# Towards reliable uncertainties in IR interferometry: The bootstrap for correlated statistical & systematic errors

## TL;DR

This paper introduces a bootstrap-based method to accurately estimate uncertainties in IR interferometry by accounting for correlated errors and systematics, improving measurement reliability for stellar diameters.

## Contribution

The authors develop a bootstrap approach that incorporates correlated statistical errors and systematics, enhancing the accuracy of interferometric measurements.

## Key findings

- Correlations and systematics significantly affect diameter estimates.
- Including these factors increases uncertainties by a factor of four.
- The method provides more reliable error estimates for under-resolved stars.

## Abstract

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 under-resolved 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 percent for most stars in our sample.