Population statistics of nanohertz gravitational wave sources

The recent detection of a nanohertz gravitational wave (GW) background by pulsar timing arrays (PTA) has sparked extensive discussions regarding its origin-whether it arises from astrophysical supermassive black hole binaries (SMBHBs) or from primordial GWs generated by various early universe processes. Previous studies suggest that a key discriminant between these two origins is the non-Gaussianity of the GW background prior to the detection of any individual source. In this Letter, we introduce a hierarchical Bayesian inference framework for inferring population properties of GW sources. This approach enables not only the measurement of evidence for different GW origins using PTA data but also the inference of population properties of astrophysical SMBHBs, by optimally leveraging non-Gaussian information in individual bright sources and in power spectrum fluctuations of the GW background.