IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v159y2019icp93-118.html

M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions

Author

Listed:
  • Xie, Junfei
  • Wan, Yan
  • Mills, Kevin
  • Filliben, James J.
  • Lei, Yu
  • Lin, Zongli

Abstract

The evaluation of output performance statistics for systems of high-dimensional uncertain input parameters is crucial for robust real-time decision-making tasks of large-scale complex systems that operate in an uncertain environment. We develop a framework that integrates Multivariate Probabilistic Collocation Method (M-PCM) and Orthogonal Fractional Factorial Design (OFFD) to achieve an effective and scalable output statistics estimation. In this paper, we prove that when the degree of each uncertain parameter does not exceed 3 and under the widely held assumption for high-dimensional systems that the interactions among uncertain input parameters are negligible beyond certain order, the integrated M-PCM–OFFD method breaks the curse of dimensionality for correct output mean estimation by maximally reducing the number of simulations from 22m to 2log2(m+1) for a system mapping of m uncertain input parameters. In addition, the resulting reduced-size simulation set is the most robust to numerical truncation errors of simulators among all subsets of the same size in the M-PCM simulation set. The analysis also provides new insightful formal interpretations of the optimality of OFFDs.

Suggested Citation

  • Xie, Junfei & Wan, Yan & Mills, Kevin & Filliben, James J. & Lei, Yu & Lin, Zongli, 2019. "M-PCM-OFFD: An effective output statistics estimation method for systems of high dimensional uncertainties subject to low-order parameter interactions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 159(C), pages 93-118.
    • Handle: RePEc:eee:matcom:v:159:y:2019:i:c:p:93-118
    DOI: 10.1016/j.matcom.2018.10.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418302817
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.10.010?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Heiss, Florian & Winschel, Viktor, 2008. "Likelihood approximation by numerical integration on sparse grids," Journal of Econometrics, Elsevier, vol. 144(1), pages 62-80, May.
    2. Haritos, Nicholas, 1988. "Monte Carlo simulation of ocean beacon response to environmental loading," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 30(1), pages 87-92.
    3. Cheng, Haiyan & Sandu, Adrian, 2009. "Efficient uncertainty quantification with the polynomial chaos method for stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(11), pages 3278-3295.
    4. Peter W. Glynn & Donald L. Iglehart, 1989. "Importance Sampling for Stochastic Simulations," Management Science, INFORMS, vol. 35(11), pages 1367-1392, November.
    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. S. Bogan Aruoba & Pablo Cuba-Borda & Kenji Higa-Flores & Frank Schorfheide & Sergio Villalvazo, 2021. "Piecewise-Linear Approximations and Filtering for DSGE Models with Occasionally Binding Constraints," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 41, pages 96-120, July.
    2. Prusty, B Rajanarayan & Jena, Debashisha, 2017. "A critical review on probabilistic load flow studies in uncertainty constrained power systems with photovoltaic generation and a new approach," Renewable and Sustainable Energy Reviews, Elsevier, vol. 69(C), pages 1286-1302.
    3. Dassios, Angelos & Jang, Jiwook & Zhao, Hongbiao, 2015. "A risk model with renewal shot-noise Cox process," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 55-65.
    4. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
    5. Santiago Pereda-Fernández, 2021. "Copula-Based Random Effects Models for Clustered Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 575-588, March.
    6. Sandeep Juneja & Perwez Shahabuddin, 2001. "Fast Simulation of Markov Chains with Small Transition Probabilities," Management Science, INFORMS, vol. 47(4), pages 547-562, April.
    7. Michael Chen & Sanjay Mehrotra & Dávid Papp, 2015. "Scenario generation for stochastic optimization problems via the sparse grid method," Computational Optimization and Applications, Springer, vol. 62(3), pages 669-692, December.
    8. Kaynar, Bahar & Ridder, Ad, 2010. "The cross-entropy method with patching for rare-event simulation of large Markov chains," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1380-1397, December.
    9. Sarah Gelper & Ralf van der Lans & Gerrit van Bruggen, 2021. "Competition for Attention in Online Social Networks: Implications for Seeding Strategies," Management Science, INFORMS, vol. 67(2), pages 1026-1047, February.
    10. Hui Chen & Antoine Didisheim & Simon Scheidegger, 2021. "Deep Structural Estimation: With an Application to Option Pricing," Papers 2102.09209, arXiv.org.
    11. Tito Homem-de-Mello, 2007. "A Study on the Cross-Entropy Method for Rare-Event Probability Estimation," INFORMS Journal on Computing, INFORMS, vol. 19(3), pages 381-394, August.
    12. N-H Shih, 2005. "Estimating completion-time distribution in stochastic activity networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(6), pages 744-749, June.
    13. Eftekhari, Aryan & Juillard, Michel & Rion, Normann & Scheidegger, Simon, 2026. "Scalable global solution techniques for high-dimensional models in Dynare," Journal of Economic Dynamics and Control, Elsevier, vol. 182(C).
    14. Lütkebohmert, Eva & Sester, Julian, 2025. "Measuring name concentrations through deep learning," International Review of Financial Analysis, Elsevier, vol. 107(C).
    15. Helton, J.C. & Johnson, J.D. & Oberkampf, W.L., 2006. "Probability of loss of assured safety in temperature dependent systems with multiple weak and strong links," Reliability Engineering and System Safety, Elsevier, vol. 91(3), pages 320-348.
    16. Daniel Gerhard & Melanie Bremer & Christian Ritz, 2014. "Estimating marginal properties of quantitative real-time PCR data using nonlinear mixed models," Biometrics, The International Biometric Society, vol. 70(1), pages 247-254, March.
    17. T. P. I. Ahamed & V. S. Borkar & S. Juneja, 2006. "Adaptive Importance Sampling Technique for Markov Chains Using Stochastic Approximation," Operations Research, INFORMS, vol. 54(3), pages 489-504, June.
    18. Joel L. Horowitz & Lars Nesheim, 2018. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," CeMMAP working papers CWP29/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Christophe Gouel & Nicolas Legrand, 2025. "The role of storage in commodity markets: Indirect inference based on grain data," Quantitative Economics, Econometric Society, vol. 16(2), pages 705-747, May.
    20. Basrak, Bojan & Conroy, Michael & Olvera-Cravioto, Mariana & Palmowski, Zbigniew, 2022. "Importance sampling for maxima on trees," Stochastic Processes and their Applications, Elsevier, vol. 148(C), pages 139-179.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:matcom:v:159:y:2019:i:c:p:93-118. 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.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.