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Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects

Vallisneri, Michele (2008) Use and abuse of the Fisher information matrix in the assessment of gravitational-wave parameter-estimation prospects. Physical Review D, 77 (4). Art. No. 042001. ISSN 2470-0010. doi:10.1103/PhysRevD.77.042001.

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The Fishermatrix 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.

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Vallisneri, Michele0000-0002-4162-0033
Additional Information:©2008 The American Physical Society. (Received 15 March 2007; published 4 February 2008) I would like to thank Yanbei Chen, Curt Cutler, Yi Pan, and Michele Zanolin for useful discussions; for reviewing this manuscript, I am grateful to John Armstrong, Emanuele Berti, Steve Drasco, Frank Estabrook, Sam Finn, Éanna Flanagan, and especially Alessandra Buonanno. My work was supported by the LISA Mission Science Office and by the Human Resources Development Fund at the Jet Propulsion Laboratory, California Institute of Technology, where it was performed under contract with the National Aeronautics and Space Administration.
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9589
Deposited By: Archive Administrator
Deposited On:11 Feb 2008
Last Modified:08 Nov 2021 21:00

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