IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i12p3959-3974.html
   My bibliography  Save this article

Calibration of computer models with multivariate output

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312002228
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.05.023?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. 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.
    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. Reichert, P. & White, G. & Bayarri, M.J. & Pitman, E.B., 2011. "Mechanism-based emulation of dynamic simulation models: Concept and application in hydrology," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1638-1655, April.
    4. Gramacy, Robert B & Lee, Herbert K. H, 2008. "Bayesian Treed Gaussian Process Models With an Application to Computer Modeling," Journal of the American Statistical Association, American Statistical Association, vol. 103(483), pages 1119-1130.
    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.
    6. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    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. 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.
    2. Perrin, G., 2020. "Adaptive calibration of a computer code with time-series output," Reliability Engineering and System Safety, Elsevier, vol. 196(C).
    3. 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.
    4. 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.
    5. Mohammadi, Hossein & Challenor, Peter & Goodfellow, Marc, 2019. "Emulating dynamic non-linear simulators using Gaussian processes," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 178-196.
    6. Bledar A. Konomi & Georgios Karagiannis & Kevin Lai & Guang Lin, 2017. "Bayesian Treed Calibration: An Application to Carbon Capture With AX Sorbent," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 37-53, January.
    7. Grant Hutchings & Bruno Sansó & James Gattiker & Devin Francom & Donatella Pasqualini, 2023. "Comparing emulation methods for a high‐resolution storm surge model," Environmetrics, John Wiley & Sons, Ltd., vol. 34(3), May.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Bozağaç, Doruk & Batmaz, İnci & Oğuztüzün, Halit, 2016. "Dynamic simulation metamodeling using MARS: A case of radar simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 69-86.
    15. 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.
    16. 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.
    17. Sun, Yang & Fang, Xiangzhong, 2024. "Efficient calibration of computer models with multivariate output," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    18. 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.
    19. 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.
    20. 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.

    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:csdana:v:56:y:2012:i:12:p:3959-3974. 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/csda .

    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.