Bayes' decision theory has been developed in the book [Duda and Hart, 1973], from which we summarize the following fundamentals.

Bayes' decision theory is a fundamental statistical approach to the problem of pattern classification. This approach is based on the assumption that the decision problem is posed in probabilistic terms, and that all of the relevant probability values are known.

The aim of the decision is to assign an object to a class. This classification is only carried out by means of measurements taken over the objects.