Selection of model discrepancy priors in Bayesian calibration

Abstract

In the Kennedy and O'Hagan framework for Bayesian calibration of physics models, selection of an appropriate prior form for the model discrepancy function is a challenging issue due to the lack of physics knowledge regarding model inadequacy. Aiming to address the uncertainty arising from the selection of a particular prior, this paper first conducts a study on possible formulations of the model discrepancy function. A first-order Taylor series expansion-based method is developed to investigate the potential redundancy caused by adding a discrepancy function to the original physics model. Further, we propose a three-step (calibration, validation, and combination) approach in order to inform the decision on the construction of model discrepancy priors. In the validation step, a reliability-based metric is used to evaluate posterior model predictions in the validation domain. The validation metric serves as a quantitative measure of how well the discrepancy formulation captures the missing physics in the model. In the combination step, the posterior distributions of model parameters and discrepancy corresponding to different priors are combined into a single distribution based on the probabilistic weights derived from the validation step. The combined distribution acknowledges the uncertainty in the prior formulation of model discrepancy function.