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Calibration for Computer Models with Time-Varying Parameter

Author

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  • Yang Sun

    (School of Mathematical Sciences, Peking University, Beijing 100871, China)

  • Xiangzhong Fang

    (School of Mathematical Sciences, Peking University, Beijing 100871, China)

Abstract

Traditional calibration methods often assume constant parameters that remain unchanged across input conditions, which can limit predictive accuracy when parameters actually vary. To address this issue, we propose a novel calibration framework with time-varying parameters. Building on the idea of profile least squares, we first apply local linear smoothing to estimate the discrepancy function between the computer model and the true process, and then use local linear smoothing again to obtain pointwise estimates of the functional calibration parameter. Through rigorous theoretical analysis, we establish the consistency and asymptotic normality of the proposed estimator. Simulation studies and an application to NASA’s OCO-2 mission demonstrate that the proposed method effectively captures parameter variation and improves predictive performance.

Suggested Citation

  • Yang Sun & Xiangzhong Fang, 2025. "Calibration for Computer Models with Time-Varying Parameter," Mathematics, MDPI, vol. 13(18), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:18:p:2969-:d:1749034
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    References listed on IDEAS

    as
    1. Yang Sun & Xiangzhong Fang, 2024. "A model calibration procedure for count response," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 53(12), pages 4272-4289, June.
    2. 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.
    3. Drignei, Dorin & Morris, Max D., 2006. "Empirical Bayesian Analysis for Computer Experiments Involving Finite-Difference Codes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1527-1536, December.
    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. Fangzheng Xie & Yanxun Xu, 2021. "Bayesian Projected Calibration of Computer Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1965-1982, October.
    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. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    Full references (including those not matched with items on IDEAS)

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