ESTIMATING EXTREME PROBABILITIES USING TAIL SIMULATED DATA

The paper presents a powerful method for estimating extreme probabilit ies of a target variable Z = h(X) which is a monotone function of a se t of basic variables X = (X-1,...,X-n). To this aim, a sample of (X-1, ...,X-n) is simulated in such a way that the corresponding values of Z are in the corresponding tail, and used to fit a Pareto distribution to the associated exceedances. For cases where this method is difficul t to apply, an alternative method is proposed, which leads to a low re jection proportion of sample values, when compared with the Monte Carl o method Both methods are shown to be very useful for sensitivity anal ysis in Bayesian networks or uncertainty in risk analysis, when very l arge confidence intervals for the marginal/conditional probabilities a re required The methods are illustrated with several examples, and one example of application to a real case is used to illustrate the whole process. (C) 1997 Elsevier Science Inc.