Reliability of global sensitivity indices

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)1939-1969
Number of pages31
JournalJournal of Statistical Computation and Simulation
Volume81
Issue number12
DOIs
StatePublished - Dec 1 2011

Keywords

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

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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