Comparing Fisher information and Bayesian statistical approaches on measuring the Hubble Constant from binary black hole merger gravitational wave signals

Gravitational waves from binary black-hole mergers can be used to provide distance and angular location information of these sources, which, upon comparison with galaxy catalogs, can be used to measure the Hubble Constant. For a given galaxy catalog, and binary merger rates associated with each galaxy, a Fisher information approach can be used to estimate the measurement error for the Hubble Constant from the dark siren approach. In this paper, we validate the predictions from the Fisher information approach by carrying out a series of Monte Carlo simulations. Except in situations with very low event rates, the Fisher information approach is shown to predict the statistical errors of the Bayesian approach with good accuracy.