to other set of bounded variables X = ( X 1,…, X n ) by an increasing (decreasing) relation Z = h( X 1,…, X n ). To this aim, variables X i , i = 1,…, n are sequentially simulated in such a manner that Z = h( x 1,…, x i − 1 , X i ,…, X n ) is guaranteed to be in the tail of Z. The method is shown to be very useful to perform an uncertainty analysis of Bayesian networks, when very large confidence intervals for the marginal/conditional probabilities are required, as in reliability or risk analysis. The method is shown to behave best when all scores coincide and is illustrated with several examples, including two examples of application to real cases. A comparison with the fast probability integration method, the best known method to date for solving this problem, shows that it gives better approximations.