Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations

Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of computational engineering applications. In this paper, we describ...

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Bibliographic Details
Published inarXiv.org
Main Authors Chun Yui Wong, Seshadri, Pranay, Duncan, Andrew B, Scillitoe, Ashley, Parks, Geoffrey
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 22.03.2022
Subjects
Approximation
Bayesian analysis
Polynomials
Structural hierarchy
Uncertainty
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Summary:Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of computational engineering applications. In this paper, we describe a Bayesian formulation of polynomial approximations capable of incorporating uncertainties in input data. Through different priors in a hierarchical structure, this permits us to incorporate expert knowledge on the inference task via different approaches. These include beliefs of sparsity in the model; approximate knowledge of the polynomial coefficients (e.g. through low-fidelity estimates) or output mean, and correlated models that share similar functional and/or physical behaviours. We show that through a Bayesian framework, such prior knowledge can be leveraged to produce orthogonal polynomial approximations with enhanced predictive accuracy.
ISSN:2331-8422