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

The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as function of the orientation two vectors; one representing optimal signal-to-noise ratio, and other maximised or F-statistic. Analytic marginalisation over angle between vectors yields marginalised which Further analytic explored using different choices prior. Monte-Carlo simulations show that ratios had identical detection power to This approach demonstrates route viewing F-statistic in Bayesian context, while retaining advantages its efficient computation.