Abstract
In this paper, the use of orthogonal arrays with strength \(s<p,\) where \(p\) is the required strength, for global sensitivity analysis is considered. We first generalize the alias matrix for ANOVA high-dimensional model representation based on matrix image, and then by sequentially minimizing the squared alias degrees, we present a approach for the estimation of sensitivity indices. A two-level orthogonal array with 16 runs and a four-level orthogonal array with 64 runs are studied for estimating both low-order and high-order significant sensitivity indices. Moreover, models containing larger than 10 input factors are also investigated. All cases show that designs with smaller squared alias degree have less bias and variance for the estimations of global sensitivity indices.
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Acknowledgments
The authors would like to thank the Editor and two anonymous referees for their valuable comments and constructive suggestions. The work was supported by National Natural Science Foundation of China (Nos. 11301073 and 11401094), Natural Science Foundation of Jiangsu Province of China (Nos. BK20141326 and BK20140617), Science Foundation of Ministry of Education of China (No. 13YJC910006), Graduate research and innovation projects in Jiangsu Province (No. KYZZ_0068).
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Appendix
Appendix
Descriptive statistics for \(\widehat{S}_N\) are given in the following Table 4. The set \(N\) is given in the first row of each case. In the second column, “M” indicates the mean of corresponding estimates of global sensitivity indices \(\widehat{S}_N\), “SD” indicates the standard deviation of \(\widehat{S}_N\).
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Chen, Xp., Lin, JG., Wang, Xd. et al. Further results on orthogonal arrays for the estimation of global sensitivity indices based on alias matrix. Stat Methods Appl 24, 411–426 (2015). https://doi.org/10.1007/s10260-014-0290-7
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DOI: https://doi.org/10.1007/s10260-014-0290-7