Bayesian Calibration of Inexact Computer Models

ABSTRACT

Bayesian calibration is used to study computer models in the presence of both a calibration parameter and model bias. The parameter in the predominant methodology is left undefined. This results in an issue, where the posterior of the parameter is suboptimally broad. There has been no generally accepted alternatives to date. This article proposes using Bayesian calibration, where the prior distribution on the bias is orthogonal to the gradient of the computer model. Problems associated with Bayesian calibration are shown to be mitigated through analytic results in addition to examples. Supplementary materials for this article are available online.

Keywords:

• Calibration
• Computer experiments
• Deterministic models
• Gaussian processes
• Identifiability
• Kriging
• Model inadequacy
• Orthogonal processes
• Uncertainty quantification

Supplementary Materials

The supplementary materials contain the MATLAB code used to generate the figures.

Acknowledgment

The authors would like to acknowledge the support from the National Science Foundation (CMMI-1266025); thank Andrew R. Ednie and Eric S. Bennett for sharing the heart cell dataset; and thank Daniel W. Apley, Robert B. Gramacy, David M. Higdon, V. Roshan Joseph, Barry L. Nelson, Rui Tuo, C. F. Jeff Wu, two anonymous reviewers and an anonymous associate editor for their comments toward improving this work.