Stronger Classical Confidence Limits

A new way of defining limits in classical statistics is presented. This is a natural extension of the original Neyman’s method, and has the desirable property that only information relevant to the problem is used in making statistical inferences. The result is a strong restriction on the allowed confidence bands, excluding in full generality pathologies as empty confidence regions or unstable solutions. The method is completely general and directly applicable to all problems of limits. Some examples are discussed. In the well-known problem of Poisson processes with background it gives limits that do not depend on background in the case of no observed events.