A theoretical framework for Bayesian adaptive training of the parameters of a discrete hidden Markov model (DHMM) and of a semi-continuous HMM (SCHMM) with Gaussian mixture state observation densities is presented. In addition to formulating the forward-backward MAP (maximum a posteriori) and the segmental MAP algorithms for estimating the above HMM parameters, a computationally efficient segmental quasi-Bayes algorithm for estimating the state-specific mixture coefficients in SCHMM is developed. For estimating the parameters of the prior densities, a new empirical Bayes method based on the moment estimates is also proposed. The MAP algorithms and the prior parameter specification are directly applicable to training speaker adaptive HMMs. Practical issues related to the use of the proposed techniques for HMM-based speaker adaptation are studied. The proposed MAP algorithms are shown to be effective especially in the cases in which the training or adaptation data are limited.
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