Use and abuse of the Fisher information matrix in the assessment of gravitationalwave parameterestimation prospects
Abstract
The Fishermatrix formalism is used routinely in the literature on gravitationalwave detection to characterize the parameterestimation performance of gravitationalwave measurements, given parametrized models of the waveforms, and assuming detector noise of known colored Gaussian distribution. Unfortunately, the Fisher matrix can be a poor predictor of the amount of information obtained from typical observations, especially for waveforms with several parameters and relatively low expected signaltonoise ratios (SNR), or for waveforms depending weakly on one or more parameters, when their priors are not taken into proper consideration. In this paper I discuss these pitfalls; show how they occur, even for relatively strong signals, with a commonly used template family for binaryinspiral waveforms; and describe practical recipes to recognize them and cope with them. Specifically, I answer the following questions: (i) What is the significance of (quasi)singular Fisher matrices, and how must we deal with them? (ii) When is it necessary to take into account prior probability distributions for the source parameters? (iii) When is the signaltonoise ratio high enough to believe the Fishermatrix result? In addition, I provide general expressions for the higherorder, beyondFishermatrix terms in the 1/SNR expansions for the expected parameter accuracies.
 Publication:

Physical Review D
 Pub Date:
 February 2008
 DOI:
 10.1103/PhysRevD.77.042001
 arXiv:
 arXiv:grqc/0703086
 Bibcode:
 2008PhRvD..77d2001V
 Keywords:

 04.80.Nn;
 02.50.Tt;
 95.55.Ym;
 Gravitational wave detectors and experiments;
 Inference methods;
 Gravitational radiation detectors;
 mass spectrometers;
 and other instrumentation and techniques;
 General Relativity and Quantum Cosmology
 EPrint:
 24 pages, 3 figures, previously known as "A User Manual for the Fisher Information Matrix"