"Gravitational-Wave Data Analysis.
Formalism and Sample Applications: The Gaussian Case"
by
Piotr Jaranowski and Andrzej Królak
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Abstract
1
Introduction
2
Response of a Detector to a Gravitational Wave
2.1
Doppler shift between freely falling particles
2.2
Long-wavelength approximation
2.3
Solar-system-based detectors
2.4
General form of the response function
3
Statistical Theory of Signal Detection
3.1
Hypothesis testing
3.2
The matched filter in Gaussian noise
3.3
Parameter estimation
3.4
Fisher information and Cramèr–Rao bound
4
Maximum-likelihood Detection in Gaussian Noise
4.1
The
-statistic
4.2
Signal-to-noise ratio and the Fisher matrix
4.3
False alarm and detection probabilities
4.4
Number of templates
4.5
Suboptimal filtering
4.6
Algorithms to calculate the
-statistic
4.7
Accuracy of parameter estimation
4.8
Upper limits
5
Network of Detectors
6
Non-stationary, Non-Gaussian, and Non-linear Data
7
Acknowledgments
References
Updates
Figures