Validating Prior-informed Fisher-matrix Analyses against GWTC Data

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.

17 pages, 7 figures (including appendices), 4 tables (including appendices). Published version (corrected typos in Eqs B12-B14, and spin components definitions in Fig. 7 and Tab. 4)

References in corpus (27)

• Array Programming with NumPy
• Observation of Gravitational Waves from a Binary Black Hole Merger
• GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs
• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
• Science Case for the Einstein Telescope
• Bilby: A user-friendly Bayesian inference library for gravitational-wave astronomy
• Sensitivity Studies for Third-Generation Gravitational Wave Observatories
• Frequency-domain gravitational waves from non-precessing black-hole binaries. I. New numerical waveforms and anatomy of the signal
• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• Computationally efficient models for the dominant and sub-dominant harmonic modes of precessing binary black holes
• Bayesian inference for compact binary coalescences with BILBY: Validation and application to the first LIGO--Virgo gravitational-wave transient catalogue
• An introduction to Bayesian inference in gravitational-wave astronomy: parameter estimation, model selection, and hierarchical models
• Science with the Einstein Telescope: a comparison of different designs
• Forecasting the detection capabilities of third-generation gravitational-wave detectors using $\text{GWFAST}$
• Inadequacies of the Fisher Information Matrix in gravitational-wave parameter estimation
• Binary Neutron Star Mergers and Third Generation Detectors: Localization and Early Warning
• Parameter estimation with gravitational waves
• Gwbench: a novel Fisher information package for gravitational-wave benchmarking
• Bilby-MCMC: An MCMC sampler for gravitational-wave inference
• $\text{GWFAST}$: a Fisher information matrix Python code for third-generation gravitational-wave detectors
• GWFish: A simulation software to evaluate parameter-estimation capabilities of gravitational-wave detector networks
• Listening to the Universe with Next Generation Ground-Based Gravitational-Wave Detectors
• Removing degeneracy and multimodality in gravitational wave source parameters
• Exploring the sky localization and early warning capabilities of third generation gravitational wave detectors in three-detector network configurations
• Pre-merger alert to detect the very-high-energy prompt emission from binary neutron-star mergers: Einstein Telescope and Cherenkov Telescope Array synergy
• Classifying binary black holes from Population III stars with the Einstein Telescope: A machine-learning approach

Cited by in corpus (8)

• The Science of the Einstein Telescope
• The Lunar Gravitational-wave Antenna: Mission Studies and Science Case
• Fast and accurate parameter estimation of high-redshift sources with the Einstein Telescope
• Accounting for the Known Unknowns: A Parametric Framework to Incorporate Systematic Waveform Errors in Gravitational-Wave Parameter Estimation
• Overlapping signals in next-generation gravitational wave observatories: A recipe for selecting the best parameter estimation technique
• Primordial black holes versus their impersonators at gravitational wave observatories
• Detectability and Parameter Estimation for Einstein Telescope Configurations with GWJulia
• Source Confusion of Massive Black Hole Binaries for the Taiji Mission