Bayesian Projected Calibration of Computer Models

@article{Xie2018BayesianPC,
  title={Bayesian Projected Calibration of Computer Models},
  author={Fangzheng Xie and Yanxun Xu},
  journal={Journal of the American Statistical Association},
  year={2018},
  volume={116},
  pages={1965 - 1982}
}
Abstract We develop a Bayesian approach called the Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L 2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the L 2… 

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References

SHOWING 1-10 OF 59 REFERENCES

An improved approach to Bayesian computer model calibration and prediction

The S-GaSP model is proposed, a novel stochastic process for calibration and prediction that not only provides a general framework for calibration, but also enables the computer model to predict well regardless of the discrepancy function.

Adjustments to Computer Models via Projected Kernel Calibration

  • Rui Tuo
  • Computer Science
    SIAM/ASA J. Uncertain. Quantification
  • 2019
A new method, called the projected kernel calibration method, to estimate model parameters, which is proven to be asymptotic normal and semi-parametric efficient and has a natural Bayesian version, which the proposed method does not have.

Bayesian calibration of computer models

A Bayesian calibration technique which improves on this traditional approach in two respects and attempts to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best‐fitting parameter values is presented.

Bayesian Calibration of Inexact Computer Models

ABSTRACT Bayesian calibration is used to study computer models in the presence of both a calibration parameter and model bias. The parameter in the predominant methodology is left undefined. This

A Theoretical Framework for Calibration in Computer Models: Parametrization, Estimation and Convergence Properties

It is shown that a simplified version of the original KO method leads to asymptotically $L_2$-inconsistent calibration, which can be remedied by modifying the original estimation procedure.

Combining Field Data and Computer Simulations for Calibration and Prediction

A statistical approach for characterizing uncertainty in predictions that are made with the aid of a computer simulation model that uses a Bayesian formulation and relies on Gaussian process models to model unknown functions of the model inputs.

A frequentist approach to computer model calibration

An attempt to solve a fundamentally important identifiability issue between the computer model parameters and the discrepancy function, the paper proposes a new and identifiable parameterization of the calibration problem and develops a two-step procedure for estimating all the relevant quantities under the new parameterization.

Efficient Calibration for Imperfect Computer Models

This work proposes a novel method, called the $L_2$ calibration, and shows its semiparametric efficiency, and the conventional method of the ordinary least squares is studied.

Robust Gaussian stochastic process emulation

We consider estimation of the parameters of a Gaussian Stochastic Process (GaSP), in the context of emulation (approximation) of computer models for which the outcomes are real-valued scalars. The

A Theoretical Framework of the Scaled Gaussian Stochastic Process in Prediction and Calibration

The explicit connection between Gaussian stochastic process (GaSP) and S-GaSP is established through the orthogonal series representation, and the predictive mean estimator in the S- GaSP calibration model converges to the reality at the same rate as the GaSP with a suitable choice of the regularization and scaling parameters.
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