Reliability of global sensitivity indices

Abstract

Uncertainty and sensitivity analysis is an essential ingredient of model development and applications. For many uncertainty and sensitivity analysis techniques, sensitivity indices are calculated based on a relatively large sample to measure the importance of parameters in their contributions to uncertainties in model outputs. To statistically compare their importance, it is necessary that uncertainty and sensitivity analysis techniques provide standard errors of estimated sensitivity indices. In this paper, a delta method is used to analytically approximate standard errors of estimated sensitivity indices for a popular sensitivity analysis method, the Fourier amplitude sensitivity test (FAST). Standard errors estimated based on the delta method were compared with those estimated based on 20 sample replicates. We found that the delta method can provide a good approximation for the standard errors of both first-order and higher-order sensitivity indices. Finally, based on the standard error approximation, we also proposed a method to determine a minimum sample size to achieve the desired estimation precision for a specified sensitivity index. The standard error estimation method presented in this paper can make the FAST analysis computationally much more efficient for complex models.

Keywords:

• Fourier amplitude sensitivity test
• sensitivity analysis
• uncertainty analysis
• standard error
• simple random sampling
• random balance design sampling

Acknowledgements

This study was supported by US Department of Agriculture McIntire-Stennis funds (MS 875-359), NIH grant R01-AI54954-0IA2, and US Construction Engineering Research Laboratory (W8IEWF82580556). We thank two anonymous reviewers for their very helpful comments which substantially improved this paper.