  We develop the maximum-entropy weak shear mass reconstruction method
presented in earlier papers by taking each background galaxy image shape as an
independent estimator of the reduced shear field and incorporating an intrinsic
smoothness into the reconstruction. The characteristic length scale of this
smoothing is determined by Bayesian methods. Within this algorithm the
uncertainties due to both the intrinsic distribution of galaxy shapes and
galaxy shape estimation are carried through to the final mass reconstruction,
and the mass within arbitrarily shaped apertures can be calculated with
corresponding uncertainties. We apply this method to two clusters taken from
n-body simulations using mock observations corresponding to Keck LRIS and
mosaiced HST WFPC2 fields. We demonstrate that the Bayesian choice of smoothing
length is sensible and that masses within apertures (including one on a
filamentary structure) are reliable, provided the field of view is not too
small. We apply the method to data taken on the cluster MS1054-03 using the
Keck LRIS (Clowe et al. 2000) and HST (Hoekstra et al. 2000), finding results
in agreement with this previous work; we also present reconstructions with
optimal smoothing lengths, and mass estimates which do not rely on any
assumptions of circular symmetry. The code used in this work (LensEnt2) is
available from the web.
