From Localization to Discovery: Bayesian Ranking of Electromagnetic Counterparts to Gravitational-Wave Events

Abstract The robust association of electromagnetic candidates discovered during follow-up of gravitational-wave alerts is challenging, not only due to the large sky areas and broad distance uncertainties, but also due to the tens to hundreds of unrelated optical transients that are observed per event. We present a Bayesian ranking framework to identify candidate electromagnetic counterparts to gravitational-wave events without requiring photometric or spectroscopic classification. The method ranks transient candidates according to their consistency with the three-dimensional gravitational-wave localization and quantifies the significance of their associations. The framework combines morphology-aware host association, physically motivated offset priors, host-inferred luminosity distance posteriors, peculiar velocity corrections, and a treatment for missing or incorrectly associated host galaxies. We apply the method to two events, GW170817 and GW190425. For GW170817, the method ranks AT2017gfo first and correctly recovers NGC\,4993 as the host galaxy. We find a candidate p-value of 0.030 for AT2017gfo and find none of the 32 background transient sources reach the ranking value of AT2017gfo. For GW190425, the highest-ranked candidate has a p-value of $5.88\times 10^{-4}$ relative to 5101 background sources. Correcting for the multiple comparisons problem using the full set of 433 candidates lowers the significance of the top-ranked candidate to a p-value of 0.255. The framework is directly applicable to transient candidates with only sky location information, enables rapid prioritization for more efficient follow-up, and leads to more reliable counterpart identification in current and future observing runs.