Asymptotic importance sampling

An importance sampling technique is described which is based on theoretical considerations about the structure of multivariate integrands in domains having small probability content. The method is formulated in the original variable space. Sampling densities are derived for a variety of practical conditions: a single point of maximum loglikelihood; several points; points located at the intersect of several failure surfaces; and, bounded variables. Sampling in the safe domain is avoided and extensive use is made of noncartesian as well as surface coordinates. The parameters of the importance sampling densities are taylored in such a way as to yield asymptotic minimum variance unbiased estimators. The quality and the efficiency of the method improves as the failure probability decreases. Parameter sensitivies are easily computed owing to the use of local surface coordinates. Several examples are provided.