Inadequacies of the Fisher Information Matrix in gravitational-wave parameter estimation

The Fisher Information Matrix (FIM) has been the standard approximation to the accuracy of parameter estimation on gravitational-wave signals from merging compact binaries due to its ease-of-use and rapid computation time. While the theoretical failings of this method, such as the signal-to-noise ratio (SNR) limit on the validity of the lowest-order expansion and the difficulty of using non-Gaussian priors, are well understood, the practical effectiveness compared to a real parameter estimation technique (e.g. Markov-chain Monte Carlo) remains an open question. We present a direct comparison between the FIM error estimates and the Bayesian probability density functions produced by the parameter estimation code lalinference_mcmc. In addition to the low-SNR issues usually considered, we find that the FIM can greatly overestimate the uncertainty in parameter estimation achievable by the MCMC. This was found to be a systematic effect for systems composed of binary black holes, with the disagreement increasing with total mass. In some cases, the MCMC search returned standard deviations on the marginalized posteriors that were smaller by several orders of magnitude than the FIM estimates. We conclude that the predictions of the FIM do not represent the capabilities of real gravitational-wave parameter estimation.