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Estimating and quantifying uncertainties on level sets using the vorob’ev expectation and deviation with gaussian process models

Clément Chevalier, David Ginsbourger, Julien Bect & Ilya Molchanov

Résumé Several methods based on Kriging have recently been 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 a 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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Citation Chevalier, C., Ginsbourger, D., Bect, J., & Molchanov, I. (2013). Estimating and quantifying uncertainties on level sets using the vorob’ev expectation and deviation with gaussian process models. Paper presented at mODa 10 – Advances in Model-Oriented Design and Analysis, Łagów Lubuski, Poland.
   
Type Actes de congrès (Anglais)
Nom de la conférence mODa 10 – Advances in Model-Oriented Design and Analysis (Łagów Lubuski, Poland)
Date de la conférence 2013
Pages 35-43
URL http://link.springer.com/chapter/10.1007%2F978-3-319-0021...