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 [145] 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 [66].

3.1 Hypothesis testing

3.1.1 Bayesian approach

3.1.2 Minimax approach

3.1.3 Neyman–Pearson approach

3.1.4 Likelihood ratio test

3.2 The matched filter in Gaussian noise

3.3 Parameter estimation

3.3.1 Bayesian estimation

3.3.2 Maximum a posteriori probability estimation

3.3.3 Maximum likelihood estimation

3.4 Fisher information and Cramèr–Rao bound

3.1.1 Bayesian approach

3.1.2 Minimax approach

3.1.3 Neyman–Pearson approach

3.1.4 Likelihood ratio test

3.2 The matched filter in Gaussian noise

3.3 Parameter estimation

3.3.1 Bayesian estimation

3.3.2 Maximum a posteriori probability estimation

3.3.3 Maximum likelihood estimation

3.4 Fisher information and Cramèr–Rao bound

Living Rev. Relativity 15, (2012), 4
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