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Calibration of computer models with multivariate output

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  • Paulo, Rui
  • García-Donato, Gonzalo
  • Palomo, Jesús

Abstract

The problem of calibrating computer models that produce multivariate output is considered, with a particular emphasis on the situation where the model is computationally demanding. The proposed methodology builds on Gaussian process-based response-surface approximations to each of the components of the output of the computer model to produce an emulator of the multivariate output. This emulator is then combined in a statistical model involving field observations, which is then used to produce calibration strategies for the parameters of the computer model. The results of applying this methodology to a simulated example and to a real application are presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:12:p:3959-3974
    DOI: 10.1016/j.csda.2012.05.023
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    References listed on IDEAS

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    1. Gramacy, Robert B. & Lee, Herbert K.H., 2008. "Gaussian processes and limiting linear models," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 123-136, September.
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    5. Alan Gelfand & Alexandra Schmidt & Sudipto Banerjee & C. Sirmans, 2004. "Nonstationary multivariate process modeling through spatially varying coregionalization," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 263-312, December.
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    7. Bayarri, M. J. & Berger, James O. & Kennedy, Marc C. & Kottas, Athanasios & Paulo, Rui & Sacks, Jerry & Cafeo, John A. & Lin, Chin-Hsu & Tu, Jian, 2009. "Predicting Vehicle Crashworthiness: Validation of Computer Models for Functional and Hierarchical Data," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 929-943.
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    Cited by:

    1. François Bachoc & Emile Contal & Hassan Maatouk & Didier Rullière, 2017. "Gaussian processes for computer experiments," Post-Print hal-01665936, HAL.
    2. Chevalier, Clément & Picheny, Victor & Ginsbourger, David, 2014. "KrigInv: An efficient and user-friendly implementation of batch-sequential inversion strategies based on kriging," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1021-1034.
    3. Bachoc, François & Lagnoux, Agnès & Nguyen, Thi Mong Ngoc, 2017. "Cross-validation estimation of covariance parameters under fixed-domain asymptotics," Journal of Multivariate Analysis, Elsevier, vol. 160(C), pages 42-67.
    4. Bachoc, François, 2013. "Cross Validation and Maximum Likelihood estimations of hyper-parameters of Gaussian processes with model misspecification," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 55-69.
    5. Lamperti, Francesco, 2018. "An information theoretic criterion for empirical validation of simulation models," Econometrics and Statistics, Elsevier, vol. 5(C), pages 83-106.
    6. Bachoc, François, 2014. "Asymptotic analysis of the role of spatial sampling for covariance parameter estimation of Gaussian processes," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 1-35.

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