Robust Calibration of Computer Models Based on Huber Loss

Recently, uncertainty quantification is getting more and more attention, especially for computer model calibration. However, most of the existing papers assume the errors follow a Gaussian or sub-Gaussian distribution, which would not be satisfied in practice. To overcome the limitation of the traditional calibration procedures, the authors develop a robust calibration procedure based on Huber loss, which can deal with responses with outliers and heavy-tail errors efficiently. The authors propose two different estimators of the calibration parameters based on ordinary least estimator and L2 calibration respectively, and investigate the nonasymptotic and asymptotic properties of the proposed estimators under certain conditions. Some numerical simulations and a real example are conducted, which verifies good performance of the proposed calibration procedure.

Automated summary

Recently, more attention has been given to uncertainty quantification in computer model calibration. However, most existing papers assume errors follow a Gaussian or sub-Gaussian distribution, which is not realistic. To overcome this limitation, the authors propose a robust calibration procedure based on Huber loss that can effectively deal with responses containing outliers and heavy-tail errors. Two different estimators of the calibration parameters are proposed using ordinary least squares and L2 calibration, respectively. Through numerical simulations and a real example, the authors verify the good performance of the proposed calibration procedure.