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

被引:477
作者
Vallisneri, Michele [1 ]
机构
[1] CALTECH, Jet Prop Lab, Pasadena, CA 91109 USA
来源
PHYSICAL REVIEW D | 2008年 / 77卷 / 04期
关键词
D O I
10.1103/PhysRevD.77.042001
中图分类号
P1 [天文学];
学科分类号
0704 ;
摘要
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.
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页数:20
相关论文
共 35 条
[1]   LIGO - THE LASER-INTERFEROMETER-GRAVITATIONAL-WAVE-OBSERVATORY [J].
ABRAMOVICI, A ;
ALTHOUSE, WE ;
DREVER, RWP ;
GURSEL, Y ;
KAWAMURA, S ;
RAAB, FJ ;
SHOEMAKER, D ;
SIEVERS, L ;
SPERO, RE ;
THORNE, KS ;
VOGT, RE ;
WEISS, R ;
WHITCOMB, SE ;
ZUCKER, ME .
SCIENCE, 1992, 256 (5055) :325-333
[2]  
[Anonymous], 1994, MATHTENSOR SYSTEM DO
[3]  
[Anonymous], 2012, Probability Theory: The Logic Of Science
[4]   Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case (vol D 71, art no 084008, 2005) [J].
Arun, KG ;
Iyer, BR ;
Sathyaprakash, BS ;
Sundararajan, PA .
PHYSICAL REVIEW D, 2005, 72 (06)
[5]   Parameter estimation of inspiralling compact binaries using 3.5 post-Newtonian gravitational wave phasing: The nonspinning case [J].
Arun, KG ;
Iyer, BR ;
Sathyaprakash, BS ;
Sundararajan, PA .
PHYSICAL REVIEW D, 2005, 71 (08) :1-16
[6]   Estimation of parameters of gravitational wave signals from coalescing binaries [J].
Balasubramanian, R ;
Dhurandhar, SV .
PHYSICAL REVIEW D, 1998, 57 (06) :3408-3422
[7]   Gravitational waves from coalescing binaries: Detection strategies and Monte Carlo estimation of parameters [J].
Balasubramanian, R ;
Sathyaprakash, BS ;
Dhurandhar, SV .
PHYSICAL REVIEW D, 1996, 53 (06) :3033-3055
[8]  
Barndorff-Nielsen OE., 1994, INFERENCE ASYMPTOTIC
[9]   Testing general relativity and probing the merger history of massive black holes with LISA [J].
Berti, E ;
Buonanno, A ;
Will, CM .
CLASSICAL AND QUANTUM GRAVITY, 2005, 22 (18) :S943-S954
[10]   Gravitational radiation from inspiralling compact binaries completed at the third post-Newtonian order -: art. no. 091101 [J].
Blanchet, L ;
Damour, T ;
Esposito-Farèse, G ;
Iyer, BR .
PHYSICAL REVIEW LETTERS, 2004, 93 (09) :091101-1