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

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.

- Bayesian inference on uncertain variables and posterior characterization
- Gaussian model
- Binomial model
- Poisson model
- Inference from a data set and sequential use of Bayes formula
- Multidimensional case -- Inferring and of a Gaussian
- Predictive distributions
- Hierarchical modelling and hyperparameters
- From Bayesian inference to maximum-likelihood and minimum chi-square model fitting
- Gaussian approximation of the posterior distribution