Bayesian Projected Calibration of Computer Models

• Activity Number: 104 - Advances in Bayesian Analysis of Computer Models
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Fangzheng Xie* and Yanxun Xu
• Companies: Indiana University and Johns Hopkins University
• Keywords: Asymptotic normality; Computer experiment; L2-projection; Semiparametric efficiency; Uncertainty quantification

Abstract

We develop a Bayesian projected calibration method to address the problem of calibrating an imperfect computer model using observational data from an unknown complex physical system. The calibration parameter and the physical system are parameterized in an identifiable fashion via the L2-projection. The physical system is imposed a Gaussian process prior distribution, which naturally induces a prior distribution on the calibration parameter through the L2-projection constraint. The calibration parameter is estimated through its posterior distribution, serving as a natural and nonasymptotic approach for uncertainty quantification. We provide rigorous large sample justifications of the proposed approach by establishing the asymptotic normality of the posterior of the calibration parameter with the efficient covariance matrix. In addition to the theoretical analysis, two convenient computational algorithms based on stochastic approximation are designed with strong theoretical support. Simulation studies and the analyses of two real datasets show that the Bayesian projected calibration can accurately estimate the calibration parameters and calibrate the computer models well.