LIGO Document G1300496-v3

Approximation Methods for Bayesian Detection Statistics in a Targeted Search for Continuous Gravitational Waves

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Prix and Krishnan [CQG _26_, 204013 (2009)] showed that the standard maximum-likelihood statistic used in continuous gravitational-wave searches, known as the F-statistic, could also be interpreted as a Bayes factor using an unphysical prior distribution on the amplitude parameter space. They defined an alternative statistic using physical priors on the amplitude parameters, particularly the geometrical parameters of neutron star inclination and polarization angles, known as the B-statistic, and showed it to be more powerful in the case where the unknown amplitude parameters are drawn from the physical prior distribution. Marginalizing over the amplitude parameters requires a multi-dimensional integral which must in general be done numerically. We describe approximation methods which allow analytic evaluation of this integral, allowing the more powerful search to be done without a large increase in computational resources.
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