Hierarchical cosmic shear power spectrum inference

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear eld and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models a posteriori without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled eectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents diculties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the eld in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear E-mode, B-mode and EB-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coecients recover the underlying simulated power spectra for both E- and B-modes, where the latter are recovered at a level of 1-2 orders of magnitude below the ellipticity noise level.