IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v284y2020i1p201-211.html
   My bibliography  Save this article

Versatile sequential sampling algorithm using Kernel Density Estimation

Author

Listed:
  • Roy, Pamphile T.
  • Jofre, Lluís
  • Jouhaud, Jean-Christophe
  • Cuenot, Bénédicte

Abstract

Understanding the physical mechanisms governing scientific and engineering systems requires performing experiments. Therefore, the construction of the Design of Experiments (DoE) is paramount for the successful inference of the intrinsic behavior of such systems. There is a vast literature on one-shot designs such as low discrepancy sequences and Latin Hypercube Sampling (LHS). However, in a sensitivity analysis context, an important property is the stochasticity of the DoE which is partially addressed by these methods. This work proposes a new stochastic, iterative DoE – named KDOE – based on a modified Kernel Density Estimation (KDE). It is a two-step process: (i) candidate samples are generated using Markov Chain Monte Carlo (MCMC) based on KDE, and (ii) one of them is selected based on some metric. The performance of the method is assessed by means of the C2-discrepancy space-filling criterion. KDOE appears to be as performant as classical one-shot methods in low dimensions, while it presents increased performance for high-dimensional parameter spaces. It is a versatile method which offers an alternative to classical methods and, at the same time, is easy to implement and offers customization based on the objective of the DoE.

Suggested Citation

  • Roy, Pamphile T. & Jofre, Lluís & Jouhaud, Jean-Christophe & Cuenot, Bénédicte, 2020. "Versatile sequential sampling algorithm using Kernel Density Estimation," European Journal of Operational Research, Elsevier, vol. 284(1), pages 201-211.
    • Handle: RePEc:eee:ejores:v:284:y:2020:i:1:p:201-211
    DOI: 10.1016/j.ejor.2019.11.070
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719309828
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.11.070?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. Crombecq, K. & Laermans, E. & Dhaene, T., 2011. "Efficient space-filling and non-collapsing sequential design strategies for simulation-based modeling," European Journal of Operational Research, Elsevier, vol. 214(3), pages 683-696, November.
    2. E. Androulakis & K. Drosou & C. Koukouvinos & Y.-D. Zhou, 2016. "Measures of uniformity in experimental designs: A selective overview," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(13), pages 3782-3806, July.
    3. V. Roshan Joseph & Evren Gul & Shan Ba, 2015. "Maximum projection designs for computer experiments," Biometrika, Biometrika Trust, vol. 102(2), pages 371-380.
    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. Leurent, Martin & Jasserand, Frédéric & Locatelli, Giorgio & Palm, Jenny & Rämä, Miika & Trianni, Andrea, 2017. "Driving forces and obstacles to nuclear cogeneration in Europe: Lessons learnt from Finland," Energy Policy, Elsevier, vol. 107(C), pages 138-150.
    2. Francisco Castillo-Zunino & Pinar Keskinocak, 2021. "Bi-criteria multiple knapsack problem with grouped items," Journal of Heuristics, Springer, vol. 27(5), pages 747-789, October.
    3. Song-Nan Liu & Min-Qian Liu & Jin-Yu Yang, 2023. "Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications," Mathematics, MDPI, vol. 11(6), pages 1-27, March.
    4. Xueru Zhang & Dennis K. J. Lin & Lin Wang, 2023. "Digital Triplet: A Sequential Methodology for Digital Twin Learning," Mathematics, MDPI, vol. 11(12), pages 1-16, June.
    5. Kleijnen, Jack P.C., 2017. "Regression and Kriging metamodels with their experimental designs in simulation: A review," European Journal of Operational Research, Elsevier, vol. 256(1), pages 1-16.
    6. Vinícius Resende Domingues & Luan Carlos de Sena Monteiro Ozelim & André Pacheco de Assis & André Luís Brasil Cavalcante, 2022. "Combining Numerical Simulations, Artificial Intelligence and Intelligent Sampling Algorithms to Build Surrogate Models and Calculate the Probability of Failure of Urban Tunnels," Sustainability, MDPI, vol. 14(11), pages 1-29, May.
    7. Guo, Hongqiang & Lu, Silong & Hui, Hongzhong & Bao, Chunjiang & Shangguan, Jinyong, 2019. "Receding horizon control-based energy management for plug-in hybrid electric buses using a predictive model of terminal SOC constraint in consideration of stochastic vehicle mass," Energy, Elsevier, vol. 176(C), pages 292-308.
    8. Koziel, Slawomir & Pietrenko-Dabrowska, Anna, 2022. "Constrained multi-objective optimization of compact microwave circuits by design triangulation and pareto front interpolation," European Journal of Operational Research, Elsevier, vol. 299(1), pages 302-312.
    9. Xiao, Ning-Cong & Zuo, Ming J. & Zhou, Chengning, 2018. "A new adaptive sequential sampling method to construct surrogate models for efficient reliability analysis," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 330-338.
    10. Tonghui Pang & Yan Wang & Jian-Feng Yang, 2022. "Asymptotically optimal maximin distance Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 405-418, May.
    11. Nicholas Davey & Nicolas Langrené & Wen Chen & Jonathan R. Rhodes & Simon Dunstall & Saman Halgamuge, 2023. "Designing higher value roads to preserve species at risk by optimally controlling traffic flow," Annals of Operations Research, Springer, vol. 320(2), pages 663-693, January.
    12. Yue Huan & Yubin Tian & Dianpeng Wang, 2022. "A Weighted Surrogate Model for Spatio-Temporal Dynamics with Multiple Time Spans: Applications for the Pollutant Concentration of the Bai River," Mathematics, MDPI, vol. 10(19), pages 1-16, October.
    13. Mu, Weiyan & Xiong, Shifeng, 2018. "A class of space-filling designs and their projection properties," Statistics & Probability Letters, Elsevier, vol. 141(C), pages 129-134.
    14. Guillaume Perrin & Christian Soize, 2020. "Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework," Computational Statistics, Springer, vol. 35(1), pages 111-133, March.
    15. Fajemisin, Adejuyigbe O. & Maragno, Donato & den Hertog, Dick, 2024. "Optimization with constraint learning: A framework and survey," European Journal of Operational Research, Elsevier, vol. 314(1), pages 1-14.
    16. Xiongxiong You & Mengya Zhang & Diyin Tang & Zhanwen Niu, 2022. "An active learning method combining adaptive kriging and weighted penalty for structural reliability analysis," Journal of Risk and Reliability, , vol. 236(1), pages 160-172, February.
    17. Yang You & Guang Jin & Zhengqiang Pan & Rui Guo, 2021. "MP-CE Method for Space-Filling Design in Constrained Space with Multiple Types of Factors," Mathematics, MDPI, vol. 9(24), pages 1-13, December.
    18. Hao Chen & Yan Zhang & Xue Yang, 2021. "Uniform projection nested Latin hypercube designs," Statistical Papers, Springer, vol. 62(4), pages 2031-2045, August.
    19. Ray, Douglas & Ramirez-Marquez, Jose, 2020. "A framework for probabilistic model-based engineering and data synthesis," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    20. A. M. Elsawah & Kai-Tai Fang & Ping He & Hong Qin, 2021. "Sharp lower bounds of various uniformity criteria for constructing uniform designs," Statistical Papers, Springer, vol. 62(3), pages 1461-1482, June.

    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:ejores:v:284:y:2020:i:1:p:201-211. 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/eor .

    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.