Importance Sampling: Promises and Limitations

Importance sampling is an unbiased sampling method used to sample random variables from different densities than originally defined. These importance sampling densities are constructed to pick 'important' values of input random variables to improve the estimation of a statistical response of interest, such as a mean or probability of failure. Conceptually, importance sampling is very attractive: for example one wants to generate more samples in a failure region when estimating failure probabilities. In practice, however, importance sampling can be challenging to implement efficiently, especially in a general framework that will allow solutions for many classes of problems. We are interested in the promises and limitations of importance sampling as applied to computationally expensive finite element simulations which are treated as 'black-box' codes. In this paper, we present a customized importance sampler that is meant to be used after an initial set of Latin Hypercube samples has been taken, to help refine a failure probability estimate. The importance sampling densities are constructed based on kernel density estimators. We examine importance sampling with respect to two main questions: is importance sampling efficient and accurate for situations where we can only afford small numbers of samples? And does importance sampling require the usemore » of surrogate methods to generate a sufficient number of samples so that the importance sampling process does increase the accuracy of the failure probability estimate? We present various case studies to address these questions.« less

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