A joint ranking statistic for multi-messenger astronomical searches with gravitational waves

Joint ranking statistics are used to distinguish real from random coincidences, ideally considering whether shared parameters are consistent with each other as well as whether the individual candidates are distinguishable from noise. We expand on previous works to include additional shared parameters, we use galaxy catalogues as priors for sky localization and distance, and avoid some approximations previously used. We develop methods to calculate this statistic both in low-latency using HEALPix sky maps, as well as with posterior samples. We show that these changes lead to a factor of one to two orders of magnitude improvement for GW170817-GRB 170817A depending on the method used, placing this significant event further into the foreground. We also examined the more tenuous joint candidate GBM-GW150914, which was largely penalized by these methods. Finally, we performed a simplistic simulation that argues these changes could better help distinguish between real and random coincidences in searches, although more realistic simulations are needed to confirm this.