Compressed Parametric and Non-Parametric Approximations to the Gravitational Wave Likelihood

TL;DR

This paper demonstrates that bounded multivariate normal likelihood approximations can accurately represent the complex likelihoods of gravitational-wave sources, enabling efficient population inference and low-latency parameter estimation.

Contribution

The authors introduce and validate bounded multivariate normal approximations for gravitational-wave likelihoods, improving computational efficiency and accuracy over traditional methods.

Findings

Likelihood approximations are sufficiently accurate for population inference.

The approximations have smaller errors than waveform model systematics.

Code and data are publicly available for further use.

Abstract

Gravitational-wave observations of quasicircular compact binary mergers imply complicated posterior measurements of their parameters. Though Gaussian approximations to the pertinent likelihoods have decades of history in the field, the relative generality and practical utility of these approximations hasn't been appreciated, given focus on careful, comprehensive generic Bayesian parameter inference. Building on our previous work in three dimensions, we demonstrate by example that bounded multivariate normal likelihood approximations are a sufficiently accurate representation of the full likelihood of observed gravitational-wave sources. Fits for each event published in the Gravitatinoal-Wave Transient Catalogs at https://gitlab.com/xevra/nal-data, along with a code release at https://gitlab.com/xevra/gwalk. We argue our approximations are more than accurate enough for popultion inference and introduce much smaller errors than waveform model systematics. To demonstrate the utility of these approximations as parametric models for the likelihood of individual gravitational-wave sources, we show examples of their application to modeling the population of observed gravitational-wave sources as well as low-latency parameter inference.