Uncertainties Assessment in Global Sensitivity Indices Estimation From Metamodels

Janon, Alexandre; Nodet, Maëlle; Prieur, Clémentine

doi:10.1615/int.j.uncertaintyquantification.2012004291

Cited by 36 publications

(46 citation statements)

References 26 publications

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“…This is determined by adding sampled points in an efficient way to explore the whole input space and having indicators showing that adequate matching has occurred. Our approach obtains a measure of the accuracy of the estimated sensitivities, which are functions of predicted point estimates, by summing two errors: the sampling error and the emulator error [19]. Sampling error is estimated by computing the sensitivities for several iterations.…”

Section: Steps Required To Provide Estimated Accuracymentioning

confidence: 99%

Sequential design for achieving estimated accuracy of global sensitivities

Guenther

Lee

Gray

2014

Appl Stoch Models Bus & Ind

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Global sensitivity analysis provides information on the relative importance of the input variables for simulator functions used in computer experiments. It is more conclusive than screening methods for determining if a variable is influential, especially if a variable's influence is derived from its interactions with other variables. In this paper, we develop a method for providing global sensitivities with estimated accuracy. A treed Gaussian process serves as a statistical emulator of the black box function. A sequential experimental design makes effective and efficient use of simulator evaluations by adaptively sampling points that are expected to provide the maximum improvement to the emulator model. The method accounts for both sampling error and emulator error.

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Section: Steps Required To Provide Estimated Accuracymentioning

confidence: 99%

Sequential design for achieving estimated accuracy of global sensitivities

Guenther

Lee

Gray

2014

Appl Stoch Models Bus & Ind

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“…In [16], we have proposed a fast, analytical method for computingŜ min u,n andŜ Max u,n . The spread betweenŜ min u,n andŜ Max u,n accounts for the error induced by the use of the metamodel to estimate the Sobol' sensitivity index S u .…”

Section: Error Quantification For Sobol' Indices Estimated Using a Mementioning

confidence: 99%

Sensitivity analysis and uncertainty quantification for environmental models

Cartailler¹,

Guaus

Janon

et al. 2014

ESAIM: Proc.

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Abstract. Environmental models often involve complex dynamic and spatial inputs and outputs.This raises specific issues when performing uncertainty and sensitivity analyses (SA). Based on applications in flood risk assessment and agro-ecology, we present current research to adapt the methods of variance-based SA to such models. After recalling the basic principles, we propose a metamodelling approach of dynamic models based on a reduced-basis approximation of PDEs and we show how the error on the subsequent sensitivity indices can be quantified. We then present a mix of pragmatic and methodological solutions to perform the SA of a dynamic agro-climatic model with non standard input factors. SA is then applied to a flood risk model with spatially distributed inputs and outputs. Block sensitivity indices are defined and a precise relationship between these indices and their support size is established. Finally, we show how the whole support landscape and its key features can be incorporated in the SA of a spatial model.

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“…Gaussian process metamodels have also been used for the estimation of Sobol' indices [28]; in particular, these surrogate models can provide credibility intervals to quantify the approximation error of such sensitivity indices. More recently, Sobol' indices have been estimated combining the estimation method developed by [19] and the Gaussian process metamodel approach [28] in order to take into account numerical and integration and metamodel errors [26].…”

Section: Introductionmentioning

confidence: 99%

Estimation of the Derivative-Based Global Sensitivity Measures Using a Gaussian Process Metamodel

Lozzo¹,

Marrel²

2016

SIAM/ASA J. Uncertainty Quantification

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Physical phenomena are often studied using numerical simulators. Such computer codes are function of uncertain input parameters and a global sensitivity analysis (GSA) can be performed to identify their impacts on the simulator outputs. Sobol' indices, based on output variance decomposition, are commonly used to perform quantitative GSA. For many years now, other tools have been studied, closer to physical practices such as the derivative-based global sensitivity measures (DGSM). However, numerical simulators rarely provide the output gradient and DGSM estimation is not directly possible. To address this limitation, we propose to estimate the DGSMs using a Gaussian process metamodel (GPM) which approximates the simulator.Based on this GPM, we propose two DGSM estimators: a plug-in one defined by the DGSM of the GPM predictor and another one defined by the expectation of the DGSM associated to the full-GPM. The latter is equal to the first one completed by a variance term and can be accompanied by a credibility interval. For Gaussian kernel and uniform input laws, analytical formula are given for both DGSM estimators. For all other situations, MonteCarlo methods for the expectation approximations are proposed: a propagative version of the Gibbs sampler and a chi-square approximation. Moreover, a significance test for the full-GPM based estimator is proposed for screening. The convergence of the two GPM-based DGSM estimators and the Monte-Carlo approaches are compared on analytical test cases. Finally, we apply our work to an environmental application.

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Uncertainties Assessment in Global Sensitivity Indices Estimation From Metamodels

Cited by 36 publications

References 26 publications

Sequential design for achieving estimated accuracy of global sensitivities

Sequential design for achieving estimated accuracy of global sensitivities

Sensitivity analysis and uncertainty quantification for environmental models

Estimation of the Derivative-Based Global Sensitivity Measures Using a Gaussian Process Metamodel

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