Efficient Gravitational Wave Searches with Pulsar Timing Arrays using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) aim to detect low-frequency gravitational waves (GWs) by looking for correlated deviations in pulse arrival times. Current Bayesian searches using Markov Chain Monte Carlo (MCMC) methods struggle to sample the large number of parameters needed to model PTA GW signals. This imposes limits on the complexity of models available for study and poses future problems with scalability as the data span increases. Hamiltonian Monte Carlo (HMC) is a Monte Carlo algorithm that utilizes Hamiltonian dynamics to make well-informed sample proposals via gradients of the model likelihood. This in turn allows it to converge faster to high dimensional and highly correlated distributions. We benchmark HMC as an alternative sampling method by performing a Bayesian analysis for the stochastic gravitational wave background, and compare the accuracy and efficiency of this method against similar analyses run with standard MCMC techniques. We also investigate the capability and performance of HMC when sampling PTA models containing both stochastic and deterministic signals.