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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. V. Roshan Joseph & Evren Gul & Shan Ba, 2015. "Maximum projection designs for computer experiments," Biometrika, Biometrika Trust, vol. 102(2), pages 371-380.
    4. 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.
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