Fully-Bayesian stacking in the presence of confusion

Abstract: Multi-wavelength astronomical studies brings a wealth of science within reach. One way to achieve a cross-wavelength analysis is via `stacking', i.e. combining precise positional information from an image at one wavelength with data from one at another wavelength in order to extract source-flux distributions and other derived quantities. For the first time we extend stacking to include the effects of confusion. We develop our algorithm in a fully Bayesian framework and apply it to the Square Kilometre Array Design Study (SKADS) simulation in order to extract galaxy number counts. Previous studies have shown that recovered source counts are highly biased high when confusion is non-negligible. With this new method, source counts are returned correctly. We also describe a novel estimator for quantifying the impact of confusion on stacking analyses. This method is an essential step in exploiting scientific return for upcoming deep radio surveys, e.g. MIGHTEE on MeerKAT.