This work studies a Bayesian (or Maximum A Posteriori MAP) approach to the adaptation of Continuous Density Hidden Markov Models (CDHMMs) to a specific condition of a speech recognition application. In order to improve the model robustness, CDHMMs formerly trained from laboratory data are then adapted using context dependent field utterances. Two specific problems have to be faced when using the MAP approach: the estimation of the a priori distribution parameters and the lack of field adaptation data for some distributions of the CDHMM. To estimate the a priori distribution parameters, we need to identify different realizations of the model parameters. Three different solutions are proposed and evaluated. To overcome the lack of adaptation data, field acoustical training frames may be shared among similar distributions. This is performed using an acoustical tree, obtained by progressively clustering the model distributions. Recognition results show that MAP adapted models significantly outperform those trained by Maximum Likelihood (ML), specifically when the field data set is small.