On the Possibility of Utilizing Wiener-Hermite Polynomial Chaos Expansion for Global Sensitivity Analysis Based on Cramér-von Mises Distance

A sensitivity analysis represents crucial part of uncertainty quantification. The paper is focused on global sensitivity analysis, specifically moment-independent importance measure based on Cramér-von Mises distance. This type of sensitivity analysis takes whole probability distribution of random variables into account in contrast to commonly used Sobol' indices. It leads to more precise sensitivity analysis. Nevertheless, such a method is highly computationally demanding. Therefore, novel idea of utilization the polynomial chaos expansion for the estimation of conditional distributions is presented herein. The paper represents a pilot study of performance of such method using simple example.