A new dependence measure for importance analysis: Application to an environmental model

Abstract

• A new dependence measure for importance analysis is presented. • The mathematical properties of the proposed measure are derived and discussed. • The nonparametric method for estimating the new measure is presented. • The new method is applied to a risk assessment model and the Level E model. • The advantages of the new measure with respect to the existing ones are highlighted. This paper presents a new dependence measure for importance analysis based on multivariate probability integral transformation (MPIT), which can assess the effect of an individual input, or a group of inputs on the whole uncertainty of model output. The mathematical properties of the new measure are derived and discussed. The nonparametric method for estimating the new measure is presented. The effectiveness of the new measure is compared with the well-known delta and extended delta indices, respectively, through a linear example, a risk assessment model and the Level E model. Results show that the proposed index can produce the same importance rankings as the delta and extended delta indices in these three examples. Yet the computation of the proposed measure is quite tractable due to the univariate nature of MPIT. The results also show that the established estimation method can provide robust estimate for the new measure in a quite efficient manner.