2007/03/31 by Michele Vallisneri · 7 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Applied mathematics #Bayesian probability #Binary number #Detection theory #Detector #Estimation theory #Fisher information #Gaussian #Gravitational wave #Mathematics #Matrix (chemical analysis) #Optics #Physics #Prior probability #Pulsars and Gravitational Waves Research #Quantum mechanics #Seismic Imaging and Inversion Techniques #Seismic Waves and Analysis #Statistical physics #Statistics #Waveform #gr-qc
paper · pdf · doi:10.1103/physrevd.77.042001
published as Phys.Rev.D77:042001,2008 · 24 pages, 3 figures, previously known as "A User Manual for the Fisher Information Matrix"; final, corrected PRD version
arxiv created 2008/02/04 · openalex publication_date 2008/02/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The Fisher-matrix formalism is used routinely in the literature on gravitational-wave detection to characterize the parameter-estimation performance of gravitational-wave 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 signal-to-noise 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 binary-inspiral 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 signal-to-noise ratio high enough to believe the Fisher-matrix result? In addition, I provide general expressions for the higher-order, beyond-Fisher-matrix terms in the 1/SNR expansions for the expected parameter accuracies.