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

TL;DR

This paper explores a Hamiltonian Monte Carlo algorithm for Bayesian inference in binary neutron star inspirals, significantly reducing computation time and increasing sampling efficiency compared to traditional methods.

Contribution

The study introduces a gradient approximation method for HMC that drastically cuts down runtime, enhancing Bayesian inference efficiency for gravitational wave data analysis.

Findings

HMC outperforms standard samplers in efficiency

Gradient approximation reduces runtime from ten weeks to one day

Effective sample size reaches 10^4 - 10^5 samples

Abstract

The coalescence of binary neutron stars are 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 behaviour 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 $10^6$ trajectory run from ten weeks, using numerical derivatives along the Hamiltonian trajectories, to one day, in the case of non-spinning 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, but a $10^6$ trajectory HMC produces an effective sample size on the order of $10^4 - 10^5$ statistically independent samples.