Normal Approximate Likelihoods to Gravitational Wave Events

TL;DR

This paper demonstrates that a simple multivariate normal approximation over a few effective parameters can accurately represent the complex likelihoods of gravitational wave events, enabling efficient analysis of large datasets.

Contribution

It introduces a method to approximate high-dimensional gravitational wave likelihoods with a low-dimensional normal distribution, simplifying data analysis.

Findings

Normal approximations accurately replicate eight-dimensional posteriors.

Provided normal fit parameters for GWTC-1 and GWTC-2 events.

Enables efficient combination of multiple gravitational wave observations.

Abstract

Gravitational wave observations of quasicircular compact binary mergers in principle provide an arbitrarily complex likelihood over eight independent intrinsic parameters: the masses and spins of the two merging objects. In this work, we demonstrate by example that a simple normal approximation over fewer (usually, three) effective dimensions provides a very accurate representation of the likelihood, and allows us to replicate the eight-dimensional posterior over the mass and spin degrees of freedom. Alongside this paper, we provide the parameters for multivariate normal fits for each event published in GWTC-1 and GWTC-2, using the posterior samples from the catalog for each associated release. These normal approximations provide a highly efficient way to characterize gravitational wave observations when combining large numbers of events.