Uncertainty Quantification and Model Validation under Epistemic Uncertainty due to Sparse and Imprecise data

This paper develops a methodology for uncertainty quantification and model validation in the presence of epistemic uncertainty due to sparse and imprecise data. 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. 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 both point data and interval data, and the extent of which the data supports the model is directly quantified. 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 numerical examples from the Sandia Epistemic Uncertainty Workshop and a heat conduction problem.