An approach to robust Bayesian regression in astronomy

TL;DR

This paper introduces a robust Bayesian linear regression method using Student's t-distributions, effectively handling outliers and model mis-specification in astronomical data analysis, with validated performance on simulated and real datasets.

Contribution

Develops a generic Bayesian regression approach based on Student's t-distributions that is robust to outliers and noise model mis-specification, and provides a Python implementation.

Findings

Less biased parameter constraints compared to normal distribution models.

Unbiased results with minimal uncertainty increase for outlier-free data.

Qualitative differences in results when compared to traditional methods.

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 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.