IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v35y2020i1d10.1007_s00180-019-00936-5.html
   My bibliography  Save this article

Adaptive method for indirect identification of the statistical properties of random fields in a Bayesian framework

Author

Listed:
  • Guillaume Perrin

    (CEA/DAM/DIF)

  • Christian Soize

    (Université Paris-Est)

Abstract

This work considers the challenging problem of identifying the statistical properties of random fields from indirect observations. To this end, a Bayesian approach is introduced, whose key step is the nonparametric approximation of the likelihood function from limited information. When the likelihood function is based on the evaluation of an expensive computer code, this work also proposes a method to select iteratively new design points to reduce the uncertainties on the results that are due to the approximation of the likelihood. Two applications are finally presented to illustrate the efficiency of the proposed procedure: a first one based on analytic data, and a second one dealing with the identification of the random elasticity field of an heterogeneous microstructure.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:35:y:2020:i:1:d:10.1007_s00180-019-00936-5
    DOI: 10.1007/s00180-019-00936-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-019-00936-5
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-019-00936-5?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. Higdon, Dave & Gattiker, James & Williams, Brian & Rightley, Maria, 2008. "Computer Model Calibration Using High-Dimensional Output," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 570-583, June.
    2. V. Roshan Joseph & Evren Gul & Shan Ba, 2015. "Maximum projection designs for computer experiments," Biometrika, Biometrika Trust, vol. 102(2), pages 371-380.
    3. Marc C. Kennedy & Anthony O'Hagan, 2001. "Bayesian calibration of computer models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(3), pages 425-464.
    4. Perrin, G. & Soize, C. & Ouhbi, N., 2018. "Data-driven kernel representations for sampling with an unknown block dependence structure under correlation constraints," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 139-154.
    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. Perrin, G., 2020. "Adaptive calibration of a computer code with time-series output," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    2. Drignei, Dorin, 2011. "A general statistical model for computer experiments with time series output," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 460-467.
    3. Hwang, Youngdeok & Kim, Hang J. & Chang, Won & Yeo, Kyongmin & Kim, Yongku, 2019. "Bayesian pollution source identification via an inverse physics model," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 76-92.
    4. Ioannis Andrianakis & Ian R Vernon & Nicky McCreesh & Trevelyan J McKinley & Jeremy E Oakley & Rebecca N Nsubuga & Michael Goldstein & Richard G White, 2015. "Bayesian History Matching of Complex Infectious Disease Models Using Emulation: A Tutorial and a Case Study on HIV in Uganda," PLOS Computational Biology, Public Library of Science, vol. 11(1), pages 1-18, January.
    5. Samantha M. Roth & Ben Seiyon Lee & Sanjib Sharma & Iman Hosseini‐Shakib & Klaus Keller & Murali Haran, 2023. "Flood hazard model calibration using multiresolution model output," Environmetrics, John Wiley & Sons, Ltd., vol. 34(2), March.
    6. White, Staci A. & Herbei, Radu, 2015. "A Monte Carlo approach to quantifying model error in Bayesian parameter estimation," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 168-181.
    7. Mevin Hooten & Christopher Wikle & Michael Schwob, 2020. "Statistical Implementations of Agent‐Based Demographic Models," International Statistical Review, International Statistical Institute, vol. 88(2), pages 441-461, August.
    8. Leatherman, Erin R. & Dean, Angela M. & Santner, Thomas J., 2017. "Designing combined physical and computer experiments to maximize prediction accuracy," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 346-362.
    9. Wu, Xu & Kozlowski, Tomasz & Meidani, Hadi, 2018. "Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data," Reliability Engineering and System Safety, Elsevier, vol. 169(C), pages 422-436.
    10. 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.
    11. Paulo, Rui & García-Donato, Gonzalo & Palomo, Jesús, 2012. "Calibration of computer models with multivariate output," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3959-3974.
    12. Jackson Samuel E. & Vernon Ian & Liu Junli & Lindsey Keith, 2020. "Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 19(2), pages 1-33, April.
    13. Stripling, H.F. & Adams, M.L. & McClarren, R.G. & Mallick, B.K., 2011. "The Method of Manufactured Universes for validating uncertainty quantification methods," Reliability Engineering and System Safety, Elsevier, vol. 96(9), pages 1242-1256.
    14. Matthew Plumlee, 2014. "Fast Prediction of Deterministic Functions Using Sparse Grid Experimental Designs," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1581-1591, December.
    15. SungKu Kang & Ran Jin & Xinwei Deng & Ron S. Kenett, 2023. "Challenges of modeling and analysis in cybermanufacturing: a review from a machine learning and computation perspective," Journal of Intelligent Manufacturing, Springer, vol. 34(2), pages 415-428, February.
    16. Manfren, Massimiliano & Aste, Niccolò & Moshksar, Reza, 2013. "Calibration and uncertainty analysis for computer models – A meta-model based approach for integrated building energy simulation," Applied Energy, Elsevier, vol. 103(C), pages 627-641.
    17. Daniel W. Gladish & Daniel E. Pagendam & Luk J. M. Peeters & Petra M. Kuhnert & Jai Vaze, 2018. "Emulation Engines: Choice and Quantification of Uncertainty for Complex Hydrological Models," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 23(1), pages 39-62, March.
    18. Chen, Yewen & Chang, Xiaohui & Luo, Fangzhi & Huang, Hui, 2023. "Additive dynamic models for correcting numerical model outputs," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    19. Kim, Wongon & Yoon, Heonjun & Lee, Guesuk & Kim, Taejin & Youn, Byeng D., 2020. "A new calibration metric that considers statistical correlation: Marginal Probability and Correlation Residuals," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    20. Bruno Sansó & Chris Forest, 2009. "Statistical calibration of climate system properties," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(4), pages 485-503, September.

    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:spr:compst:v:35:y:2020:i:1:d:10.1007_s00180-019-00936-5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.