# Prior-informed Uncertainty Modelling with Bayesian Polynomial Approximations

arXiv: https://arxiv.org/abs/2203.03508 · HTML: https://mlsanity.com/paper/2203.03508/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Mar 2022.

## Built on by (most cited first, 1 of 1)

- [New methods to compute the generalized chi-square distribution](https://mlsanity.com/paper/2404.05062/) (2024)

## Abstract (arXiv)

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.