  We extend the Bayesian model fitting shape measurement method presented in
Miller et al. (2007) and use the method to estimate the shear from the Shear
TEsting Programme simulations (STEP). The method uses a fast model fitting
algorithm which uses realistic galaxy profiles and analytically marginalises
over the position and amplitude of the model by doing the model fitting in
Fourier space. This is used to find the full posterior probability in
ellipticity so that the shear can be estimated in a fully Bayesian way. The
Bayesian shear estimation allows measurement bias arising from the presence of
random noise to be removed. In this paper we introduce an iterative algorithm
that can be used to estimate the intrinsic ellipticity prior and show that this
is accurate and stable. By using the method to estimate the shear from the
STEP1 simulations we find the method to have a shear bias of m ~ 0.005 and a
variation in shear offset with PSF type of sigma_c ~ 0.0002. These values are
smaller than for any method presented in the STEP1 publication that behaves
linearly with shear. Using the method to estimate the shear from the STEP2
simulations we find than the shear bias and offset are m ~ 0.002 and c ~
-0.0007 respectively. In addition we find that the bias and offset are stable
to changes in magnitude and size of the galaxies. Such biases should yield any
cosmological constraints from future weak lensing surveys robust to systematic
effects in shape measurement.
