Neyman-Pearson Testing under Interval Probability by Globally Least Favorable Pairs: A Survey of Huber-Strassen Theory and Some Results on its Extension to General Interval Probability

The paper studies the extension of one of the basic issues of
classical statistics to interval probability. It is concerned with
the Generalized Neyman-Pearson problem, i.e. an alternative testing
problem where both hypotheses are described by interval
probability. First the Huber-Strassen theorem and the literature
based on it is reviewed. Then some results are presented indicating
that the restrictive assumption of C-probability (two-monotonicity)
underlying all that work can be overcome in favor of considering
general interval probability in the sense of Weichselberger
(1999A). So the full expressive power, which is provided by
interval probability, can also be utilized in testing hypotheses.