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Abstract

While there have been multiple reports of potential links between astrophysical sources and high-energy neutrinos, definitively identifying these sources remains challenging. No single result has surpassed the significance threshold for discovery, and the theoretical interpretation of these observations has revealed new questions for the bigger picture of neutrino astrophysics. In response to these difficulties, we propose a novel approach that combines state-of-the-art methods with the wealth of information from multi-messenger observations and theoretical models. Our physics-first strategy utilizes advanced techniques such as Hamiltonian Monte Carlo and hierarchical modelling to navigate the high-dimensional space of parameters and uncertainties in this complex setting. Implementing these methods within a Bayesian framework offers a unique perspective on source discovery while enabling us to avoid pitfalls associated with trial factors. Furthermore, considering source populations provides additional constraints from observations and uncovers further implications from a broader perspective, making the most of the existing high-energy neutrino data. We demonstrate the impact of these methods through application to simulated data, considering relevant multi-messenger scenarios for sources and their populations. Our approach complements existing techniques while offering increased sensitivity and interpretability in the context of investigating specific physical models, potentially accelerating decisive discoveries.