Almanac: Weak Lensing power spectra and map inference on the masked sphere

We present a field-based signal extraction of weak lensing from noisy observations on the curved and masked sky. We test the analysis on a simulated Euclid-like survey, using a Euclid-like mask and noise level. To make optimal use of the information available in such a galaxy survey, we present a Bayesian method for inferring the angular power spectra of the weak lensing fields, together with an inference of the noise-cleaned tomographic weak lensing shear and convergence (projected mass) maps. The latter can be used for field-level inference with the aim of extracting cosmological parameter information including non-gaussianity of cosmic fields. We jointly infer all-sky \(E\)-mode and \(B\)-mode tomographic auto- and cross-power spectra from the masked sky, and potentially parity-violating \(EB\)-mode power spectra, up to a maximum multipole of \(\ell_{\rm max}=2048\). We use Hamiltonian Monte Carlo sampling, inferring simultaneously the power spectra and denoised maps with a total of \(\sim 16.8\) million free parameters. The main output and natural outcome is the set of samples of the posterior, which does not suffer from leakage of power from \(E\) to \(B\) unless reduced to point estimates. However, such point estimates of the power spectra, the mean and most likely maps, and their variances and covariances, can be computed if desired.