Beyond Fisher: exact sampling distributions of the maximum-likelihood estimator in gravitational-wave parameter estimation

Abstract

Gravitational-wave astronomers often wish to characterize the expected parameter-estimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximum-likelihood estimator across noise realizations, as well as the leading-order width of the posterior probability, but it is limited to high signal strengths often not realized in practice. By contrast, Monte Carlo Bayesian inference provides the full posterior for any signal strength, but it is too expensive to repeat for a representative set of noises. Here I describe an efficient semianalytical technique to map the exact sampling distribution of the maximum-likelihood estimator across noise realizations, for any signal strength. This technique can be applied to any estimation problem for signals in additive Gaussian noise.

4 pages, 3 figures, RevTeX 4.1. Fixed typos, revised for clarity

References in corpus (2)

• Use and Abuse of the Fisher Information Matrix in the Assessment of Gravitational-Wave Parameter-Estimation Prospects
• Parameter estimation from Gravitational waves generated by non-spinning binary black holes with laser interferometers: beyond the Fisher information

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