Comments on the Unified approach to the construction of Classical confidence intervals

Abstract

The paper comments on properties of the so-called "Unified approach to the construction of classical confidence intervals", in which confidence intervals are computed in a Neyman construction using the likelihood ratio as ordering quantity. In particular, two of the main results of a paper by Feldman and Cousins (F&C) are discussed. It is shown that in the case of central intervals the so-called flip-flopping problem, occuring in the specific scenario where the experimenter decides to quote a standard upper limit or a confidence interval depending on the measurement, can be easily avoided by choosing appropriate confidence levels for the standard upper limits and confidence intervals. In the F&C paper "upper limit" is defined as the upper edge of a confidence interval, whose lower edge coincides with the physical limit. With this definition of upper limit (F&C limit), in an approach which uses the likelihood ratio as ordering quantity, two-sided confidence intervals automatically change over to "upper limits" as the signal becomes weaker (Unified approach). In the present paper it is pointed out that this behaviour is not a special property of this approach, because approaches with other ordering principles, like central intervals, symmetric intervals or highest-probability intervals, exhibit the same behaviour. The Unified approach is presented in the F&C paper as a solution to the flip-flopping problem. This might suggest that the F&C limit is a standard upper limit. In order to exclude any misunderstanding, it is proposed in the present paper to call the F&C limit "upper edge of the confidence interval", even if its lower edge coincides with the physical limit.