Title:A hierarchical Bayesian approach to point source analysis in high-energy neutrino telescopes

Abstract:We propose a novel approach to the detection of point-like sources of high-energy neutrinos. Motivated by evidence for emerging sources in existing data, we focus on the characterisation and interpretation of these sources. The hierarchical Bayesian model is implemented in the Stan platform, enabling computation of the posterior distribution with Hamiltonian Monte Carlo. We simulate a population of weak neutrino sources detected by the IceCube experiment and use the resulting data set to demonstrate and validate our framework. We show that even for the challenging case of sources at the threshold of detection and using limited prior information, it is possible to correctly infer the source properties. Additionally, we demonstrate how modelling flexible connections between similar sources can be used to recover the contribution of sources that would not be detectable individually, going beyond what is possible with existing stacking methods.