Formalism and Sample Applications: The Gaussian Case

**Update available:
http://www.livingreviews.org/lrr-2012-4**

Institute of Theoretical Physics

University of Białystok

Lipowa 41

15–424 Białystok, Poland

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

This article has been revised on
26 July 2007
(see changes in detail).

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.

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