Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of
  structure
  A crucial aspect of mass-mapping, via weak lensing, is quantification of the
uncertainty introduced during the reconstruction process. Properly accounting
for these errors has been largely ignored to date. We present a new method to
reconstruct maximum a posteriori (MAP) convergence maps by formulating an
unconstrained Bayesian inference problem with Laplace-type l1-norm
sparsity-promoting priors, which we solve via convex optimization. Approaching
mass-mapping in this manner allows us to exploit recent developments in
probability concentration theory to infer theoretically conservative
uncertainties for our MAP reconstructions, without relying on assumptions of
Gaussianity. For the first time these methods allow us to perform hypothesis
testing of structure, from which it is possible to distinguish between physical
objects and artifacts of the reconstruction. Here we present this new
formalism, demonstrate the method on simulations, before applying the developed
formalism to two observational datasets of the Abel-520 cluster. Initial
reconstructions of the Abel-520 catalogs reported the detection of an anomalous
'dark core' -- an over dense region with no optical counterpart -- which was
taken to be evidence for self-interacting dark-matter. In our Bayesian
framework it is found that neither Abel-520 dataset can conclusively determine
the physicality of such dark cores at 99% confidence. However, in both cases
the recovered MAP estimators are consistent with both sets of data.
