Extended sample-based approach for efficient sensitivity analysis of group of random variables

This paper proposes an extended sample-based approach for efficient sensitivity analysis of the group of random variables by extending the original sample-based approach proposed by Jia and Taflanidis. The original sample-based approach can efficiently estimate the sensitivity indices (i.e., Sobol’ indices) for individual and low-dimensional inputs by using kernel density estimation (KDE). However, due to the curse of dimensionality of KDE, it is challenging to directly apply the original sample-based approach to estimate sensitivity indices for high-dimensional groups of inputs. To address the challenges, the proposed approach converts estimating the sensitivity index for groups of inputs with potentially high dimensionality to estimating the sensitivity indices for individual inputs in the group and their lower-order (e.g., second or third) interactions using the idea of variance decomposition, thus limiting the dimension of the required KDE to be low (e.g., only two or three) if higher-order interactions are negligible. Different estimators for the main and total sensitivity indices are proposed to reduce the error accumulation and improve estimation accuracy. Overall, the proposed approach can be used to efficiently estimate the sensitivity indices (including main and total sensitivity indices) for both individual and groups of inputs when higher-order interactions have negligible contributions. The good efficiency and accuracy of the proposed approach are demonstrated through three benchmark examples.