Towards Selecting Appropriate Statistical Characteristics: The Basics of Decision Theory and the Notion of Utility

Abstract

In the previous chapter, we mentioned that in general, the problem of estimating statistical characteristics under interval uncertainty is NP-hard. This means, crudely speaking, that it is not possible to design a feasible algorithm that would compute all statistics under interval uncertainty. It is therefore necessary to restrict ourselves to statistical characteristics which are practically useful.

Which statistical characteristics should we estimate? One of the main objectives of data processing is to make decisions. Thus, to find the most appropriate statistical characteristics, let us recall the traditional way of making decisions based on user’s preference: the decision theory.