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  Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II. Bayesian analyses

Allen, B., Creighton, J. D. E., Flanagan, E. E., & Romano, J. D. (2003). Robust statistics for deterministic and stochastic gravitational waves in non-Gaussian noise. II. Bayesian analyses. Physical Review D, 67(12): 122002. doi:10.1103/PhysRevD.67.122002.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5222-3 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-5223-1
Genre: Journal Article

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prd-03-67-122002.pdf (Publisher version), 133KB
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Allen, Bruce1, Author              
Creighton, Jolien D. E., Author
Flanagan, Eanna E., Author
Romano, Joseph D., Author
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1Observational Relativity and Cosmology, AEI-Hannover, MPI for Gravitational Physics, Max Planck Society, escidoc:24011              

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 Abstract: In a previous paper (paper I), we derived a set of near-optimal signal detection techniques for gravitational wave detectors whose noise probability distributions contain non-Gaussian tails. The methods modify standard methods by truncating or clipping sample values which lie in those non-Gaussian tails. The methods were derived, in the frequentist framework, by minimizing false alarm probabilities at fixed false detection probability in the limit of weak signals. For stochastic signals, the resulting statistic consisted of a sum of an autocorrelation term and a cross-correlation term; it was necessary to discard “by hand” the autocorrelation term in order to arrive at the correct, generalized cross-correlation statistic. In the present paper, we present an alternative derivation of the same signal detection techniques from within the Bayesian framework. We compute, for both deterministic and stochastic signals, the probability that a signal is present in the data, in the limit where the signal-to-noise ratio squared per frequency bin is small, where the signal is nevertheless strong enough to be detected (integrated signal-to-noise ratio large compared to 1), and where the total probability in the non-Gaussian tail part of the noise distribution is small. We show that, for each model considered, the resulting probability is to a good approximation a monotonic function of the detection statistic derived in paper I. Moreover, for stochastic signals, the new Bayesian derivation automatically eliminates the problematic autocorrelation term.

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 Dates: 2003-06-06
 Publication Status: Published in print
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Title: Physical Review D
Source Genre: Journal
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Pages: - Volume / Issue: 67 (12) Sequence Number: 122002 Start / End Page: - Identifier: ISSN: 0556-2821