Info-gap’s uncertainty model

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 u:

  • An uncertainty space, \mathscr{U}, that is a set consisting of all the possible/plausible values of u.
  • A point estimate of the true value of u, call it \tilde{u}.

As in the case of radius of stability models, info-gap decision theory imposes a neighborhood structure on \mathscr{U}. That is, a fundamental assumption of this theory is that there is a family of nested sets N(\rho,\tilde{u}),\rho\ge 0, centered at \tilde{u} where N(\rho,\tilde{u})\subseteq \mathscr{U} denotes a neighborhood of size (radius) \rho around \tilde{u}. These neighborhoods are assumed to have the following two basic properties:

  • N(0,\tilde{u}) = \{\tilde{u}\} (contraction)
  • N(\rho,\tilde{u}) \subseteq  N(\rho + \varepsilon,\tilde{u}), \forall \rho,\varepsilon\ge 0 (nesting)

The parameter \rho 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 \mathscr{U} can be vast (e.g. unbounded)
  • The point estimate \tilde{u} 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 u is more/less likely to be in the neighborhood of any particular value of u\in \mathscr{U}. Specifically, there are no grounds to assume that the true value of u is more/less likely to be in the neighborhood of the point estimate \tilde{u} than in the neighborhood of any other u\in \mathscr{U}.

More …

Advertisements

Your comment:

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s