The problem of model identification in the presence of outliers has received great attention and a wide variety of outlier identification approaches have been proposed. Yet, there is a great need to seek for more general solutions and a unified framework to solving various practical problems. We propose to formulate the model identification problem under a robust unified framework consisting of consecutive levels of Bayesian inference. The proposed Bayesian inference scheme not only yields maximum a posteriori (MAP) estimates of model parameters, but also provides an automated mechanism for determining hyperparameters of the model parameters' prior distributions and for investigating the quality of each data point. The effectiveness of the developed robust framework will be demonstrated on the simulated data-sets.