Abstract: This talk will be divided in two parts. In the first part, we will give an overview of the Bayesian approach to statistical inference, including modern computational techniques. In the second part, we will talk about a relatively new area of research, that of uncertainty quantification, in which the Bayesian methodology has proved to be particularly useful. We will discuss how concepts and ideas from this area can be applicable to economic models, with an emphasis on the concept of model discrepancy.