One of the pillar generative machine learning approaches in time series data study and analysis is the hidden Markov model (HMM). Early research focused on the speech recognition application of the model with later expansion into numerous fields, including video classification, action recognition, and text translation. The recently developed generalized Dirichlet HMMs have proven efficient in proportional sequential data modeling. As such, we focus on investigating a maximum a posteriori (MAP) framework for the inference of its parameters. The proposed approach differs from the widely deployed Baum-Welch through the placement of priors that regularizes the estimation process. A feature selection paradigm is also integrated simultaneously in the algorithm. For validation, we apply our proposed approach in the classification of dynamic textures and the recognition of infrared actions.