Abstract
Astronomical radio-interferometric imaging typically uses published observations of standard flux-calibrator sources to calibrate the spectral response of the instrument. The spectra of standard flux-calibrator sources are usually provided as polynomial models of flux-density as a function of frequency. In this paper we show that there is significant covariance in these polynomial coefficients, and that failing to take this into account leads to significantly larger variance when sampling from the polynomial models. This paper presents polynomial models of calibrator sources that include the covariance structure of the coefficients which are computed using Markov Chain Monte Carlo sampling. In addition a data-free inference technique is presented that can be used to estimate the covariance structure from a simple polynomial model when access to the original data is not available. This data-free technique is compared with estimates of covariance calculated from original observation data. The data-free technique is shown to provide reasonable agreement with covariances calculated from source data. A python package is described that implements this inference, and a catalogue of common flux-calibrator models including covariance is provided. We suggest that when polynomial models of flux-calibrators are used as priors in a Bayesian context, then taking this correlation structure into account will lead to significantly reduced posterior variance.