  Coincident multi-messenger observation of cosmic sources can offer numerous
benefits. One significant advantage is enhancing the detection significance of
separate detectors by correlating their data and assuming a joint emission. We
have formulated an approach for updating the Bayesian posterior probability of
an astrophysical origin, namely $p_{\rm astro}$, relying on multi-messenger
coincidences. We demonstrated this with candidate coincident gravitational
waves and high-energy neutrinos. Applying our method to the public data of
candidate coincident high-energy neutrinos with subthreshold gravitational-wave
triggers, we found that in the case of highly energetic neutrino coincidences,
$p_{\rm astro}$ can increase from approximately $\sim 0.1$ to $\sim 0.9$. This
marked improvement makes subthreshold detections much more confident.
