Rights statement: Copyright 2019 American Institute of Physics. The following article appeared in Physical Review D, 98, 2019 and may be found at https://doi.org/10.1103/PhysRevD.98.063001 This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Hierarchical Bayesian method for detecting continuous gravitational waves from an ensemble of pulsars
AU - Pitkin, M.
AU - Messenger, C.
AU - Fan, X.
PY - 2018/9/5
Y1 - 2018/9/5
N2 - When looking for gravitational wave signals from known pulsars, targets have been treated using independent searches. Here we use a hierarchical Bayesian framework to combine observations from individual sources for two purposes: to produce a detection statistic for the whole ensemble of sources within a search, and, to estimate the hyperparameters of the underlying distribution of pulsar ellipticities. Both purposes require us to assume some functional form of the ellipticity distribution, and as a proof of principle we take two toy distributions. One is an exponential distribution,defined by its mean, and the other is a half-Gaussian distribution defined by its width. We show that by incorporating a common parameterized prior ellipticity distribution we can be more efficient at detecting gravitational waves from the whole ensemble of sources than trying to combine observations with a simpler non-hierarchical method. This may allow us to detect gravitational waves from the ensemble before there is confident detection of any single source. We also apply this method using data for 92 pulsars from LIGO's sixth science run. No evidence for a signal was seen, but 90\% upper limits of $3.9\ee{-8}$ and $4.7\ee{-8}$ were set on the mean of an assumed exponential ellipticity distribution and the width of an assumed half-Gaussian ellipticity distribution, respectively.
AB - When looking for gravitational wave signals from known pulsars, targets have been treated using independent searches. Here we use a hierarchical Bayesian framework to combine observations from individual sources for two purposes: to produce a detection statistic for the whole ensemble of sources within a search, and, to estimate the hyperparameters of the underlying distribution of pulsar ellipticities. Both purposes require us to assume some functional form of the ellipticity distribution, and as a proof of principle we take two toy distributions. One is an exponential distribution,defined by its mean, and the other is a half-Gaussian distribution defined by its width. We show that by incorporating a common parameterized prior ellipticity distribution we can be more efficient at detecting gravitational waves from the whole ensemble of sources than trying to combine observations with a simpler non-hierarchical method. This may allow us to detect gravitational waves from the ensemble before there is confident detection of any single source. We also apply this method using data for 92 pulsars from LIGO's sixth science run. No evidence for a signal was seen, but 90\% upper limits of $3.9\ee{-8}$ and $4.7\ee{-8}$ were set on the mean of an assumed exponential ellipticity distribution and the width of an assumed half-Gaussian ellipticity distribution, respectively.
U2 - 10.1103/PhysRevD.98.063001
DO - 10.1103/PhysRevD.98.063001
M3 - Journal article
VL - 98
JO - Physical Review D
JF - Physical Review D
SN - 1550-7998
M1 - 063001
ER -