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 { h 0 , cos iota , psi , phi 0 } 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 phi 0 , which avoids signal degeneracy problems in the psi -phi 0 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 MonteCarlo 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 h 95% 0 on the gravitational -wave amplitude of approximately 7 x 10 - 27 , comparable with a previous frequentist upper limit.