Variance-based sensitivity indices for models with dependent inputs

A set of variance-based sensitivity indices are proposed to perform sensitivity analysis of models with dependent inputs and allow us to distinguish between the mutual dependent contribution and the independent contribution of an input to the model response variance.

Abstract

Computational models are intensively used in engineering for risk analysis or prediction of future\noutcomes. Uncertainty and sensitivity analyses are of great help in these purposes. Although several\nmethods exist to perform variance-based sensitivity analysis of model output with independent inputs\nonly a few are proposed in the literature in the case of dependent inputs. This is explained by the fact\nthat the theoretical framework for the independent case is set and a univocal set of variance-based\nsensitivity indices is defined. In the present work, we propose a set of variance-based sensitivity indices\nto perform sensitivity analysis of models with dependent inputs. These measures allow us to\ndistinguish between the mutual dependent contribution and the independent contribution of an input\nto the model response variance. Their definition relies on a specific orthogonalisation of the inputs and\nANOVA-representations of the model output. In the applications, we show the interest of the new\nsensitivity indices for model simplification setting.