Towards reliable uncertainties in IR interferometry: the bootstrap for correlated statistical and systematic errors

• Published in: Monthly notices of the Royal Astronomical Society Vol. 484; no. 2; pp. 2656 - 2673
• Main Authors: Lachaume, Régis, Rabus, Markus, Jordán, Andrés, Brahm, Rafael, Boyajian, Tabetha, von Braun, Kaspar, Berger, Jean-Philippe
• Format: Journal Article
• Language: English
• Published: Oxford University Press (OUP): Policy P - Oxford Open Option A 01.04.2019
• Subjects: Astrophysics; Sciences of the Universe; stars: fundamental parameters; methods: data analysis; techniques: interferometric; Astrophysics - Instrumentation and Methods for Astrophysics
• ISSN: 0035-8711; 1365-2966
• DOI: 10.1093/mnras/stz114

We propose a method to overcome the usual limitation of current data processing techniques in optical and infrared long-baseline interferometry: most reduction pipelines assume uncorrelated statistical errors and ignore systematics. We use the bootstrap method to sample the multivariate probability density function of the interferometric observables. It allows us to determine the correlations between statistical error terms and their deviation from a Gaussian distribution. In addition, we introduce systematics as an additional, highly correlated error term whose magnitude is chosen to fit the data dispersion. We have applied the method to obtain accurate measurements of stellar diameters for underresolved stars, i.e. smaller than the angular resolution of the interferometer. We show that taking correlations and systematics has a significant impact on both the diameter estimate and its uncertainty. The robustness of our diameter determination comes at a price: we obtain 4 times larger uncertainties, of a few per cent for most stars in our sample.