2024/11/04 by Martin, William, Mortlock, Daniel J. · 2 citations
#FOS: Computer and information sciences #FOS: Physical sciences #Instrumentation and Methods for Astrophysics (astro-ph.IM) #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2411.02380
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.