From global fit to catalog: solving the label switching problem

In the next-generation space-based gravitational-wave detector, LISA, gravitational-wave signals from millions of ultra-compact binaries exist in the detector at any moment during the mission's lifetime. Detecting tens of thousands of these sources is made possible by a simultaneous fit of all sources in the detector data stream, sometimes called the ``global fit.'' However, turning a global fit posterior into a catalog of astrophysical sources presents several nontrivial challenges. First, the global fit uses a trans-dimensional sampling algorithm that includes sources in some iterations which are not present in others. Further, parameter posteriors may be multi-modal. Finally, swapping positions of sources in the posterior chain doesn't change the likelihood, resulting in the label switching problem. Here we present a novel method to label individual sources from a posterior chain.