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Quantification of the significance of a candidate multi-messenger detectionof cosmic events is an emerging need in the astrophysics and astronomycommunities. In this paper we show that a model-independent optimal search doesnot exist, and we present a general Bayesian method for the optimalmodel-dependent search, which is scalable to any number and any kind ofmessengers, and applicable to any model. In the end, we demonstrate it throughan example for a joint gravitational wave, high-energy neutrino, shortgamma-ray burst event search; which has not been examined heretofore.

How to search for multiple messengers -- a general framework beyond two messengers