Moment-independent sensitivity analysis using copula

In risk assessment, the moment-independent sensitivity analysis (SA) technique for reducing the model uncertainty has attracted a great deal of attention from analysts and practitioners. It aims at measuring the relative importance of an individual input, or a set of inputs, in determining the uncertainty of model output by looking at the entire distribution range of model output. In this article, along the lines of Plischke et al., we point out that the original moment-independent SA index (also called delta index) can also be interpreted as the dependence measure between model output and input variables, and introduce another moment-independent SA index (called extended delta index) based on copula. Then, nonparametric methods for estimating the delta and extended delta indices are proposed. Both methods need only a set of samples to compute all the indices; thus, they conquer the problem of the "curse of dimensionality." At last, an analytical test example, a risk assessment model, and the levelE model are employed for comparing the delta and the extended delta indices and testing the two calculation methods. Results show that the delta and the extended delta indices produce the same importance ranking in these three test examples. It is also shown that these two proposed calculation methods dramatically reduce the computational burden.