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# Inferring numerical values of physics quantities -- General ideas and basic examples

In physics we are concerned about models ('theories') and the numerical values of physical quantities related to them. Models and the value of quantities are, generally speaking, the hypothesis we want to infer, given the observations. In the previous section we have learned how to deal with simple hypotheses, `simple' in the sense that they do not depend on internal parameters.

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.

Subsections

Next: Bayesian inference on uncertain Up: Bayesian Inference in Processing Previous: Inference for simple hypotheses
Giulio D'Agostini 2003-05-13