In this paper, we use the Bayesian method in the application of hypothesis testing and model selection to determine the order of a Markov chain. The criteria used are based on Bayes factors with noninformative priors. Comparisons with the commonly used AIC and BIC criteria are made through an example and computer simulations. The results show that the proposed method is better than the AIC and BIC criteria, especially for Markov chains with higher orders and larger state spaces.
