Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches

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, and the other representing the maximised likelihood ratio or F-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio, which is a function of the F-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 had identical detection power to the F-statistic. This approach demonstrates a route to viewing the F-statistic in a Bayesian context, while retaining the advantages of its efficient computation.