{"title":"Gravitational-Wave Data Analysis. Formalism and Sample Applications: The Gaussian Case","authors":"Piotr Jaranowski, Andrzej Królak","doi":"10.12942/lrr-2012-4","DOIUrl":null,"url":null,"abstract":"<p>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, <span>\\({\\mathcal F}\\)</span>-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.</p>","PeriodicalId":686,"journal":{"name":"Living Reviews in Relativity","volume":"15 1","pages":""},"PeriodicalIF":26.3000,"publicationDate":"2012-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.12942/lrr-2012-4","citationCount":"41","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Living Reviews in Relativity","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.12942/lrr-2012-4","RegionNum":2,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, PARTICLES & FIELDS","Score":null,"Total":0}
引用次数: 41
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, \({\mathcal F}\)-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.
期刊介绍：
Living Reviews in Relativity is a peer-reviewed, platinum open-access journal that publishes reviews of research across all areas of relativity. Directed towards the scientific community at or above the graduate-student level, articles are solicited from leading authorities and provide critical assessments of current research. They offer annotated insights into key literature and describe available resources, maintaining an up-to-date suite of high-quality reviews, thus embodying the "living" aspect of the journal's title.
Serving as a valuable tool for the scientific community, Living Reviews in Relativity is often the first stop for researchers seeking information on current work in relativity. Written by experts, the reviews cite, explain, and assess the most relevant resources in a given field, evaluating existing work and suggesting areas for further research.
Attracting readers from the entire relativity community, the journal is useful for graduate students conducting literature surveys, researchers seeking the latest results in unfamiliar fields, and lecturers in need of information and visual materials for presentations at all levels.
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