  The principles of measuring the shapes of galaxies by a model-fitting
approach are discussed in the context of shape-measurement for surveys of weak
gravitational lensing. It is argued that such an approach should be optimal,
allowing measurement with maximal signal-to-noise, coupled with estimation of
measurement errors. The distinction between likelihood-based and Bayesian
methods is discussed. Systematic biases in the Bayesian method may be evaluated
as part of the fitting process, and overall such an approach should yield
unbiased shear estimation without requiring external calibration from
simulations. The principal disadvantage of model-fitting for large surveys is
the computational time required, but here an algorithm is presented that
enables large surveys to be analysed in feasible computation times. The method
and algorithm is tested on simulated galaxies from the Shear TEsting Program
(STEP).
