Bayesian Adaptive Polynomial Chaos Expansions
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914121561145344 |
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| author | Rumsey, Kellin N. Francom, Devin Gibson, Graham C. Tucker, J. Derek Huerta, Gabriel |
| author_facet | Rumsey, Kellin N. Francom, Devin Gibson, Graham C. Tucker, J. Derek Huerta, Gabriel |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_25036 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bayesian Adaptive Polynomial Chaos Expansions Rumsey, Kellin N. Francom, Devin Gibson, Graham C. Tucker, J. Derek Huerta, Gabriel Methodology Machine Learning 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. |
| title | Bayesian Adaptive Polynomial Chaos Expansions |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2510.25036 |