Statistics within a Generalized Concept of Probability --- Hypothesis Testing with Interval Probabilities

Abstract

Interval probability (IP) (or imprecise probability) is a substantial extension of the usual calculus of probability aiming at a more comprehensive modelling of uncertainty. The talk starts with an informal introduction into the basic ideas of IP and its interpretation independent, unifying axiomization by Weichselberger (1999). Then the generalized Neyman Pearson problem, where both hypotheses are described by IP, is studied and its relation to maximin testing in case of complex, nonparametric, composite hypotheses is made apparent. Huber's and Strassen's "Neyman Pearson lemma for capacities" and the work following it is reviewed and extended to general IP. Finally, the construction of optimal tests in the general multivariate situation on finite spaces by linear programming is discussed and dualization is utilized to construct locally least favorable pairs.