The gravitational-wave signal will be buried in the noise of the detector and the data from the detector will be a random (or stochastic) process. Consequently, the problem of extracting the signal from the noise is a statistical one. The basic idea behind signal detection is that the presence of the signal changes the statistical characteristics of the data , in particular its probability distribution. When the signal is absent the data have probability density function (pdf) , and when the signal is present the pdf is .
A thorough introduction to probability theory and mathematical statistics can be found, e.g., in [51, 130, 131, 101]. A full exposition of statistical theory of signal detection that is only outlined here can be found in the monographs [147, 74, 143, 139, 87, 58, 107]. A general introduction to stochastic processes is given in  and advanced treatment of the subject can be found in [84, 146]. A concise introduction to the statistical theory of signal detection and time series analysis is contained in Chapters 3 and 4 of .
Living Rev. Relativity 15, (2012), 4
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