Rapid inference of gravitational-wave signals in the time domain using a heterodyned likelihood

TL;DR

This paper introduces a heterodyned likelihood framework that significantly accelerates time-domain gravitational-wave parameter estimation, making it feasible for long-duration signals with minimal loss of accuracy.

Contribution

The authors develop a novel heterodyned likelihood method that enables rapid, accurate inference of gravitational-wave signals in the time domain, applicable to arbitrary mode content.

Findings

Achieves at least 400x speedup over standard methods for 128-second signals.

Recovers posterior distributions indistinguishable from traditional likelihood-based inference.

Demonstrates unbiased and reliable results through percentile-percentile tests.

Abstract

Parameter estimation of gravitational wave signals is computationally intensive and typically requires millions of likelihood evaluations to construct posterior probability distributions. This computational cost increases significantly in the time domain, which requires non-diagonal covariance matrices to compute the likelihood. Consequently, parameter estimation of long-duration gravitational wave signals, such as binary neutron star mergers, becomes computationally infeasible in time domain. In this work, we detail a framework for the heterodyned likelihood that enables rapid inference in the time domain. Our method is applicable to signals with arbitrary mode content, and leverages the smoothness of the ratio of complex-valued waveform modes, approximating the ratio as a linear function within appropriately chosen time bins. This allows downsampling of the waveform modes and a reformulation of the likelihood, such that it depends only on the bin edges. We demonstrate that this likelihood recovers posteriors that are indistinguishable from those obtained using the standard likelihood in the time domain. We also observe dramatic improvement in speed - for a 128 seconds-long gravitational wave signal, our method is at least $\sim 400$ times faster than the standard time-domain analysis, reducing the wall clock time to just a few hours. We also demonstrate the reliability and unbiasedness of the likelihood using percentile-percentile tests for binary black hole and binary neutron star injections. We use the Gohberg-Semencul representation of the inverse of Toeplitz covariance matrix to accelerate matrix-vector products, which has potential applications even in non heterodyned time-domain inference.