Deformetrica implements three estimation methods for minimizing the loss functions of the different models: a simple gradient ascent, the L-BFGS algorithm from SciPy.org, and a stochastic version of the EM algorithm (still unstable).
In general, we advise the use of the ScipyLBFGS estimator, which converges faster. The GradientAscent estimator might prove more robust in some situations, and is chosen by default for this reason.
The McmcSaem estimator can only be used with the bayesian and longitudinal atlas. This algorithm is still under development, its full support with the bayesian atlas is scheduled for Deformetrica 4.2.0.