On Data-Based Checking of Hypotheses in the Presence of Uncertain Knowledge

Interval-probability (IP) is a substantial generalization of classical probability. It allows to adequately model different aspects of uncertainty without loosing the neat connection to the methodology of classical statistics. Therefore it provides a well-founded basis for data-based reasoning in the presence of uncertain knowledge. — The paper supports that claim by outlining the generalization of Neyman-Pearson-tests to IP. After introducing some basics of the theory of IP according to Weichselberger (1995, 1998) the fundamental concepts for tests are extended to IP; then the Huber-Strassen-theory is briefly reviewed in this context and related theorems for general IP are given. Finally further results are sketched.