A Modern Retrospective on Probabilistic Numerics
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866916533167456256 |
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| author | Oates, C. J. Sullivan, T. J. |
| author_facet | Oates, C. J. Sullivan, T. J. |
| contents | This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern formal treatment. We highlight in particular the parallel contributions of Sul'din and Larkin in the 1960s and how their pioneering early ideas have reached a degree of maturity in the intervening period, mediated by paradigms such as average-case analysis and information-based complexity. We provide a subjective assessment of the state of research in probabilistic numerics and highlight some difficulties to be addressed by future works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_04457 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Modern Retrospective on Probabilistic Numerics Oates, C. J. Sullivan, T. J. Numerical Analysis History and Overview Probability Machine Learning 62-03, 65-03, 01A60, 01A65, 01A67 This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern formal treatment. We highlight in particular the parallel contributions of Sul'din and Larkin in the 1960s and how their pioneering early ideas have reached a degree of maturity in the intervening period, mediated by paradigms such as average-case analysis and information-based complexity. We provide a subjective assessment of the state of research in probabilistic numerics and highlight some difficulties to be addressed by future works. |
| title | A Modern Retrospective on Probabilistic Numerics |
| topic | Numerical Analysis History and Overview Probability Machine Learning 62-03, 65-03, 01A60, 01A65, 01A67 |
| url | https://arxiv.org/abs/1901.04457 |