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