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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 characterization and interpretation of these sources rather than the rejection of the background-only hypothesis. The hierarchical Bayesian model is implemented in the Stan platform, enabling computation of the posterior distribution with a Hamiltonian Monte Carlo algorithm. 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 modeling flexible connections between similar sources can be used to recover the contribution of sources that would not be detectable individually. While a direct comparison of our method to existing approaches is challenged by the fundamental differences in frequentist and Bayesian frameworks, we draw parallels where possible. In particular, we highlight how including more complexity into the source modeling can increase the sensitivity to sources and their populations.