Targeted search for continuous gravitational waves: Bayesian versus maximum-likelihood statistics

We investigate the Bayesian framework for detection of continuous gravitational waves (GWs) in the context of targeted searches, where the phase evolution of the GW signal is assumed to be known, while the four amplitude parameters are unknown. We show that the orthodox maximum-likelihood statistic (known as F-statistic) can be rediscovered as a Bayes factor with an unphysical prior in amplitude parameter space. We introduce an alternative detection statistic ('B-statistic') using the Bayes factor with a more natural amplitude prior, namely an isotropic probability distribution for the orientation of GW sources. Monte Carlo simulations of targeted searches show that the resulting Bayesian B-statistic is more powerful in the Neyman-Pearson sense (i.e., has a higher expected detection probability at equal false-alarm probability) than the frequentist F-statistic.