Validating prior-informed Fisher-matrix analyses against GWTC data

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 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 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 parametrization, 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 Einstein Telescope science-case studies.