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Abstract:
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We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical system are parametrized in an identifiable fashion via L2-projection. The physical process is imposed a Gaussian process prior, which naturally induces a prior on the calibration parameter through the L2-projection constraint. The calibration parameter is estimated through its posterior distribution, which provides a natural way for uncertainty quantification. We provide rigorous large-sample justifications of the proposed approach by establishing the asymptotic normality of the posterior of the calibration parameter with the efficient covariance matrix. In addition, two efficient computational algorithms based on stochastic approximation are designed with strong theoretical support. Through extensive simulation studies and two real-world datasets analyses, we show that Bayesian projected calibration can accurately estimate the calibration parameters, calibrate the computer models, and compare favorably to alternative approaches.
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