Bayesian hierarchical modelling of weak lensing - the golden goal

TL;DR

This paper develops a Bayesian hierarchical model for weak lensing data that enables simultaneous sampling of shear fields and power spectra, effectively handling masked data and intrinsic alignments, demonstrated with simulated data.

Contribution

It introduces a comprehensive Bayesian hierarchical framework for weak lensing analysis that efficiently samples high-dimensional parameter spaces and recovers underlying signals.

Findings

Successfully recovers shear fields and power spectra from simulated data.

Handles masked data and intrinsic alignments effectively.

Achieves accurate results below shot noise levels.

Abstract

To accomplish correct Bayesian inference from weak lensing shear data requires a complete statistical description of the data. The natural framework to do this is a Bayesian Hierarchical Model, which divides the chain of reasoning into component steps. Starting with a catalogue of shear estimates in tomographic bins, we build a model that allows us to sample simultaneously from the the underlying tomographic shear fields and the relevant power spectra (E-mode, B-mode, and E-B, for auto- and cross-power spectra). The procedure deals easily with masked data and intrinsic alignments. Using Gibbs sampling and messenger fields, we show with simulated data that the large (over 67000-)dimensional parameter space can be efficiently sampled and the full joint posterior probability density function for the parameters can feasibly be obtained. The method correctly recovers the underlying shear fields and all of the power spectra, including at levels well below the shot noise.