Bayesian Adaptive Polynomial Chaos Expansions

TL;DR

This paper introduces a fully Bayesian adaptive polynomial chaos expansion method with an R implementation, enhancing uncertainty quantification tasks through data-driven interaction selection and tailored priors.

Contribution

It presents a novel Bayesian PCE approach with an innovative proposal distribution and g-prior, filling a gap in Bayesian PCE methods and providing an accessible R package.

Findings

Competitive performance in surrogate modeling

Effective for global sensitivity analysis

Applicable to ordinal regression tasks

Abstract

Polynomial chaos expansions (PCE) are widely used for uncertainty quantification (UQ) tasks, particularly in the applied mathematics community. However, PCE has received comparatively less attention in the statistics literature, and fully Bayesian formulations remain rare, especially with implementations in R. Motivated by the success of adaptive Bayesian machine learning models such as BART, BASS, and BPPR, we develop a new fully Bayesian adaptive PCE method with an efficient and accessible R implementation: khaos. Our approach includes a novel proposal distribution that enables data-driven interaction selection, and supports a modified g-prior tailored to PCE structure. Through simulation studies and real-world UQ applications, we demonstrate that Bayesian adaptive PCE provides competitive performance for surrogate modeling, global sensitivity analysis, and ordinal regression tasks.