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We demonstrate highly accurate recovery of weak gravitational lensing shearusing an implementation of the Bayesian Fourier Domain (BFD) method proposed byBernstein & 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 assignshapes to galaxies, instead compressing the pixel data D into a vector ofmoments M, such that we have an analytic expression for the probability P(M|g)of obtaining the observations with gravitational lensing distortion g along theline of sight. We implement an algorithm for conducting BFD's integrations overthe population of unlensed source galaxies which measures ~10galaxies/second/core with good scaling properties. Initial tests of this codeon ~10^9 simulated lensed galaxy images recover the simulated shear to afractional accuracy of m=0.0021+-0.0004, substantially more accurate than hasbeen demonstrated previously for any generally applicable method. Deep skyexposures generate a sufficiently accurate approximation to the noiseless,unlensed galaxy population distribution assumed as input to BFD. Potentialextensions of the method include simultaneous measurement of magnification andshear; multiple-exposure, multi-band observations; and joint inference ofphotometric redshifts and lensing tomography.

An accurate and practical method for inference of weak gravitational lensing from galaxy images