Bayesian Validation of Computer Models

Abstract

Computer models are mathematical representations of real systems developed for understanding and investigating the systems. They are particularly useful when physical experiments are either cost- prohibitive or time-prohibitive. Before a computer model is used, it often must be validated by comparing the computer outputs with physical experiments. This article proposes a Bayesian approach to validating computer models that overcomes several difficulties of the frequentist approach proposed by Oberkampf and Barone. Kennedy and O’Hagan proposed a similar Bayesian approach. A major difference between their approach and ours is that theirs focuses on directly deriving the posterior of the true output, whereas our approach focuses on first deriving the posteriors of the computer model and model bias (difference between computer and true outputs) separately, then deriving the posterior of the true output. As a result, our approach provides a clear decomposition of the expected prediction error of the true output. This decomposition explains why and how combining computer outputs and physical experiments can provide more accurate prediction compared with using only computer outputs or only physical experiments. Two examples are used to illustrate our proposed approach and compare it with the approach Kennedy and O’Hagan. This article has supplementary material online.

Keywords:  :

• Bayesian
• Computer model
• Gaussian process
• Model bias
• Model validation
• Physical experiments