Signal reconstruction for fields using probabilistic forward modeling

Many inference tasks in observational astronomy take the form of reconstruction problems where the underlying quantities of interest are fields (functions of space, time and/or frequency) that have to be recovered from noisy and incomplete observational data. These problems are in general ill-posed, as many different field configurations may be consistent with the observed data, and therefore their solutions are inherently of probabilistic nature. Forward modeling, that is combining an accurate description of the observing instrument’s response to a field configuration occurring in nature with the rules of probability & information theory provides a robust and scalable framework to solve such problems. I will give a brief overview on the involved theoretical concepts and numerical techniques employed to do so in practice, and show a selection of applications to real-world astrophysical data-analysis problems ranging from results in the radio- up to the gamma-ray-regime.