Sparse Bayesian mass-mapping with uncertainties: peak statistics and feature locations

Abstract

Weak lensing convergence maps - upon which higher order statistics can be calculated - can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic - the peak count as a function of signal to noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well defined confidence levels.

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• KaRMMa -- Kappa Reconstruction for Mass Mapping
• Cosmological studies from tomographic weak lensing peak abundances and impacts of photo-z errors
• Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
• Accurate Kappa Reconstruction Algorithm for masked shear catalog (AKRA)
• AKRA 2.0: Accurate Kappa Reconstruction Algorithm for masked shear catalog
• Generative modelling for mass-mapping with fast uncertainty quantification
• Bayesian variational regularization on the ball