  We infer gravitational lensing shear and convergence fields from galaxy
ellipticity catalogs under a spatial process prior for the lensing potential.
We demonstrate the performance of our algorithm with simulated
Gaussian-distributed cosmological lensing shear maps and a reconstruction of
the mass distribution of the merging galaxy cluster Abell 781 using galaxy
ellipticities measured with the Deep Lens Survey. Given interim posterior
samples of lensing shear or convergence fields on the sky, we describe an
algorithm to infer cosmological parameters via lens field marginalization. In
the most general formulation of our algorithm we make no assumptions about weak
shear or Gaussian distributed shape noise or shears. Because we require
solutions and matrix determinants of a linear system of dimension that scales
with the number of galaxies, we expect our algorithm to require parallel
high-performance computing resources for application to ongoing wide field
lensing surveys.
