Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty

Efficient propagation of imprecise probability models is one of the most important, yet challenging tasks, for uncertainty quantification in many areas and engineering practices, especially when the involved epistemic uncertainty is substantial due to the extreme lack of information. In this work, a new methodology framework, named as Non-intrusive Imprecise Probabilistic Integration (NIPI), is developed for achieving the above target, and specifically, the distributional probability-box model and the estimation of the corre-sponding probabilistic moments of model responses are of concern. The NIPI owns two attractive characters. First, the spatial correlation information in both aleatory and epistemic uncertainty spaces, revealed by the Gaussian Process Regression (GPR) model, is fully integrated for deriving NIPI estimations of high accuracy by using Bayesian inference. Second, the numerical errors are regarded as a kind of epistemic uncertainty, by analytically propagating them, the posterior variances are derived for indicating the errors of the NIPI estimations. Further, an adaptive experiment design strategy is developed to accelerate the convergence of NIPI by making full use of the information of contribution to posterior variance revealed by the GPR model. The performance of the proposed methods is demonstrated by numerical and engineering examples. (c) 2020 Elsevier Ltd. All rights reserved.

Automated summary

Efficient propagation of imprecise probability models is achieved through the development of a new methodology framework named NIPI, focusing on the distributional probability-box model and the estimation of probabilistic moments of model responses. By integrating spatial correlation information revealed by the GPR model, NIPI estimations with high accuracy are derived, and numerical errors are treated as epistemic uncertainty.