It has been shown previously that systems based on local features and relatively complex generative models, namely 1D Hidden Markov Models (HMMs) and pseudo-2D HMMs, are suitable for face recognition (here we mean both identification and verification). Recently a simpler generative model, namely the Gaussian Mixture Model (GMM), was also shown to perform well. In this paper we first propose to increase the performance of the GMM approach (without sacrificing its simplicity) through the use of local features with embedded positional information; we show that the performance obtained is comparable to 1D HMMs. Secondly, we evaluate different training techniques for both GMM and HMM based systems. We show that the traditionally used Maximum Likelihood (ML) training approach has problems estimating robust model parameters when there is only a few training images available; we propose to tackle this problem through the use of Maximum a Posteriori (MAP) training, where the lack of data problem can be effectively circumvented; we show that models estimated with MAP are significantly more robust and are able to generalize to adverse conditions present in the BANCA database.