The main objective of this study is to handle the identification problem for the moving average (MA) models from a Bayesian point of view. Two Bayesian approaches of identification, namely the direct and indirect approaches, are considered with two analytical approximations for the error term, namely Newbold and Broemeling-Shaarawy approximations. The two proposed techniques have been developed using each approximation and evaluated for MA models. The behavior of the Bayesian techniques has been checked and compared via a comprehensive simulation study. The simulation results show that performance of the direct and indirect techniques is affected by the approximation used, and the prior function. We have found that the direct technique seems to be more efficient than the indirect one. Moreover, the use of the Newbold approximation slightly improves the results more than the use of the Broemeling- Shaarawy   approximation.