Rational approximation and intrinsic Gaussian processes
Fuente:
arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866914574665515008 |
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| author | Beattie, Christopher Higdon, David House, Leanna Stakun-Pickering, Colby Clark, Jared |
| author_facet | Beattie, Christopher Higdon, David House, Leanna Stakun-Pickering, Colby Clark, Jared |
| contents | Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption has lagged behind traditional, covariance-based approaches, in part because the intrinsic formulation has lacked an accompanying toolkit of computational methods and dependence specifications that facilitate fitting and prediction. We develop here a systematic framework for modeling intrinsic GPs and introduce practical algorithms and dependence/variogram models for modeling, inference and computation that parallel those of traditional, stationary GPs. We explore a close connection between intrinsic GP models and rational approximation, which clarifies the underlying problem structure. Numerical examples illustrate how the new tools can be deployed in practice, highlighting the advantages of intrinsic-field modeling in terms of robustness, interpretability, and computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_17168 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rational approximation and intrinsic Gaussian processes Beattie, Christopher Higdon, David House, Leanna Stakun-Pickering, Colby Clark, Jared Numerical Analysis 60G15, 62M30, 62M20, 65C20 Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption has lagged behind traditional, covariance-based approaches, in part because the intrinsic formulation has lacked an accompanying toolkit of computational methods and dependence specifications that facilitate fitting and prediction. We develop here a systematic framework for modeling intrinsic GPs and introduce practical algorithms and dependence/variogram models for modeling, inference and computation that parallel those of traditional, stationary GPs. We explore a close connection between intrinsic GP models and rational approximation, which clarifies the underlying problem structure. Numerical examples illustrate how the new tools can be deployed in practice, highlighting the advantages of intrinsic-field modeling in terms of robustness, interpretability, and computational efficiency. |
| title | Rational approximation and intrinsic Gaussian processes |
| topic | Numerical Analysis 60G15, 62M30, 62M20, 65C20 |
| url | https://arxiv.org/abs/2605.17168 |