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

Chevalier, Clément; Ginsbourger, David; Bect, Julien; Molchanov, Ilya (2013). Estimating and quantifying uncertainties on level sets using the Vorob'ev expectation and deviation with Gaussian process models. In: Uciński, Dariusz; Atkinson, Anthony C; Patan, Maciej (eds.) mODa 10 - Advances in Model-Oriented Design and Analysis. Proceedings of the 10th International Workshop in Model-Oriented Design and Analysis Held in Łagów Lubuski, Poland, June 10–14, 2013. Contributions to Statistics (pp. 35-43). Springer 10.1007/978-3-319-00218-7_5

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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.

Item Type:

Book Section (Book Chapter)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Chevalier, Clément; Ginsbourger, David and Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISSN:

1431-1968

ISBN:

978-3-319-00217-0

Series:

Contributions to Statistics

Publisher:

Springer

Language:

English

Submitter:

Lutz Dümbgen

Date Deposited:

01 Apr 2014 03:18

Last Modified:

08 Aug 2016 15:55

Publisher DOI:

10.1007/978-3-319-00218-7_5

URI:

https://boris.unibe.ch/id/eprint/41307

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