Efficient Calibration for Imperfect Computer Models

TL;DR

This paper introduces the $L_2$ calibration method for imperfect computer models with stochastic data, demonstrating its efficiency and superiority over traditional methods through theoretical analysis and numerical experiments.

Contribution

The paper proposes a novel $L_2$ calibration approach that is semiparametrically efficient for models with stochastic physical data, extending previous Gaussian process-based methods.

Findings

$L_2$ calibration is semiparametrically efficient.

The method outperforms existing calibration techniques.

Theoretical analysis confirms consistency and efficiency.

Abstract

Many computer models contain unknown parameters which need to be estimated using physical observations. Kennedy and O'Hagan (2001) shows that the calibration method based on Gaussian process models proposed by Kennedy and O'Hagan (2001) may lead to unreasonable estimate for imperfect computer models. In this work, we extend their study to calibration problems with stochastic physical data. We propose a novel method, called the $L_2$ calibration, and show its semiparametric efficiency. The conventional method of the ordinary least squares is also studied. Theoretical analysis shows that it is consistent but not efficient. Numerical examples show that the proposed method outperforms the existing ones.