A randomized orthogonal array-based procedure for the estimation of first- and second-order Sobol' indices

SIAM/ASA J Uncertain Quantification. 2013;1:19–41], but the quantities they estimate still depend linearly on the dimension d . In this paper, we introduce a new approach to estimate all the first- and second-order SI by using only two input vectors. We establish theoretical properties of such a method for the estimation of first-order SI and discuss the generalization to higher order indices.

In particular, we prove on numerical examples that this procedure is tractable and competitive for the estimation of all first- and second-order SI. As an illustration, we propose to apply this new approach to a marine ecosystem model of the Ligurian sea (northwestern Mediterranean) in order to study the relative importance of its several parameters. The calibration process of this kind of chemical simulators is well known to be quite intricate, and a rigorous and robust – that is, valid without strong regularity assumptions – sensitivity analysis, as the method of Sobol' provides, could be of great help.

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