Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes

The paper investigates a nonparametric regression method based on smoothing spline analysis of variance (ANOVA) approach to address the problem of global sensitivity analysis (GSA) of complex and computationally demanding computer codes. The two steps algorithm of this method involves an estimation procedure and a variable selection. The latter can become computationally demanding when dealing with high dimensional problems. Thus, we proposed a new algorithm based on Landweber iterations. Using the fact that the considered regression method is based on ANOVA decomposition, we introduced a new direct method for computing sensitivity indices. Numerical tests performed on several analytical examples and on an application from petroleum reservoir engineering showed that the method gives competitive results compared to a more standard Gaussian process approach.