Symmetrical design for symmetrical global sensitivity analysis of model output

Symmetrical global sensitivity analysis (SGSA) can help practitioners focusing on the symmetrical terms of inputs whose uncertainties have an impact on the model output, which allows reducing the complexity of the model. However, there remains the challenging problem of finding an efficient method to get symmetrical global sensitivity indices (SGSI) when the functional form of the symmetrical terms is unknown, including numerical and non-parametric situations. In this study, we propose a novel sampling plan, called symmetrical design, for SGSA. As a preliminary experiment for model feature extracting, such plan offers the virtue of run-size economy due to its closure respective to the given group. Using the design, we give estimation methods of SGSI as well as their asymptotic properties respectively for numerical model and non-parametrical model directly by the model outputs, and further propose a significance test for SGSI in non-parametric situation. A case study for a benchmark of GSA and a real data analysis show the effectiveness of the proposed design.