Simultaneous Determination of Tuning and Calibration Parameters for Computer Experiments

TLDR

Tuning and calibration are processes for improving the representativeness of a computer simulation code to a physical phenomenon. This article introduces a statistical methodology for simultaneously determining tuning and calibration parameters when both computer code and physical experiment data are available. The method sets tuning parameters by minimizing a discrepancy measure and estimates calibration parameters via a hierarchical Bayesian model that treats the output as a Gaussian stochastic process with hyper‑priors, with posterior samples obtained by MCMC. The methodology is benchmarked against an alternative approach in examples and applied to a biomechanical engineering case study. Supplemental materials, including software and a user manual, are available online and can be requested from the first author.

Abstract

Tuning and calibration are processes for improving the representativeness of a computer simulation code to a physical phenomenon. This article introduces a statistical methodology for simultaneously determining tuning and calibration parameters in settings where data are available from a computer code and the associated physical experiment. Tuning parameters are set by minimizing a discrepancy measure while the distribution of the calibration parameters are determined based on a hierarchical Bayesian model. The proposed Bayesian model views the output as a realization of a Gaussian stochastic process with hyper-priors. Draws from the resulting posterior distribution are obtained by the Markov chain Monte Carlo simulation. Our methodology is compared with an alternative approach in examples and is illustrated in a biomechanical engineering application. Supplemental materials, including the software and a user manual, are available online and can be requested from the first author.