Gravitational-wave data analysis. Formalism and sample applications: the Gaussian Case. (English) Zbl 1316.83027
Summary: 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, \(\mathcal F\)-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.
Update to the authors’ paper [Zbl 1071.83520]: Material of the previous version of the review was partially reorganized and updated, 46 new references were added.
1. Section 2 was rewritten and extended, several new references were added.
2. Some parts of the former Section 4 were moved to the present Section 3, which is now a brief general introduction to the statistical theory of signal detection and of estimation of signals parameters. Some new references were added.
3. The present Section 4 is a partially rewritten (using some new, more convenient notation) and extended version of the former Sections 4.3-4.9. The gravitational-wave signal considered here was generalized from a 4-amplitude-parameter case to an \(n\)-amplitude-parameter case, where n is arbitrary. New Section 4.1.1 about targeted searches was added, and new Section 4.4.1 on the covering problem was created with references to constructions of various grids of templates for searches of continuous gravitational waves.
4. The present Section 5 is an expanded version of the former Section 4.10 with addition of several recent references.
5. The present Section 6 is an expanded version of the former Section 4.11 with new discussion of optimal filtering for non-stationary data and description of a test (Grubbs’ test) to detect outliers in data.
Update to the authors’ paper [Zbl 1071.83520]: Material of the previous version of the review was partially reorganized and updated, 46 new references were added.
1. Section 2 was rewritten and extended, several new references were added.
2. Some parts of the former Section 4 were moved to the present Section 3, which is now a brief general introduction to the statistical theory of signal detection and of estimation of signals parameters. Some new references were added.
3. The present Section 4 is a partially rewritten (using some new, more convenient notation) and extended version of the former Sections 4.3-4.9. The gravitational-wave signal considered here was generalized from a 4-amplitude-parameter case to an \(n\)-amplitude-parameter case, where n is arbitrary. New Section 4.1.1 about targeted searches was added, and new Section 4.4.1 on the covering problem was created with references to constructions of various grids of templates for searches of continuous gravitational waves.
4. The present Section 5 is an expanded version of the former Section 4.10 with addition of several recent references.
5. The present Section 6 is an expanded version of the former Section 4.11 with new discussion of optimal filtering for non-stationary data and description of a test (Grubbs’ test) to detect outliers in data.
MSC:
| 83C35 | Gravitational waves |
| 83-02 | Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory |
| 83B05 | Observational and experimental questions in relativity and gravitational theory |
Citations:
Zbl 1071.83520Software:
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