Bayesian inference for binary neutron star inspirals using a Hamiltonian Monte Carlo algorithm

The coalescence of binary neutron stars is one of the main sources of gravitational waves for ground-based gravitational wave detectors. As Bayesian inference for binary neutron stars is computationally expensive, more efficient and faster converging algorithms are always needed. In this work, we conduct a feasibility study using a Hamiltonian Monte Carlo algorithm (HMC). The HMC is a sampling algorithm that takes advantage of gradient information from the geometry of the parameter space to efficiently sample from the posterior distribution, allowing the algorithm to avoid the random-walk behavior commonly associated with stochastic samplers. As well as tuning the algorithm's free parameters specifically for gravitational wave astronomy, we introduce a method for approximating the gradients of the log-likelihood that reduces the runtime for a 1 0⁶ trajectory run from ten weeks, using numerical derivatives along the Hamiltonian trajectories, to one day, in the case of nonspinning neutron stars. Testing our algorithm against a set of neutron star binaries using a detector network composed of Advanced LIGO and Advanced Virgo at optimal design, we demonstrate that not only is our algorithm more efficient than a standard sampler, i.e., in general the HMC takes 1-7 seconds to produce a statistically independent sample, as compared to 77-227 seconds in previous studies, but a 1 0⁶ trajectory HMC produces an effective sample size on the order of 1 0⁴- 10⁵ statistically independent samples.