In our previous work, we introduced our Bayesian Hidden Markov Model with eigenvoice priors, which has been recently recognized as the state-of-the-art model for Speaker Diarization. In this article we present a more complete analysis of the Diarization system. The inference of the model is fully described and derivations of all update formulas are provided for a complete understanding of the algorithm. An extensive analysis on the effect, sensitivity and interactions of all model parameters is provided, which might be used as a guide for their optimal setting. The newly introduced speaker regularization coefficient allows us to control the number of speakers inferred in an utterance. A naive speaker model merging strategy is also presented, which allows to drive the variational inference out of local optima. Experiments for the different diarization scenarios are presented on CALLHOME and DIHARD datasets.