We derive a Bayesian criterion for assessing whether signals observed in two separate data sets originate from a common source. The Bayes factor for a common versus unrelated origin of signals includes an overlap integral of the posterior distributions over the common-source parameters. Focusing on multimessenger gravitational-wave astronomy, we apply the method to the spatial and temporal association of independent gravitational-wave and electromagnetic (or neutrino) observations. As an example, we consider the coincidence between the recently discovered gravitational-wave signal GW170817 from a binary neutron star merger and the gamma-ray burst GRB 170817A: we find that the common-source model is enormously favored over a model describing them as unrelated signals.