Bayesian power-spectrum inference for large-scale structure data

We describe an exact, flexible and computationally efficient algorithm for a joint inference of the large-scale structure and its power spectrum, building on a Gibbs sampling framework and present its implementation ares (Algorithm for REconstruction and Sampling). ares is designed to reconstruct the 3D power spectrum together with the underlying dark matter density field in a Bayesian framework, under the reasonable assumption that the long-wavelength Fourier components are Gaussian distributed. As a result ares does not only provide a single estimate but samples from the joint posterior of the power spectrum and density field conditional on a set of observations. This enables us to calculate any desired statistical summary, in particular we are able to provide joint uncertainty information. We apply our method to mock catalogues, with highly structured observational masks and selection functions, in order to demonstrate its ability to infer the power spectrum from real data sets, while fully accounting for any mask induced mode coupling.