IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v80y2014icp153-166.html
   My bibliography  Save this article

Bounding rare event probabilities in computer experiments

Author

Listed:
  • Auffray, Yves
  • Barbillon, Pierre
  • Marin, Jean-Michel

Abstract

Bounding probabilities of rare events in the context of computer experiments is an important concern in reliability studies. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. That is why a strategy based on importance sampling methods is proposed. This strategy relies on Kriging meta-modeling and manages to achieve sharp upper confidence bounds on the rare events probabilities. The variability due to the Kriging meta-modeling step is properly taken into account. The proposed methodology is applied to an artificial example and compared with more standard Bayesian bounds. Eventually, a challenging real case is analyzed. It consists in finding an upper bound for the probability that the trajectory of an airborne load will collide with the aircraft that released it.

Suggested Citation

  • Auffray, Yves & Barbillon, Pierre & Marin, Jean-Michel, 2014. "Bounding rare event probabilities in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 80(C), pages 153-166.
    • Handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:153-166
    DOI: 10.1016/j.csda.2014.06.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947314002023
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2014.06.023?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Helton, Jon C. & Johnson, Jay D. & Sallaberry, Cédric J., 2011. "Quantification of margins and uncertainties: Example analyses from reactor safety and radioactive waste disposal involving the separation of aleatory and epistemic uncertainty," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1014-1033.
    2. Reichert, P. & White, G. & Bayarri, M.J. & Pitman, E.B., 2011. "Mechanism-based emulation of dynamic simulation models: Concept and application in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1638-1655, April.
    3. Marrel, Amandine & Iooss, Bertrand & Van Dorpe, François & Volkova, Elena, 2008. "An efficient methodology for modeling complex computer codes with Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4731-4744, June.
    4. Bachoc, François, 2013. "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 55-69.
    5. Jeremy Oakley, 2004. "Estimating percentiles of uncertain computer code outputs," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 83-93, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    2. Betancourt, José & Bachoc, François & Klein, Thierry & Idier, Déborah & Pedreros, Rodrigo & Rohmer, Jérémy, 2020. "Gaussian process metamodeling of functional-input code for coastal flood hazard assessment," Reliability Engineering and System Safety, Elsevier, vol. 198(C).
    3. Lee, Dongjin & Kramer, Boris, 2023. "Multifidelity conditional value-at-risk estimation by dimensionally decomposed generalized polynomial chaos-Kriging," Reliability Engineering and System Safety, Elsevier, vol. 235(C).
    4. Picheny, Victor & Ginsbourger, David, 2014. "Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1035-1053.
    5. Kucherenko, Sergei & Song, Shufang & Wang, Lu, 2019. "Quantile based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 35-48.
    6. Acharki, Naoufal & Bertoncello, Antoine & Garnier, Josselin, 2023. "Robust prediction interval estimation for Gaussian processes by cross-validation method," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    7. Veiga, Sébastien Da & Marrel, Amandine, 2020. "Gaussian process regression with linear inequality constraints," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    8. Cao, Jiaokun & Du, Farong & Ding, Shuiting, 2013. "Global sensitivity analysis for dynamic systems with stochastic input processes," Reliability Engineering and System Safety, Elsevier, vol. 118(C), pages 106-117.
    9. Helton, Jon C. & Brooks, Dusty M. & Sallaberry, Cédric J., 2020. "Property values associated with the failure of individual links in a system with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    10. Barbillon, Pierre & Celeux, Gilles & Grimaud, Agnès & Lefebvre, Yannick & De Rocquigny, Étienne, 2011. "Nonlinear methods for inverse statistical problems," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 132-142, January.
    11. Tang, Zhang-Chun & Zuo, Ming J. & Xiao, Ningcong, 2016. "An efficient method for evaluating the effect of input parameters on the integrity of safety systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 111-123.
    12. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    13. Touzani, Samir & Busby, Daniel, 2013. "Smoothing spline analysis of variance approach for global sensitivity analysis of computer codes," Reliability Engineering and System Safety, Elsevier, vol. 112(C), pages 67-81.
    14. Sun, Zhili & Wang, Jian & Li, Rui & Tong, Cao, 2017. "LIF: A new Kriging based learning function and its application to structural reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 152-165.
    15. Binois, M. & Ginsbourger, D. & Roustant, O., 2015. "Quantifying uncertainty on Pareto fronts with Gaussian process conditional simulations," European Journal of Operational Research, Elsevier, vol. 243(2), pages 386-394.
    16. Michael Kohler & Adam Krzyżak & Reinhard Tent & Harro Walk, 2018. "Nonparametric quantile estimation using importance sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 439-465, April.
    17. Pasanisi, Alberto & Keller, Merlin & Parent, Eric, 2012. "Estimation of a quantity of interest in uncertainty analysis: Some help from Bayesian decision theory," Reliability Engineering and System Safety, Elsevier, vol. 100(C), pages 93-101.
    18. Bachoc, François & Lagnoux, Agnès & Nguyen, Thi Mong Ngoc, 2017. "Cross-validation estimation of covariance parameters under fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 42-67.
    19. Nott, David J. & Marshall, Lucy & Fielding, Mark & Liong, Shie-Yui, 2014. "Mixtures of experts for understanding model discrepancy in dynamic computer models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 491-505.
    20. Kleijnen, Jack P.C. & Mehdad, E., 2013. "Conditional simulation for efficient global optimization," Other publications TiSEM 52e4860d-9887-4a63-b19a-7, Tilburg University, School of Economics and Management.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:80:y:2014:i:c:p:153-166. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.