An Implementation of Bayesian Lensing Shear Measurement
  The Bayesian gravitational shear estimation algorithm developed by Bernstein
and Armstrong (2014) can potentially be used to overcome multiplicative noise
bias and recover shear using very low signal-to-noise ratio (S/N) galaxy
images. In that work the authors confirmed the method is nearly unbiased in a
simplified demonstration, but no test was performed on images with realistic
pixel noise. Here I present a full implementation for fitting models to galaxy
images, including the effects of a point spread function (PSF) and
pixelization. I tested the implementation using simulated galaxy images modeled
as Sersic profiles with n=1 (exponential) and n=4 (De Vaucouleurs'), convolved
with a PSF and a flat pixel response function. I used a round Gaussian model
for the PSF to avoid potential PSF-fitting errors. I simulated galaxies with
mean observed, post-PSF full-width at half maximum equal to approximately 1.2
times that of the PSF, with log-normal scatter. I also drew fluxes from a
log-normal distribution. I produced independent simulations, each with pixel
noise tuned to produce different mean S/N ranging from 10-1000. I applied a
constant shear to all images. I fit the simulated images to a model with the
true Sersic index to avoid modeling biases. I recovered the input shear with
fractional error less than 2 x 10^{-3} in all cases. In these controlled
conditions, and in the absence of other multiplicative errors, this
implementation is sufficiently unbiased for current surveys and approaches the
requirements for planned surveys.
