Empirical Bayes estimation of parameters in Markov transition probability matrix with computational methods

Empirical Bayes estimator for the transition probability matrix is worked out in the cases where we have belief regarding the parameters, For example, where the states seem to be equal or not. In both cases, priors are in accordance with our beliefs. Using EM algorithm, computational methods for different hyperparameters of the empirical Bayes are described. Also, robustness of empirical Bayes procedure is investigated.