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Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case

Author(s): Piotr Jaranowski | Andrzej Królak

Journal: Living Reviews in Relativity
ISSN 1433-8351

Volume: 15;
Start page: 4;
Date: 2012;
Original page

Keywords: signal detection | gravitational waves | parameter estimation

The article reviews the statistical theory of signal detection in application to analysis of deterministic gravitational-wave signals in the noise of a detector. Statistical foundations for the theory of signal detection and parameter estimation are presented. Several tools needed for both theoretical evaluation of the optimal data analysis methods and for their practical implementation are introduced. They include optimal signal-to-noise ratio, Fisher matrix, false alarm and detection probabilities, ℱ-statistic, template placement, and fitting factor. These tools apply to the case of signals buried in a stationary and Gaussian noise. Algorithms to efficiently implement the optimal data analysis techniques are discussed. Formulas are given for a general gravitational-wave signal that includes as special cases most of the deterministic signals of interest.

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