# Info-gap’s uncertainty model

December 29, 2011 Leave a comment

Info-gap’s uncertainty model — designed to give expression to the uncertainty conditions that the theory deals with — is precisely the uncertainty model underlying radius of stability models, except that info-gap’s terminology is slightly different. In other words, info-gap’s uncertainty model consists of the following objects that are associated with a parameter of interest, call it :

- An
**uncertainty space**, , that is a set consisting of all the possible/plausible values of . - A
**point estimate**of the true value of , call it .

As in the case of radius of stability models, info-gap decision theory imposes a **neighborhood** structure on . That is, a fundamental assumption of this theory is that there is a family of nested sets centered at where denotes a neighborhood of size (radius) around . These neighborhoods are assumed to have the following two basic properties:

- (contraction)
- (nesting)

The parameter representing the size (radius) of the neighborhoods is called the **horizon of uncertainty**.

The **severity** of the uncertainty under consideration is manifested in these three characteristics:

- The uncertainty space can be
**vast**(e.g. unbounded) - The point estimate is
**poor**and can be**substantially wrong**. - The uncertainty is
**likelihood-free**.

The last means, among other things, that there are no grounds to assume that the true value of is more/less likely to be in the neighborhood of any particular value of . Specifically, there are no grounds to assume that the true value of is more/less likely to be in the neighborhood of the point estimate than in the neighborhood of any other .