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mODa 10 – Advances in Model-Oriented Design and Analysis pp 35–43Cite as

Estimating and Quantifying Uncertainties on Level Sets Using the Vorob’ev Expectation and Deviation with Gaussian Process Models

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Abstract

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.

Keywords

  • Gaussian Process
  • Bottom Left Plot
  • Infill Asymptotics
  • Adaptive Design Strategy
  • Gaussian Process Framework

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Author information

Authors and Affiliations

  1. Institute of Mathematical Statistics and Actuarial Science, University of Bern, Sidlerstrasse 5 and Alpeneggstrasse 22, 3012, Bern, Switzerland

    Clément Chevalier, David Ginsbourger & Ilya Molchanov

  2. Supélec Sciences des Systèmes, EA4454 (E3S), SUPELEC, Plateau de Moulon, 3 rue Joliot-Curie, 91192, Gif-sur-Yvette cedex, France

    Julien Bect

Authors
  1. Clément Chevalier
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  2. David Ginsbourger
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  3. Julien Bect
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  4. Ilya Molchanov
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Corresponding author

Correspondence to Clément Chevalier .

Editor information

Editors and Affiliations

  1. University of Zielona Góra, Podgorna 50, Zielona Góra, 65-246, Poland

    Dariusz Ucinski

  2. London School of Economics, Houghton Street, London, WC2A 2AE, United Kingdom

    Anthony C. Atkinson

  3. University of Zielona Góra, Podgorna 50, Zielona Góra, 65-246, Poland

    Maciej Patan

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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. In: Ucinski, D., Atkinson, A., Patan, M. (eds) mODa 10 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00218-7_5

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