Living Reviews in Relativity

"Gravitational-Wave Data Analysis.
Formalism and Sample Applications: The Gaussian Case"
Piotr Jaranowski and Andrzej Królak 

Hide Subsections

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 ℱ-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 ℱ-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
Open References References