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.
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