Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty

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  • Northwestern Polytechnical University
  • Universidad Tecnica Federico Santa Maria
  • University of Liverpool
  • Tongji University
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Original languageEnglish
Article number107219
JournalMechanical Systems and Signal Processing
Volume149
Early online date24 Aug 2020
Publication statusPublished - 15 Feb 2021

Abstract

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 corresponding 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.

Keywords

    Active learning, Bayesian inference, Epistemic uncertainty, Gaussian process regression, Imprecise probabilities, Probabilistic integration, Uncertainty quantification

ASJC Scopus subject areas

Cite this

Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty. / Wei, Pengfei; Liu, Fuchao; Valdebenito, Marcos et al.
In: Mechanical Systems and Signal Processing, Vol. 149, 107219, 15.02.2021.

Research output: Contribution to journalArticleResearchpeer review

Wei P, Liu F, Valdebenito M, Beer M. Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty. Mechanical Systems and Signal Processing. 2021 Feb 15;149:107219. Epub 2020 Aug 24. doi: 10.1016/j.ymssp.2020.107219
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title = "Bayesian probabilistic propagation of imprecise probabilities with large epistemic uncertainty",
abstract = "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 corresponding 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.",
keywords = "Active learning, Bayesian inference, Epistemic uncertainty, Gaussian process regression, Imprecise probabilities, Probabilistic integration, Uncertainty quantification",
author = "Pengfei Wei and Fuchao Liu and Marcos Valdebenito and Michael Beer",
note = "Funding Information: This work is supported by the National Natural Science Foundation of China (NSFC 51905430). The first author is also supported by the Alexander von Humboldt Foundation of Germany and the Top International University Visiting Program for Outstanding Young Scholars of Northwestern Polytechnical University. The third author would also like to acknowledge the support from ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271.",
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AU - Beer, Michael

N1 - Funding Information: This work is supported by the National Natural Science Foundation of China (NSFC 51905430). The first author is also supported by the Alexander von Humboldt Foundation of Germany and the Top International University Visiting Program for Outstanding Young Scholars of Northwestern Polytechnical University. The third author would also like to acknowledge the support from ANID (National Agency for Research and Development, Chile) under its program FONDECYT, grant number 1180271.

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