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

TL;DR

This paper compares Bayesian and maximum-likelihood methods for detecting continuous gravitational waves, showing the Bayesian approach with a natural prior improves detection power over the traditional F-statistic.

Contribution

It introduces the B-statistic, a Bayesian detection method with a physically motivated amplitude prior, demonstrating its superior performance in targeted GW searches.

Findings

B-statistic outperforms F-statistic in simulations

Bayesian framework clarifies the interpretation of detection statistics

Natural amplitude prior enhances detection sensitivity

Abstract

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.