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

## TL;DR

This paper introduces novel Bayesian methods to quantify uncertainties in weak lensing convergence maps, enabling more reliable peak statistics and feature localization in cosmological surveys.

## Contribution

It presents new techniques for Bayesian uncertainty quantification in mass-mapping, specifically for feature locations and peak counts, within a sparse hierarchical framework.

## Key findings

- Successfully applied to N-body simulations
- Provides Bayesian confidence intervals for peak statistics
- Enhances robustness of mass-mapping analysis

## 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.