Making best use of model evaluations to compute sensitivity indices

Abstract

This paper deals with computations of sensitivity indices in sensitivity analysis. Given a mathematical or computational model y= f( x 1, x 2,…, x k ), where the input factors x i 's are uncorrelated with one another, one can see y as the realization of a stochastic process obtained by sampling each of the x i from its marginal distribution. The sensitivity indices are related to the decomposition of the variance of y into terms either due to each x i taken singularly (first order indices), as well as into terms due to the cooperative effects of more than one x i . In this paper we assume that one has computed the full set of first order sensitivity indices as well as the full set of total-order sensitivity indices (a fairly common strategy in sensitivity analysis), and show that in this case the same set of model evaluations can be used to compute double estimates of: • the total effect of two factors taken together, for all such k 2 couples, where k is the dimensionality of the model; • the total effect of k−2 factors taken together, for all k 2 such ( k−2) ples. We further introduce a new strategy for the computation of the full sets of first plus total order sensitivity indices that is about 50% cheaper in terms of model evaluations with respect to previously published works. We discuss separately the case where the input factors x i 's are not independent from each other.