# Sparse Bayesian mass-mapping with uncertainties: local credible intervals

## TL;DR

This paper introduces a sparse Bayesian method for weak gravitational lensing mass-mapping that efficiently quantifies uncertainties with local credible intervals, outperforming traditional MCMC techniques in speed while maintaining comparable accuracy.

## Contribution

The paper presents a novel sparse hierarchical Bayesian framework for mass-mapping that provides efficient uncertainty quantification using local credible intervals, significantly reducing computational costs.

## Key findings

- Uncertainties are conservative and highly correlated with MCMC results.
- The method achieves a computational efficiency increase of about one million times.
- Applicable to large-scale surveys like LSST and Euclid.

## Abstract

Until recently mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we draw on the concept of local credible intervals (cf. Bayesian error bars) as an extension of the uncertainty quantification techniques previously detailed. These uncertainty quantification techniques are benchmarked against those recovered via Px-MALA - a state of the art proximal Markov Chain Monte Carlo (MCMC) algorithm. We find that typically our recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient $\geq 0.85$) with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of $\mathcal{O}(10^6)$ when using our sparse Bayesian approach over MCMC techniques. This computational saving is critical for the application of Bayesian uncertainty quantification to large-scale stage IV surveys such as LSST and Euclid.