A semi-analytic approach to gravitational wave background detection in pulsar timing arrays

I present the most recent advances in gravitational wave background (GWB) detection techniques of pulsar timing arrays (PTAs) using Fourier coefficients. Fourier coefficients are analytically marginalized in current Bayesian frameworks. Even though such marginalization results in a flexible likelihood function to fit any desired model to, the burden of such fit lies heavily on parallel tempering Monte-Carlo simulations whose performance scales poorly with increase in the baseline and the number of pulsars considered.

We investigate the use of semi-analytical approaches to Bayesian inferences of pulsar timing arrays using Fourier coefficients which avoid the poor scaling of the current techniques and provide an extremely fast alternative to perform GWB inferences. In particular, the use of Gibbs-sampling in single and multi-pulsar detection analyses is discussed.