Estimating extreme probabilities using tail simulated data

The paper presents a powerful method for estimating extreme probabilities of a target variable Z = h(X) which is a monotone function of a set 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 difficult to apply, an alternative method is proposed, which leads to a low rejection proportion of sample values, when compared with the Monte Carlo method Both methods are shown to be very useful for sensitivity analysis in Bayesian networks or uncertainty in risk analysis, when very large confidence intervals for the marginal/conditional probabilities are 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.