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Estimating percentiles of uncertain computer code outputs

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  • Jeremy Oakley

Abstract

Summary. A deterministic computer model is to be used in a situation where there is uncertainty about the values of some or all of the input parameters. This uncertainty induces uncertainty in the output of the model. We consider the problem of estimating a specific percentile of the distribution of this uncertain output. We also suppose that the computer code is computationally expensive, so we can run the model only at a small number of distinct inputs. This means that we must consider our uncertainty about the computer code itself at all untested inputs. We model the output, as a function of its inputs, as a Gaussian process, and after a few initial runs of the code use a simulation approach to choose further suitable design points and to make inferences about the percentile of interest itself. An example is given involving a model that is used in sewer design.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jorssc:v:53:y:2004:i:1:p:83-93
    DOI: 10.1046/j.0035-9254.2003.05044.x
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    Cited by:

    1. Kucherenko, Sergei & Song, Shufang & Wang, Lu, 2019. "Quantile based global sensitivity measures," Reliability Engineering and System Safety, Elsevier, vol. 185(C), pages 35-48.
    2. Wei Xie & Barry L. Nelson & Russell R. Barton, 2014. "A Bayesian Framework for Quantifying Uncertainty in Stochastic Simulation," Operations Research, INFORMS, vol. 62(6), pages 1439-1452, December.
    3. Kleijnen, Jack P.C., 2009. "Kriging metamodeling in simulation: A review," European Journal of Operational Research, Elsevier, vol. 192(3), pages 707-716, February.
    4. 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.
    5. Qiyun Pan & Eunshin Byon & Young Myoung Ko & Henry Lam, 2020. "Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models," Naval Research Logistics (NRL), John Wiley & Sons, vol. 67(7), pages 524-547, October.
    6. Michael Ludkovski & James Risk, 2017. "Sequential Design and Spatial Modeling for Portfolio Tail Risk Measurement," Papers 1710.05204, arXiv.org, revised May 2018.
    7. 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.
    8. Wang, Lei & Zhang, Xufang & Zhou, Yangjunjian, 2018. "An effective approach for kinematic reliability analysis of steering mechanisms," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 62-76.
    9. O’Hagan, A., 2006. "Bayesian analysis of computer code outputs: A tutorial," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1290-1300.
    10. 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.

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