MAP Estimation of Continuous Density HMM: Theory and Applications 
 
 We discuss maximum a posteriori estimation of continuous density hidden Markov models (CDHMM) . The classical MLE reestimation algorithms , namely the forward-backward algorithm and the segmental k-means algorithm , are expanded and reestimation formulas are given for HMM with Gaussian mixture observation densities . Because of its adaptive nature, Bayesian learning serves as a unified approach for the following four speech recognition applications, namely parameter smoothing , speaker adaptation , speaker group modeling and corrective training . New experimental results on all four applications are provided to show the effectiveness of the MAP estimation approach . 