Towards optimal integration of multi-messenger information in a multi-trigger population study analysis

We present an algorithm for population parameter estimation that optimally incorporates multi-messenger information from triggered events. The assignment of suitable weights needs to take into account the background astrophysical distribution to be estimated. However, current methods lack suitable weight factors applied to the triggers besides trivial ones like a hard cutoff on flux. Our approach is an improvement in that the background distribution plays a direct role in the parameter estimation procedure. We use a likelihood-based method where the multi-messenger data is incorporated into a common likelihood before the population parameters are estimated. To demonstrate the method, we present preliminary results of this method as applied to simulated triggers that contain combined electromagnetic and gravitational radiation.