Beyond the FisherMatrix Formalism: Exact Sampling Distributions of the MaximumLikelihood Estimator in GravitationalWave Parameter Estimation
Abstract
Gravitationalwave astronomers often wish to characterize the expected parameterestimation accuracy of future observations. The Fisher matrix provides a lower bound on the spread of the maximumlikelihood estimator across noise realizations, as well as the leadingorder 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 maximumlikelihood estimator across noise realizations, for any signal strength. This technique can be applied to any estimation problem for signals in additive Gaussian noise.
 Publication:

Physical Review Letters
 Pub Date:
 November 2011
 DOI:
 10.1103/PhysRevLett.107.191104
 arXiv:
 arXiv:1108.1158
 Bibcode:
 2011PhRvL.107s1104V
 Keywords:

 04.80.Nn;
 04.25.Nx;
 04.30.Db;
 95.55.Ym;
 Gravitational wave detectors and experiments;
 PostNewtonian approximation;
 perturbation theory;
 related approximations;
 Wave generation and sources;
 Gravitational radiation detectors;
 mass spectrometers;
 and other instrumentation and techniques;
 General Relativity and Quantum Cosmology;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 4 pages, 3 figures, RevTeX 4.1. Fixed typos, revised for clarity