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We develop a method to perform an untargeted Bayesian search for anisotropicgravitational-wave backgrounds that can efficiently and accurately reconstructthe background intensity map. Our method employs an analytic marginalization ofthe posterior of the spherical-harmonic components of the intensity map,without assuming the background possesses any specific angular structure. Thekey idea is that the likelihood function of the spherical-harmonic componentsis a multivariate Gaussian when the intensity map is expressed as a linearcombination of the spherical-harmonic components and the noise is stationaryand Gaussian. If a uniform and wide prior of these spherical-harmoniccomponents is prescribed, the marginalized posterior and the Bayes factor canbe well approximated by a high-dimensional Gaussian integral. The analyticalmarginalization allows us to regard the spherical-harmonic components of theintensity map of the background as free parameters, and to construct theirindividual marginalized posterior distribution in a reasonable time, eventhough many spherical-harmonic components are required. The marginalizedposteriors can, in turn, be used to accurately construct the intensity map ofthe background. By applying our method to mock data, we show that we canrecover precisely the angular structures of various simulated anisotropicbackgrounds, without assuming prior knowledge of the relation between thespherical-harmonic components predicted by a given model. Our method allows usto bypass the time-consuming numerical sampling of a high-dimensionalposterior, leading to a more model-independent and untargeted Bayesianmeasurement of the angular structures of the gravitational-wave background.

Untargeted Bayesian search of anisotropic gravitational-wave backgrounds through the analytical marginalization of the posterior