Bayesian calibration of inexact computer models

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 sub-optimally broad. There has been no generally accepted alternatives to date. This paper 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.