After the discovery of the gravitational waves and the observation of neutrinos of cosmic origin, we have entered a new and exciting era where cosmic rays, neutrinos, photons and gravitational waves will be used simultaneously to study the highest energy phenomena in the Universe. Here we present a fully Bayesian approach to the challenge of combining and comparing the wealth of measurements from existing and upcoming experimental facilities. We discuss the procedure from a theoretical point of view and using simulations, we also demonstrate the feasibility of the method by incorporating the use of information provided by different theoretical models and different experimental measurements.