Statistical Methods for Model Validation under Uncertainty

*† Model uncertainties and limited experimental data in many engineering applications make the model validation essentially a statistical exercise. This paper investigates various statistical methods to quantitatively assess how close the prediction is to the observation. Interval-based hypothesis testing is found to be more practically useful than point null hypothesis testing. Both classical and Bayesian statistical techniques are implemented for this purpose. Also, a more direct approach is proposed by formulating model validation as a reliability estimation problem. The model reliability metric is extended for validating models with multivariate outputs. The proposed methods are illustrated and compared using numerical examples.