An Analytic Approximation to the Bayesian Detection Statistic for Continuous Gravitational Waves

• Published in: arXiv.org
• Main Authors: Bero, John J, Whelan, John T
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 16.08.2018
• Subjects: Approximation; Bayesian analysis; Computer simulation; Continuous radiation; Gravitation; Gravitational waves; Hypergeometric functions; Monte Carlo simulation; Parameters; Physics - General Relativity and Quantum Cosmology
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1808.05453

We consider the Bayesian detection statistic for a targeted search for continuous gravitational waves, known as the \(\mathcal{B}\)-statistic. This is a Bayes factor between signal and noise hypotheses, produced by marginalizing over the four amplitude parameters of the signal. We show that by Taylor-expanding to first order in certain averaged combinations of antenna patterns (elements of the parameter space metric), the marginalization integral can be performed analytically, producing a closed-form approximation in terms of confluent hypergeometric functions. We demonstrate using Monte Carlo simulations that this approximation is as powerful as the full \(\mathcal{B}\)-statistic, and outperforms the traditional maximum-likelihood \(\mathcal{F}\)-statistic, for several observing scenarios which involve an average over sidereal times. We also show that the approximation does not perform well for a near-instantaneous observation, so the approximation is suited to long-time continuous wave observations rather than transient modelled signals such as compact binary inspiral.