In this paper, we discuss the formulation and solution to the newsvendor problem under a Bayesian framework that allows the incorporation of uncertainty on the parameters of the demand model (introduced by the estimation process of these parameters). We present an application of this model with an analytical solution and we conduct experiments to compare the results under the proposed method and a classical approach. Furthermore, we illustrate the estimation of the optimal order size using stochastic simulation, when the complexity of the model does not allow the finding of a closed form expression for the solution.