LIGO series, dimension of embedding and Kolmogorov's complexity (original) (raw)
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Noise hunting is a critical requirement for realizing design sensitivity of a detector, and consequently, noise origins and its features have been revealed partially. Among the noise sources to be hunted, sources of nonlinearly correlated noise, such up-conversion noise, are hard to find and can limit the sensitivity of gravitational wave searches with advanced detectors. We propose using a correlation analysis method called maximal information coefficient (MIC) to find both nonlinear and linear correlations. We apply MIC to the scattered light noise correlated between the seismic activity and the strain signal, which limited the sensitivity of the Virgo detector during the first science run. The results show that MIC can find nonlinearly correlated noise more efficiently than the Pearson correlation method. When the data is linearly correlated, the efficiency of the Pearson method and MIC is comparable. On the other hand, when the data is known to be nonlinearly correlated, MIC finds the correlation while the Pearson method fails completely.
Progress of Theoretical and Experimental Physics
Data analysis in modern science using extensive experimental and observational facilities, such as gravitational-wave detectors, is essential in the search for novel scientific discoveries. Accordingly, various techniques and mathematical principles have been designed and developed to date. A recently proposed approximate correlation method based on information theory has been widely adopted in science and engineering. Although the maximal information coefficient (MIC) method remains in the phase of improving its algorithm, it is particularly beneficial in identifying the correlations of multiple noise sources in gravitational-wave detectors including non-linear effects. This study investigates various prospects for determining MIC parameters to improve the reliability of handling multi-channel time-series data, reduce high computing costs, and propose a novel method of determining optimized parameter sets for identifying noise correlations in gravitational-wave data.
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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, 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.
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