A method for the identification of single input single output linear systems is presented. The method employs a Bayesian approach to compute the posterior distribution of the model parameters given the data-set. Since this distribution is often unavailable in closed form, a Metropolis Hastings algorithm is implemented to draw samples from it. To implement the sampler, the inclusion of prior information regarding the model order of the identified system is discussed. As one of the main contributions of this work, a prior over the Hankel singular values of the model is imposed. Numerical examples illustrate the method.