Derivative-Based Sensitivity Measures for Interactions
Résumé
Global sensitivity analysis is used to quantify the influence of uncertain variables, and their interactions, on the response variability of a numerical model. Variance-based importance measures (called Sobol' indices) are now widely used but their estimation requires a large number of model evaluations, especially when interaction effects are of interest. The derivative-based global sensitivity measures (DGSM) have recently shown their relevance and efficiency for the identification of non-influential inputs. In this paper, we extend previous works by studying the so-called crossed DGSM which are based on second-order derivatives of model output. By using a L2-Poincaré inequality, we provide a general inequality link between crossed DGSM and superset importance (i.e. total Sobol' indices of a set of inputs). It provides a crossed-DGSM based maximal bound for the superset importance. In order to apply this result, we discuss how to estimate the Poincaré constant for various probability distributions. A particular emphasis is placed on the detection of influential interactions between two inputs. Several analytical and numerical tests show the performance of the bound and allow to develop a generic strategy for interaction screening.
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