Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations
Abstract
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.
Cite
@article{arxiv.2203.03508,
title = {Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations},
author = {Chun Yui Wong and Pranay Seshadri and Andrew B. Duncan and Ashley Scillitoe and Geoffrey Parks},
journal= {arXiv preprint arXiv:2203.03508},
year = {2022}
}