Advances in Gravitational Wave Bayesian Inference Techniques of Pulsar Timing Arrays

The announcement in the summer of 2023 about the discovery of evidence for a gravitational wave background (GWB) using pulsar timing arrays (PTAs) has ignited both the PTA and the larger scientific community's interest in the experiment and the scientific implications of its findings. As a result, numerous scientific works have been published analyzing and further developing various aspects of the experiment, from performing tests of gravity to improving the efficiency of the current data analysis techniques. In this regard, we contribute to the recent advancements in the field of PTAs by presenting general, agnostic, per-frequency Bayesian searches for a low-frequency (red) noise process in these data. Our new methods involve the use of Jeffrey's-like and Lewandowski-Kurowicka-Joe (LKJ) multivariate priors which allow one to model all unique parameters of the global PTA-level red noise covariance matrix as a separate model parameter for which a marginalized posterior-probability distribution can be found via Gibbs or HMC sampling.