Validating Prior-informed Fisher-matrix Analyses against GWTC Data

TL;DR

This study evaluates the accuracy of Fisher-matrix methods in gravitational-wave parameter estimation by comparing them with real GWTC data and explores the role of priors in these analyses.

Contribution

The paper introduces a sampling algorithm to incorporate priors into Fisher analyses and assesses their importance relative to waveform degeneracies.

Findings

Fisher-matrix methods are generally valid for ET science-case studies.

The impact of priors varies with waveform degeneracy levels.

Including priors improves the accuracy of Fisher analyses in high degeneracy scenarios.

Abstract

Fisher-matrix methods are widely used to predict how accurately parameters can be estimated. Being computationally efficient, this approach is prompted by the large number of signals simulated in forecast studies for future gravitational-wave (GW) detectors, for which adequate analysis tools and computational resources are still unavailable to the scientific community. However, approximating the full likelihood function with a Gaussian may lead to inaccuracies, which we investigate in this work. To assess the accuracy of the Fisher approximation, we compare the results of the Fisher code GWFish against real data from the Gravitational Wave Transient Catalogs (GWTCs) provided by the Virgo/LIGO Bayesian analyses. Additionally, we present a sampling algorithm to include priors in GWFish, not only to ensure a fair comparison between GWFish results and the Virgo/LIGO posteriors but also to investigate the role of prior information and to assess the need to include it in standard Fisher analyses. We find that the impact of priors depends mostly on the level of signal-dependent degeneracy of the waveform parameterization, and priors are generally more important when the level of degeneracy is high. Our findings imply that Fisher-matrix methods are a valid tool for ET science-case studies.