An approach to robust Bayesian regression in astronomy
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911132475719680 |
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| author | Martin, William Mortlock, Daniel J. |
| author_facet | Martin, William Mortlock, Daniel J. |
| contents | Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms which are sensitive to arbitrary thresholds (e.g. sigma-clipping). For any given dataset, the optimal approach will be to develop a bespoke statistical model of the data generation and measurement processes, but these come with a development cost; there is hence utility in having generic modelling approaches that are both principled and robust to model mis-specification. Here we develop and implement a generic Bayesian approach to linear regression, based on Student's t-distributions, that is robust to outliers and mis-specification of the noise model. Our method is validated using simulated datasets with various degrees of model mis-specification; the derived constraints are shown to be systematically less biased than those from a similar model using normal distributions. We demonstrate that, for a dataset without outliers, a worst-case inference using t-distributions would give unbiased results with $\lesssim\!10$ per cent increase in the reported parameter uncertainties. We also compare with existing analyses of real-world datasets, finding qualitatively different results where normal distributions have been used and agreement where more robust methods have been applied. A Python implementation of this model, t-cup, is made available for others to use. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_02380 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An approach to robust Bayesian regression in astronomy Martin, William Mortlock, Daniel J. Instrumentation and Methods for Astrophysics Methodology Model mis-specification (e.g. the presence of outliers) is commonly encountered in astronomical analyses, often requiring the use of ad hoc algorithms which are sensitive to arbitrary thresholds (e.g. sigma-clipping). For any given dataset, the optimal approach will be to develop a bespoke statistical model of the data generation and measurement processes, but these come with a development cost; there is hence utility in having generic modelling approaches that are both principled and robust to model mis-specification. Here we develop and implement a generic Bayesian approach to linear regression, based on Student's t-distributions, that is robust to outliers and mis-specification of the noise model. Our method is validated using simulated datasets with various degrees of model mis-specification; the derived constraints are shown to be systematically less biased than those from a similar model using normal distributions. We demonstrate that, for a dataset without outliers, a worst-case inference using t-distributions would give unbiased results with $\lesssim\!10$ per cent increase in the reported parameter uncertainties. We also compare with existing analyses of real-world datasets, finding qualitatively different results where normal distributions have been used and agreement where more robust methods have been applied. A Python implementation of this model, t-cup, is made available for others to use. |
| title | An approach to robust Bayesian regression in astronomy |
| topic | Instrumentation and Methods for Astrophysics Methodology |
| url | https://arxiv.org/abs/2411.02380 |