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The consistency of the Bayesian estimation of a parameter is shown for aclass of ergodic discrete Markov chains. J.L. Doob's method was used, offeredearlier for the i.i.d. situation. The result may be useful in the reliabilitytheory for models with unknown parameters, in the risk management in financialmathematics, and in other applications.

On consistency of Bayesian parameter estimations for a class of ergodic Markov models