Searches for Gravitational Waves from Supermassive Black Hole Binaries using Hamiltonian Monte Carlo

Pulsar timing arrays (PTAs) can detect low-frequency gravitational waves by looking for correlated deviations in pulse arrival times. Current Bayesian searches using PTAs are hampered by the large number of parameters needed to be sampled concurrently with Markov Chain Monte Carlo methods. As the data span increases, this problem will only worsen. An alternative Monte Carlo sampling method, Hamiltonian Monte Carlo (HMC), utilizes Hamiltonian dynamics to produce sample proposals informed by first-order gradients of the model likelihood. This in turn allows it to converge faster to high dimensional distributions. We implement HMC as an alternative sampling method in our search for an isotropic stochastic gravitational wave background, and present the accuracy and efficiency of the algorithm for this analysis. We also discuss implications of tailoring this algorithm to additional gravitational wave searches.