Gary M. Bernstein, Robert Armstrong
We derive an estimator of weak gravitational lensing shear from background galaxy images that avoids noise-induced biases through a rigorous Bayesian treatment of the measurement. The Bayesian formalism requires a prior describing the (noiseless) distribution of the target galaxy population over some parameter space; this prior can be constructed from low-noise images of a subsample of the target population, attainable from long integrations of a fraction of the survey field. We find two ways to combine this exact treatment of noise with rigorous treatment of the effects of the instrumental point-spread function and sampling. The Bayesian model fitting (BMF) method assigns a likelihood of the pixel data to galaxy models (e.g. Sersic ellipses), and requires the unlensed distribution of galaxies over the model parameters as a prior. The Bayesian Fourier domain (BFD) method compresses galaxies to a small set of weighted moments calculated after PSF correction in Fourier space. It requires the unlensed distribution of galaxy moments as a prior, plus derivatives of this prior under applied shear. BFD is the first shear measurement algorithm that is model-free and requires no approximations or {\it ad hoc} assumptions in correcting for the effects of PSF, noise, or sampling on the galaxy images. These algorithms are good candidates for attaining the part-per-thousand shear inference required for hemisphere-scale weak gravitational lensing surveys.
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http://arxiv.org/abs/1304.1843
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