Computing first-order sensitivity indices with contribution to the sample mean plot

In this paper, we investigate the use of the contribution to the sample mean plot (CSM plot) as a graphical tool for sensitivity analysis (SA) of computational models. We first provide an exact formula that links, for each uncertain model input Xj, the CSM plot Cj(·) with the first-order variance-based sensitivity index Sj. We then build a new estimate for Sj using polynomial regression of the CSM plot. This estimation procedure allows the computation of Sj from given data, without any SA-specific design of experiment. Numerical results show that this new Sj estimate is efficient for large sample sizes, but that at small sample sizes it does not compare well with other Sj estimation techniques based on given data, such as the effective algorithm for computing global sensitivity indices method or metamodel-based approaches.