Bayesian Model Selection for the Validation of Computer Codes

Complex physical systems are increasingly modeled by computer codes which aim at predicting the reality as accurately as possible. During the last decade, code validation has benefited from a large interest within the scientific community because of the requirement to assess the uncertainty affecting the code outputs. Inspiring from past contributions to this task, a testing procedure is proposed in this paper to decide either a pure code prediction or a discrepancy‐corrected one should be used to provide the best approximation of the physical system. In a particular case where the computer code depends on uncertain parameters, this problem of model selection can be carried out in a Bayesian setting. It requires the specification of proper prior distributions that are well known as having a strong impact on the results. Another way consists in specifying non‐informative priors. However, they are sometimes improper, which is a major barrier for computing the Bayes factor. A way to overcome this issue is to use the so‐called intrinsic Bayes factor (IBF) in order to replace the ill‐defined Bayes factor when improper priors are used. For computer codes which depend linearly on their parameters, the computation of the IBF is made easier, thanks to some explicit marginalization. In the paper, we present a special case where the IBF is equal to the standard Bayes factor when the right‐Haar prior is specified on the code parameters and the scale of the code discrepancy. On simulated data, the IBF has been computed for several prior distributions. A confounding effect between the code discrepancy and the linear code is pointed out. Finally, the IBF is computed for an industrial computer code used for monitoring power plant production.