Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 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 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.

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The categories of this paper are: hep-ph
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph