A two-stage method for the estimation of global sensitivity indices of non-parametric models

ABSTRACT

This article aims to propose a method to effectively estimate global sensitivity indices under non-parametric models. The new method involves two stages. First, all the non-influential sensitivity indices are filtered out by an adjustive W-statistic test process with low cost, and then the remaining significant sensitivity indices are precisely estimated by an orthogonal array (OA) with large number of levels and low strength. The method avoids complicated prototype building and shows a much lower experimental cost. The performance of this method as well as comparisons with polynomial regression method, Gaussian Process (GP) method, and component selection and smoothing operator (COSSO) method are tested on three numerical models that are widely used in engineering and statistical areas. Finally, a real data example is analyzed.

KEYWORDS:

• Global sensitivity indices
• Non-parametric
• Orthogonal array
• W statistic

MATHEMATICS SUBJECT CLASSIFICATION:

• 62-07

Acknowledgments

The work was supported by Natural Science Foundation of China (11601538).

Notes

1 A design is called saturated if there are only enough degrees of freedom to estimate the effects specified in the model.