A Compound Poisson Generator approach to Point-Source Inference in Astrophysics

TL;DR

This paper introduces a new Compound Poisson Generator (CPG) likelihood method for point-source inference in astrophysics, demonstrating advantages over existing methods and addressing prior biases in flux estimation.

Contribution

The paper develops a novel CPG-based likelihood approach that incorporates instrumental effects from first principles, improving point-source inference accuracy over existing methods like NPTF.

Findings

CPG outperforms NPTF in test scenarios with complex instrumental effects.

The new prior parametrization reduces biases in flux fraction estimation.

CPG correctly identifies unconstrainted flux fractions in the diffuse limit.

Abstract

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