Relative Binning and Fast Likelihood Evaluation for Gravitational Wave Parameter Estimation

We present a method to accelerate the evaluation of the likelihood in gravitational wave parameter estimation. Parameter estimation codes compute likelihoods of similar waveforms, whose phases and amplitudes differ smoothly with frequency. We exploit this by precomputing frequency-binned overlaps of the best-fit waveform with the data. We show how these summary data can be used to approximate the likelihood of any waveform that is sufficiently probable within the required accuracy. We demonstrate that $\simeq 60$ bins suffice to accurately compute likelihoods for strain data at a sampling rate of $4096\,$Hz and duration of $T=2048\,$s around the binary neutron star merger GW170817. Relative binning speeds up parameter estimation for frequency domain waveform models by a factor of $\sim 10^4$ compared to naive matched filtering and $\sim 10$ compared to reduced order quadrature.