Uncertainty Quantification for Extreme Quantile Estimation With Stochastic Computer Models

Abstract

Extreme quantiles are important measures in reliability analysis. At the system design stage, quantiles are often estimated via stochastic simulations. This article aims to quantify quantile estimation uncertainties by constructing confidence intervals using importance sampling when quantiles are estimated via stochastic computer models. We validate the asymptotic normality for the importance sampling quantile estimator and construct a theoretically valid confidence interval in a closed form. A drawback of the theoretical confidence interval is that it needs to consistently estimate a variance parameter. To resolve the limitation of the theoretical confidence interval, we present batching-based approaches that are also built upon the asymptotic normality of the quantile estimator. We compare the estimation performance of studied methods and other alternative methods using numerical examples and wind turbine case study.