Augmented sample-based approach for efficient evaluation of risk sensitivity with respect to epistemic uncertainty in distribution parameters

Abstract

This paper proposes a novel augmented sample-based approach for efficient evaluation of risk sensitivity with respect to epistemic uncertainty. Calculation of the risk sensitivity (i.e., Sobol’ indices) with respect to uncertain distribution parameters entails significant computational challenges due to the need to evaluate multi-dimensional integrals, e.g., using Monte Carlo Simulation (MCS). The proposed approach addresses the challenges by defining a joint auxiliary density in the augmented space of both the uncertain distribution parameters and input random variables. It first generates one set of samples from the joint auxiliary density and then based on the corresponding marginal samples estimates the marginal auxiliary densities for the uncertain distribution parameters using kernel density estimation (KDE). Then the KDE estimates are used to efficiently calculate the Sobol’ indices. It relies on only one set of simulations to estimate Sobol’ index for all uncertain distribution parameters without the need to repeat MCS for each distribution parameter. It is especially useful and efficient for evaluation of risk sensitivity for systems with expensive models and large number of inputs and uncertain distribution parameters. The good accuracy and high efficiency of the proposed approach are demonstrated through two illustrative examples and also for different risk definitions.