Crossed-derivative based sensitivity measures for interaction screening

Global sensitivity analysis is used to quantify the influence of input variables on a numerical model output. Sobol’ indices are now classical sensitivity measures. However their estimation requires a large number of model evaluations, especially when interaction effects are of interest. Derivative-based global sensitivity measures (DGSM) have recently shown their efficiency for the identification of non-influential inputs. In this paper, we define crossed DGSM, based on second-order derivatives of model output. By using a L2-Poincaré inequality, we provide a crossed-DGSM based maximal bound for the superset importance (i.e. total Sobol’ indices of an interaction between two inputs). In order to apply this result, we discuss how to estimate the Poincaré constant for various probability distributions. Several analytical and numerical tests show the performance of the bound and allow to develop a generic strategy for interaction screening.