Statistical notes on the problem of experimental observations near an unphysical region.

Abstract

We discuss the statistical problem of determining confidence intervals for a random variable from data near or within an unphysical region. As a typical example we use the case of the upper limit of the electron-neutrino mass as observed in tritium \ensuremath{\beta} decay. We argue that it is important to publish the value of the variable actually observed (the neutrino mass squared) for which the resolution function is known (e.g., Gaussian), even if a large part of this distribution lies in an unphysical region (negative squared mass). When having to choose between quoting a result which is unbiased and one which is physical, we argue that the unbiased result is to be preferred, largely because only unbiased results can be combined meaningfully. When a measured value falls in or near a nonphysical region, then the calculation of confidence limits is necessarily a subjective procedure which represents the physicist's personal interpretation of his results, and in that sense is less fundamental than the actual measured value.