An implementation of Bayesian lensing shear measurement.

The Bayesian gravitational shear estimation algorithm developed by Bernstein & Armstrong 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 that 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 modelled as Sérsic 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 lognormal scatter. I also drew fluxes from a lognormal 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 fitted the simulated images to a model with the true Sérsic index to avoid modelling biases. I recovered the input shear with fractional error Δg/g < 2 × 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.