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

Abstract

Pulsar timing arrays (PTAs) detect low-frequency gravitational waves (GWs) bylooking for correlated deviations in pulse arrival times. Current Bayesiansearches use Markov Chain Monte Carlo (MCMC) methods, which struggle to samplethe large number of parameters needed to model the PTA and GW signals. As thedata span and number of pulsars increase, this problem will only worsen. Analternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC),utilizes Hamiltonian dynamics to produce sample proposals informed byfirst-order gradients of the model likelihood. This in turn allows it toconverge faster to high dimensional distributions. We implement HMC as analternative sampling method in our search for an isotropic stochastic GWbackground, and show that this method produces equivalent statistical resultsto similar analyses run with standard MCMC techniques, while requiring 100-200times fewer samples. We show that the speed of HMC sample generation scales as$\mathcal{O}(N_\mathrm{psr}^{5/4})$ where $N_\mathrm{psr}$ is the number ofpulsars, compared to $\mathcal{O}(N_\mathrm{psr}^2)$ for MCMC methods. Thesefactors offset the increased time required to generate a sample using HMC,demonstrating the value of adopting HMC techniques for PTAs.<br