The current study handles the direct Bayesian identification of moving average processes based on different well known Informative and Non-Informativv priors. The priors considered in the article are g prior, natural-conjugate prior as well as Jeffreys' prior. Posterior probability mass functions for the order of moving average models are developed using the above mentioned three priors. Then, the value of the order with maximum probability is selected as the identified order of the model. In order to ease and simplify the computations, the likelihood function of the moving average process is approximated. Effectiveness of each posterior mass function in identifying an order for the model is assessed via Mont-Carlo simulations. Numerical results support the use of the proposed Bayesian technique to solve the identification problem of moving average processes. Furthermore, the performance of the technique using g prior is better than its performance using the natural-conjugate prior which, in turn, is slightly better than the performance using Jeffreys' prior.