An approach to robust Bayesian regression in astronomy
File(s)
Published version
Author(s)
Martin, William
Mortlock, Daniel
Type
Journal Article
Abstract
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 data set, 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 data sets 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 data set without outliers, a worst-case inference using t-distributions would give unbiased results with
per cent increase in the reported parameter uncertainties. We also compare with existing analyses of real-world data sets, 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.
per cent increase in the reported parameter uncertainties. We also compare with existing analyses of real-world data sets, 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.
Date Issued
2025-08-13
Date Acceptance
2025-07-31
Citation
RAS Techniques and Instruments, 2025, 4
ISSN
2752-8200
Publisher
Oxford University Press
Journal / Book Title
RAS Techniques and Instruments
Volume
4
Copyright Statement
© 2025 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/),which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
License URL
Publication Status
Published
Article Number
rzaf035
Date Publish Online
2025-08-13