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Toward a More Robust Variance-based Global Sensitivity Analysis of Model Outputs.

PB2012100592

Publication Date	2007
Personal Author	Tong, C.
Page Count	20
Abstract	Global sensitivity analysis (GSA) measures the variation of a model output as a function of the variations of the model inputs given their ranges. In this paper we consider variance-based GSA methods that do not rely on certain assumptions about the model structure such as linearity or monotonicity. These variance-based methods decompose the output variance into terms of increasing dimensionality called 'sensitivity indices', first introduced by Sobol'. Sobol' developed a method of estimating these sensitivity indices using Monte Carlo simulations. McKay proposed an efficient method using replicated Latin hypercube sampling to compute the 'correlation ratios' or 'main effects', which have been shown to be equivalent to Sobol's first-order sensitivity indices. Practical issues with using these variance estimators are how to choose adequate sample sizes and how to assess the accuracy of the results. This paper proposes a modified McKay main effect method featuring an adaptive procedure for accuracy assessment and improvement. We also extend our adaptive technique to the computation of second-order sensitivity indices. Details of the proposed adaptive procedure as wells as numerical results are included in this paper.
Keywords	Sensitivity analysis Variations Global Monte Carlo method Simulation Accuracy Sampling Mathematical models Probability Correlations Global sensitivity analysis
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Lawrence Livermore National Lab., CA.
Document Type	Technical Report
NTIS Issue Number	201126
Contract Number	DE-AC52-07NA27344

Toward a More Robust Variance-based Global Sensitivity Analysis of Model Outputs.

Toward a More Robust Variance-based Global Sensitivity Analysis of Model Outputs.
PB2012100592

Publication Date	2007
Personal Author	Tong, C.
Page Count	20
Abstract	Global sensitivity analysis (GSA) measures the variation of a model output as a function of the variations of the model inputs given their ranges. In this paper we consider variance-based GSA methods that do not rely on certain assumptions about the model structure such as linearity or monotonicity. These variance-based methods decompose the output variance into terms of increasing dimensionality called 'sensitivity indices', first introduced by Sobol'. Sobol' developed a method of estimating these sensitivity indices using Monte Carlo simulations. McKay proposed an efficient method using replicated Latin hypercube sampling to compute the 'correlation ratios' or 'main effects', which have been shown to be equivalent to Sobol's first-order sensitivity indices. Practical issues with using these variance estimators are how to choose adequate sample sizes and how to assess the accuracy of the results. This paper proposes a modified McKay main effect method featuring an adaptive procedure for accuracy assessment and improvement. We also extend our adaptive technique to the computation of second-order sensitivity indices. Details of the proposed adaptive procedure as wells as numerical results are included in this paper.
Keywords	Sensitivity analysis Variations Global Monte Carlo method Simulation Accuracy Sampling Mathematical models Probability Correlations Global sensitivity analysis
Source Agency	Technical Information Center Oak Ridge Tennessee
Corporate Authors	Lawrence Livermore National Lab., CA.
Document Type	Technical Report
NTIS Issue Number	201126
Contract Number	DE-AC52-07NA27344