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Adaptive importance sampling for extreme quantile estimation with stochastic black box computer models

Author

Listed:
  • Qiyun Pan
  • Eunshin Byon
  • Young Myoung Ko
  • Henry Lam

Abstract

Quantile is an important quantity in reliability analysis, as it is related to the resistance level for defining failure events. This study develops a computationally efficient sampling method for estimating extreme quantiles using stochastic black box computer models. Importance sampling has been widely employed as a powerful variance reduction technique to reduce estimation uncertainty and improve computational efficiency in many reliability studies. However, when applied to quantile estimation, importance sampling faces challenges, because a good choice of the importance sampling density relies on information about the unknown quantile. We propose an adaptive method that refines the importance sampling density parameter toward the unknown target quantile value along the iterations. The proposed adaptive scheme allows us to use the simulation outcomes obtained in previous iterations for steering the simulation process to focus on important input areas. We prove some convergence properties of the proposed method and show that our approach can achieve variance reduction over crude Monte Carlo sampling. We demonstrate its estimation efficiency through numerical examples and wind turbine case study.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:navres:v:67:y:2020:i:7:p:524-547
    DOI: 10.1002/nav.21938
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    References listed on IDEAS

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    1. Neddermeyer, Jan C., 2009. "Computationally Efficient Nonparametric Importance Sampling," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 788-802.
    2. Jean-Marie Cornuet & Jean-Michel Marin & Antonietta Mira & Christian P. Robert, 2012. "Adaptive Multiple Importance Sampling," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 798-812, December.
    3. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    4. repec:dau:papers:123456789/10690 is not listed on IDEAS
    5. Mark Broadie & Yiping Du & Ciamac C. Moallemi, 2011. "Efficient Risk Estimation via Nested Sequential Simulation," Management Science, INFORMS, vol. 57(6), pages 1172-1194, June.
    6. Kohler, Michael & Krzyżak, Adam & Walk, Harro, 2014. "Nonparametric recursive quantile estimation," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 102-107.
    7. Bardou O. & Frikha N. & Pagès G., 2009. "Computing VaR and CVaR using stochastic approximation and adaptive unconstrained importance sampling," Monte Carlo Methods and Applications, De Gruyter, vol. 15(3), pages 173-210, January.
    8. Bruce Ankenman & Barry L. Nelson & Jeremy Staum, 2010. "Stochastic Kriging for Simulation Metamodeling," Operations Research, INFORMS, vol. 58(2), pages 371-382, April.
    9. Stéphane Bulteau & Mohamed El Khadiri, 2002. "A new importance sampling Monte Carlo method for a flow network reliability problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(2), pages 204-228, March.
    10. Wen Shi & Xi Chen, 2018. "Efficient budget allocation strategies for elementary effects method in stochastic simulation," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(3), pages 218-241, April.
    11. 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.
    12. Yunpeng Sun & Daniel W. Apley & Jeremy Staum, 2011. "Efficient Nested Simulation for Estimating the Variance of a Conditional Expectation," Operations Research, INFORMS, vol. 59(4), pages 998-1007, August.
    13. Feng Yang & Bruce Ankenman & Barry L. Nelson, 2007. "Efficient generation of cycle time‐throughput curves through simulation and metamodeling," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(1), pages 78-93, February.
    14. R. A. Rigby & D. M. Stasinopoulos, 2005. "Generalized additive models for location, scale and shape," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 54(3), pages 507-554, June.
    15. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
    16. L. Jeff Hong & Sandeep Juneja & Guangwu Liu, 2017. "Kernel Smoothing for Nested Estimation with Application to Portfolio Risk Measurement," Operations Research, INFORMS, vol. 65(3), pages 657-673, June.
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