Bayesian F -statistic-based parameter estimation of continuous gravitational waves from known pulsars

We present a new method and implementation to obtain Bayesian posteriors on the amplitude parameters {h0,cosι,ψ,φ0} of continuous gravitational waves emitted by known pulsars. This approach leverages the well-established F-statistic framework and software. We further explore the benefits of employing a likelihood function that is analytically marginalized over φ0, which avoids signal degeneracy problems in the ψ-φ0 subspace. The method is tested on simulated signals, hardware injections in Advanced-LIGO detector data, and by performing percentile-percentile self-consistency tests of the posteriors via Monte-Carlo simulations. We apply our methodology to PSR J1526-2744, a recently discovered millisecond pulsar. We find no evidence for a signal and obtain a Bayesian upper limit h095% on the gravitational-wave amplitude of approximately 7×10-27, comparable with a previous frequentist upper limit.