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Calibration of Computational Models With Categorical Parameters and Correlated Outputs via Bayesian Smoothing Spline ANOVA

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  • Curtis B. Storlie
  • William A. Lane
  • Emily M. Ryan
  • James R. Gattiker
  • David M. Higdon

Abstract

It has become commonplace to use complex computer models to predict outcomes in regions where data do not exist. Typically these models need to be calibrated and validated using some experimental data, which often consists of multiple correlated outcomes. In addition, some of the model parameters may be categorical in nature, such as a pointer variable to alternate models (or submodels) for some of the physics of the system. Here, we present a general approach for calibration in such situations where an emulator of the computationally demanding models and a discrepancy term from the model to reality are represented within a Bayesian smoothing spline (BSS) ANOVA framework. The BSS-ANOVA framework has several advantages over the traditional Gaussian process, including ease of handling categorical inputs and correlated outputs, and improved computational efficiency. Finally, this framework is then applied to the problem that motivated its design; a calibration of a computational fluid dynamics (CFD) model of a bubbling fluidized which is used as an absorber in a CO 2 capture system. Supplementary materials for this article are available online.

Suggested Citation

  • Curtis B. Storlie & William A. Lane & Emily M. Ryan & James R. Gattiker & David M. Higdon, 2015. "Calibration of Computational Models With Categorical Parameters and Correlated Outputs via Bayesian Smoothing Spline ANOVA," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 68-82, March.
    • Handle: RePEc:taf:jnlasa:v:110:y:2015:i:509:p:68-82
    DOI: 10.1080/01621459.2014.979993
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    References listed on IDEAS

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    1. Storlie, Curtis B. & Swiler, Laura P. & Helton, Jon C. & Sallaberry, Cedric J., 2009. "Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models," Reliability Engineering and System Safety, Elsevier, vol. 94(11), pages 1735-1763.
    2. Jeremy E. Oakley & Anthony O'Hagan, 2004. "Probabilistic sensitivity analysis of complex models: a Bayesian approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 751-769, August.
    3. Helton, J.C. & Johnson, J.D. & Sallaberry, C.J. & Storlie, C.B., 2006. "Survey of sampling-based methods for uncertainty and sensitivity analysis," Reliability Engineering and System Safety, Elsevier, vol. 91(10), pages 1175-1209.
    4. 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.
    5. Storlie, Curtis B. & Reich, Brian J. & Helton, Jon C. & Swiler, Laura P. & Sallaberry, Cedric J., 2013. "Analysis of computationally demanding models with continuous and categorical inputs," Reliability Engineering and System Safety, Elsevier, vol. 113(C), pages 30-41.
    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.
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    Cited by:

    1. 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.
    2. K. Sham Bhat & David S. Mebane & Priyadarshi Mahapatra & Curtis B. Storlie, 2017. "Upscaling Uncertainty with Dynamic Discrepancy for a Multi-Scale Carbon Capture System," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1453-1467, October.
    3. Chao Wang & Zhijie Xu & Canhai Lai & Greg Whyatt & Peter Marcy & Xin Sun, 2017. "Hierarchical calibration and validation for modeling bench‐scale solvent‐based carbon capture. Part 1: Non‐reactive physical mass transfer across the wetted wall column," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 7(4), pages 706-720, August.
    4. Raymond K. W. Wong & Curtis B. Storlie & Thomas C. M. Lee, 2017. "A frequentist approach to computer model calibration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 635-648, March.

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