Making best use of model evaluations to compute sensitivity indices

This paper deals with computations of sensitivity indices in sensitivity analysis. Given a mathematical or computational model y=f(x1,x2,…,xk), where the input factors xi's are uncorrelated with one another, one can see y as the realization of a stochastic process obtained by sampling each of the xi from its marginal distribution. The sensitivity indices are related to the decomposition of the variance of y into terms either due to each xi taken singularly (first order indices), as well as into terms due to the cooperative effects of more than one xi. 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 k2 couples, where k is the dimensionality of the model; the total effect of k−2 factors taken together, for all k2 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 xi's are not independent from each other.