A fast computational method for moment-independent uncertainty importance measure

This work focuses on the fast computation of the moment-independent importance measure δiδi. We first analyse why δiδi is associated with a possible computational complexity problem. One of the reasons that we thought of is the use of two-loop Monte Carlo simulation, because its rate of convergence is O(N−1/4)O(N−1/4), and another one is the computation of the norm of the difference between a density and a conditional density. We find that these problems are nonessential difficulties and try to give associated improvements. A kernel estimate is introduced to avoid the use of two-loop Monte Carlo simulation, and a moment expansion of the associated norm which is not simply obtained by using the Edgeworth series is proposed to avoid the density estimation. Then, a fast computational method is introduced for δiδi. In our method, all δiδi can be obtained by using a single sample set. From the comparison of the numerical error analyses, we believe that the proposed method is clearly helpful for improving computational efficiency.