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Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models
Abstract : 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.
Cited literature [14 references]
https://hal.archives-ouvertes.fr/hal-00731783
Contributor : David Ginsbourger <>
Submitted on : Monday, July 22, 2013 - 11:03:02 AM
Last modification on : Thursday, March 29, 2018 - 11:06:05 AM
Document(s) archivé(s) le : Wednesday, April 5, 2017 - 3:45:33 PM
Contributor : David Ginsbourger <>
Submitted on : Monday, July 22, 2013 - 11:03:02 AM
Last modification on : Thursday, March 29, 2018 - 11:06:05 AM
Document(s) archivé(s) le : Wednesday, April 5, 2017 - 3:45:33 PM
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MODA10_Chevalier.pdf
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