Exploring the Capabilities of Gibbs Sampling in Pulsar Timing Arrays

We explore the use of Gibbs sampling in estimating the noise properties of individual pulsars and illustrate its effectiveness using the NANOGrav 11-year data set. We find that Gibbs sampling noise modeling (GM) is more efficient than the current standard Bayesian techniques (SM) for single pulsar analyses by yielding model parameter posteriors with average effective-sample-size ratio (GM/SM) of 6 across all parameters and pulsars. Furthermore, the output of GM contains posteriors for the Fourier coefficients that can be used to characterize the underlying red noise process of any pulsar's timing residuals, which are absent in current implementations of SM. Through simulations, we demonstrate the potential for such coefficients to measure the spatial cross-correlations between pulsar pairs produced by a gravitational wave background.