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