An accurate and practical method for inference of weak gravitational
  lensing from galaxy images
  We demonstrate highly accurate recovery of weak gravitational lensing shear
using an implementation of the Bayesian Fourier Domain (BFD) method proposed by
Bernstein & Armstrong (2014, BA14), extended to correct for selection biases.
The BFD formalism is rigorously correct for Nyquist-sampled,
background-limited, uncrowded image of background galaxies. BFD does not assign
shapes to galaxies, instead compressing the pixel data D into a vector of
moments M, such that we have an analytic expression for the probability P(M|g)
of obtaining the observations with gravitational lensing distortion g along the
line of sight. We implement an algorithm for conducting BFD's integrations over
the population of unlensed source galaxies which measures ~10
galaxies/second/core with good scaling properties. Initial tests of this code
on ~10^9 simulated lensed galaxy images recover the simulated shear to a
fractional accuracy of m=0.0021+-0.0004, substantially more accurate than has
been demonstrated previously for any generally applicable method. Deep sky
exposures generate a sufficiently accurate approximation to the noiseless,
unlensed galaxy population distribution assumed as input to BFD. Potential
extensions of the method include simultaneous measurement of magnification and
shear; multiple-exposure, multi-band observations; and joint inference of
photometric redshifts and lensing tomography.
