Geoff G. Murphy, Philip Bull, Mario G. Santos, Zheng Zhang, Steven Cunnington

Foreground removal remains an ongoing challenge in radio cosmology, and increasingly sensitive experiments necessitate more robust analysis techniques. In this work, we model simulated data from a single-dish intensity mapping experiment, and use the Gibbs sampling and Gaussian constrained realisation (GCR) techniques to draw samples from the posterior probability distribution of the model parameters. This allows for a separation of the foregrounds and 21 cm signal at the map level, as well as recovery of the 1-dimensional HI power spectrum to within statistical uncertainties. Despite the model consisting of over 2 million free parameters in the example presented here, these methods allow us to sample from the Bayesian posterior at a rate of $<30$ seconds per iteration. This framework is also resilient to frequency channel flagging (e.g. due to RFI excision), with the GCR steps effectively in-painting the missing data with statistically-consistent model realisations. The power spectrum is recovered accurately in the presence of strong foreground contamination and RFI flagging -- the estimate falling within $2σ$ of the true model in our example, similar to the commonly-used transfer function correction method. Statistical realisations of foreground and HI maps are also recovered, with associated uncertainties available from the full joint posterior distribution of all parameters.