A screening approach for non-parametric global sensitivity analysis

Abstract

Global sensitivity analysis (GSA) can help practitioners focusing on the inputs whose uncertainties have an impact on the model output, which allows reducing the complexity of the model. Screening, as the qualitative method of GSA, is to identify and exclude non- or less-influential input variables in high-dimensional models. However, for non-parametric problems, there remains the challenging problem of finding an efficient screening procedure, as one needs to properly handle the non-parametric high-order interactions among input variables and keep the size of the screening experiment economically feasible. In this study, we design a novel screening approach based on analysis of variance decomposition of the model. This approach combines the virtues of run-size economy and model independence. The core idea is to choose a low-level complete orthogonal array to derive the sensitivity estimates for all input factors and their interactions with low cost, and then develop a statistical process to screen out the non-influential ones without assuming the effect-sparsity of the model. Simulation studies show that the proposed approach performs well in various settings.

Keywords:

• screening
• non-parametric
• global sensitivity analysis
• orthogonal array

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. A complete OA, also called a complete factorial, is a $(p_1\cdots p_m)\times m$ design consisting of all possible runs in which the first factor takes any level between 1 and $p_1$, the second factor takes any level between 1 and $p_2$, etc.

2. In the ANOVA, the sum of squares of the $i_1$th, …, $i_s$th factors, denoted as $S_{i_1\cdots i_s}^2$, is a quadratic form of Y and there exists a unique symmetric matrix $A_{i_1\cdots i_s}$ such that $S_{i_1\cdots i_s}^2=Y^{\prime }{A}_{i_1\cdots i_s}Y$. The matrix $A_{i_1\cdots i_s}$ is called the MI of columns $i_1,\dots ,i_s$ of H.

3. An OA H is called having strength d if each $n\times d$ submatrix of H contains all possible $1\times d$ row vectors with the same frequency.

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant no. 71301172], the Discipline Construction Fund of Central University of Finance and Economics.