Dec. 14 2009 2:00PM

Dec. 14 2009 3:30PM

Decision theory is, in particular in economics, medical expert systems and statistics, an important tool for determining optimal decisions under uncertainty. Since the arising uncertainties are often too complex to be described by classical precise probability assessments, different concepts of imprecise probabilities have been developed where single probabilities are replaced by whole sets of probabilities - called credal sets. In order to successfully deal with data-based decision theory, topological properties of credal sets are crucial. This is because minimax theorems play an important role in decision theory and such theorems are based on topological properties. In the talk, different concepts of imprecise probabilities are compared and it is demonstrated that, in particular, Walley's concept of coherent lower previsions appears to have advantageous properties for applications in decision theory. However, it is also pointed out that modeling with coherent lower previsions needs some care because an unfortunate choice may lead to arbitrary results. This is a consequence of the fact that the commonly used method of natural extension suffers from a severe instability.

Pravidelný seminář Inteligentní systémy (Kontaktní osoba: Tomáš Kroupa)