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Pré-Publication, Document De Travail Année : 2012

Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviance with Gaussian process models

Résumé

Several methods based on Kriging have been recently proposed for calculating a probability of failure involving costly-to-evaluate functions. A closely related problem is to estimate the set of inputs leading to a response exceeding a given threshold. Now, estimating such level set - and not solely its volume - and quantifying uncertainties on it are not straightforward. Here we use notions from random set theory to obtain an estimate of the level set, together with a quantification of estimation uncertainty. We give explicit formulae in the Gaussian process set-up, and provide a consistency result. We then illustrate how space-filling versus adaptive design strategies may sequentially reduce level set estimation uncertainty.
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Dates et versions

hal-00731783 , version 1 (13-09-2012)
hal-00731783 , version 2 (22-07-2013)

Identifiants

  • HAL Id : hal-00731783 , version 1

Citer

Clément Chevalier, David Ginsbourger, Julien Bect, Ilya Molchanov. Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviance with Gaussian process models. 2012. ⟨hal-00731783v1⟩
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