The different models

A statistical problem can be characterized by the fact that observations are given from an unknown probability distribution, and a decision has to be made on the basis of these observations. This decision can be a point estimate, a test, a confidence interval, a forecast... .

The set of observed variables is summarized by a random variable X, with values in a space E, and whose law μ _X belongs to the family P of possible laws. The triplet M = (E, B, P), where B is the class of probabilistic parts of E, is then...