The Bayesian Global Sky Model (B-GSM): validation of a data-driven Bayesian simultaneous component separation and calibration algorithm for EoR foreground modelling

ABSTRACT We introduce the Bayesian Global Sky Model (B-GSM), a novel data-driven Bayesian approach to modelling radio foregrounds at frequencies <400 MHz. B-GSM aims to address the limitations of previous models by incorporating robust error quantification and calibration. Using nested sampling, we compute Bayesian evidence and posterior distributions for the spectra and spatial amplitudes of emission components. Bayesian model comparison is used to determine the optimal number of emission components and their spectral parametrization. Posterior sky predictions are conditioned on both diffuse emission and absolute temperature data sets, enabling simultaneous component separation and calibration. B-GSM is validated against a synthetic data set that mimics the partial sky coverage, thermal noise, and calibration uncertainties present in real observations. B-GSM successfully identifies a model parametrization with two emission components featuring curved power-law spectra. The Bayesian evidence strongly rejects incorrect models, confirming B-GSM’s capability to use the data set to determine model parametrization. The posterior sky predictions agree with the true sky within statistical uncertainty. The root-mean-square residuals between the true and posterior predictions for the sky temperature as a function of local sidereal time are significantly reduced, compared to the uncalibrated data set. This indicates that B-GSMs posterior sky predictions are accurately calibrated to the independent absolute temperature data set. We note that the spectral parameters and component amplitudes exhibit sensitivity to prior assumptions, however the posterior sky predictions remain robust across a selection of different priors. This paper is focused on validation of B-GSM; a later paper will present results for real data and introduce the low-frequency sky model.