Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches
arXiv:2104.14829 · doi:10.3390/universe7060174
Abstract
The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, the other representing the maximised likelihood ratio or -statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio which is a function of the -statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihood ratios have identical detection power to the -statistic. This approach demonstrates a route to viewing the -statistic in a Bayesian context, while retaining the advantages of its efficient computation.
arXiv comment15 pages, 7 figures; accepted for publication in Universe special issue "Continuous Gravitational Waves"
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