Gravitational-Wave Data Analysis.
Formalism and Sample Applications: The Gaussian Case
Update available: http://www.livingreviews.org/lrr-2012-4
Piotr Jaranowski
Institute of Theoretical Physics
University of Białystok
Lipowa 41
15–424 Białystok, Poland
Andrzej Królak
Max-Planck-Institut für Gravitationsphysik
Am Mühlenberg 1
D-14476 Golm, Germany
on leave of absence from:
Institute of Mathematics
Polish Academy of Sciences
Śniadeckich 8
00–950 Warsaw, Poland
Abstract
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, 
-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.
