A Frequentist Approach to Computer Model Calibration

TL;DR

This paper introduces a new frequentist framework for calibrating computer models that addresses identifiability issues and provides efficient estimation and uncertainty quantification methods, demonstrated through simulations and fluid dynamics applications.

Contribution

It proposes a novel identifiable parametrization for computer model calibration within a frequentist semi-parametric framework, enabling reliable estimation and uncertainty quantification.

Findings

Estimation procedure achieves fast convergence rates.

Bootstrapping provides valid confidence regions.

Method performs well in simulations and fluid dynamics application.

Abstract

This paper considers the computer model calibration problem and provides a general frequentist solution. Under the proposed framework, the data model is semi-parametric with a nonparametric discrepancy function which accounts for any discrepancy between the physical reality and the computer model. In an attempt to solve a fundamentally important (but often ignored) identifiability issue between the computer model parameters and the discrepancy function, this paper proposes a new and identifiable parametrization of the calibration problem. It also develops a two-step procedure for estimating all the relevant quantities under the new parameterization. This estimation procedure is shown to enjoy excellent rates of convergence and can be straightforwardly implemented with existing software. For uncertainty quantification, bootstrapping is adopted to construct confidence regions for the quantities of interest. The practical performance of the proposed methodology is illustrated through simulation examples and an application to a computational fluid dynamics model.