Hierarchical Cosmic Shear Power Spectrum Inference

TL;DR

This paper introduces a Bayesian hierarchical method for cosmic shear power spectrum inference that effectively handles survey complexities and masks, enabling accurate posterior sampling of shear fields and spectra from simulated data.

Contribution

It presents a novel Gibbs sampling approach for joint posterior inference of shear maps and power spectra, overcoming survey geometry challenges in cosmic shear analysis.

Findings

Successfully recovers simulated shear power spectra

Handles complex survey masks and geometries

Provides accurate posterior distributions for shear spectra

Abstract

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear field 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 \emph{a posteriori} without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled effectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents difficulties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the field 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 coefficients recover the underlying simulated power spectra for both $E$- and $B$-modes.