A Compound Poisson Generator Approach to Point-source Inference in Astrophysics

The identification and description of point sources is one the oldest problems in astronomy; yet, even today correct statistical treatment for remains field's hardest problems. For dim or crowded sources, likelihood based inference methods are required to estimate uncertainty on characteristics source population. In this work, a new parametric constructed problem using Compound Poisson Generator (CPG) functionals which incorporate instrumental effects from first principles. We demonstrate that CPG approach exhibits number advantages over Non-Poissonian Template Fitting (NPTF) - an existing method series test scenarios context X-ray astronomy. These demonstrations show effect point-spread function, effective area, choice point-source spatial distribution cannot, generally, be factorised as they NPTF, while construction validated these scenarios. Separately, examination diffuse-flux emission limit used most simple choices priors standard parameterisation population model can result unexpected biases: when comprising both diffuse component applied limit, nearly all observed flux will assigned either component. A parametrisation presented properly estimates uncertainties limit. priors, correctly identifies fraction cannot constrained by data.