Model validation under epistemic uncertainty

This paper develops a methodology to assess the validity of computational models when some quantities may be affected by epistemic uncertainty. Three types of epistemic uncertainty regarding input random variables – interval data, sparse point data, and probability distributions with parameter uncertainty – are considered. When the model inputs are described using sparse point data and/or interval data, a likelihood-based methodology is used to represent these variables as probability distributions. Two approaches – a parametric approach and a non-parametric approach – are pursued for this purpose. While the parametric approach leads to a family of distributions due to distribution parameter uncertainty, the principles of conditional probability and total probability can be used to integrate the family of distributions into a single distribution. The non-parametric approach directly yields a single probability distribution. The probabilistic model predictions are compared against experimental observations, which may again be point data or interval data. A generalized likelihood function is constructed for Bayesian updating, and the posterior distribution of the model output is estimated. The Bayes factor metric is extended to assess the validity of the model under both aleatory and epistemic uncertainty and to estimate the confidence in the model prediction. The proposed method is illustrated using a numerical example.