Energy-distance-minimizing support points and projected support points are shown to be robust Gaussian process emulation designs, with a theory linking them to maximum-entropy, minimax, and maximin designs.
Adjustments to Computer Models via Projected Kernel Calibration
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abstract
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 semi-parametric 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) 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) 425-464] can be rectified by a simple modification of the kernel matrix.
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Robust designs for Gaussian process emulation of computer experiments
Energy-distance-minimizing support points and projected support points are shown to be robust Gaussian process emulation designs, with a theory linking them to maximum-entropy, minimax, and maximin designs.