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

TL;DR

This paper introduces an efficient semi-analytical method to determine the exact sampling distribution of the maximum-likelihood estimator in gravitational-wave parameter estimation, applicable across all signal strengths and noise realizations.

Contribution

It develops a novel semi-analytical approach that extends beyond Fisher matrix limitations to accurately characterize estimator distributions in Gaussian noise.

Findings

Provides exact sampling distribution for any signal strength.

Applicable to any estimation problem in additive Gaussian noise.

Offers a computationally efficient alternative to Monte Carlo methods.

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.