On the other hand, in many applications we have strong beliefs about what model to use to interpret the measurements. Thus, we focus our attention on the model parameters, which we consider as uncertain variables that we want to infer. The method which deals with these applications is usually referred as parametric inference, and it will be shown with examples in this section. In our models, the value of the relevant physical quantities are usually described in terms of a continuous uncertain variable. Bayes' theorem, properly extended to uncertain quantities (see Tab.1), plays a central role in this inference process.
A more complicate case is when we are also uncertain about the model (and each possible model has its own set of parameter, usually associated with different physics quantities). We shall analyse this problem in Sect. 7.