Adjustments to Computer Models via Projected Kernel Calibration
Rui Tuo · SIAM/ASA Journal on Uncertainty Quantification · 2019
Identification of model parameters in computer simulations is an important topic in computer experiments. We propose a new method, called the projected kernel calibration method, to estimate these model parameters. The proposed method is proven to be asymptotic normal and semiparametric efficient. As a frequentist method, the proposed method is as efficient as the $L_2$ calibration method proposed by Tuo and Wu [ Ann. Statist., 43 (2015), pp. 2331--2352]. On the other hand, the proposed method has a natural Bayesian version, which the $L_2$ method does not have. This Bayesian version allows users to calculate the credible region of the calibration parameters without using a large sample approximation. We also show that the inconsistency problem of the calibration method proposed by Kennedy and O'Hagan [ J. R. Stat. Soc. Ser. B. Stat. Methodol., 63 (2001), pp. 425--464] can be rectified by a simple modification of the kernel matrix.