``A 95% confidence level lower bound of is obtained for the mass of the Standard Model Higgs boson.''may be misleading, because it transmits information which is inconsistent with the experimental observation. The interpretation of the result () is limited to
What are our rational beliefs on , on the basis of experiment A, releasing the condition ? The data cannot help much because there is no experimental sensitivity, and the conclusions depend essentially on the priors.
To summarize, the result of the inference is:
As a final remark on the presentation of the result, I would like to comment on the three significative digits with which the result on the `conditional lower bound' has been given. For the sake of the exercise the mass bound has been evaluated from the condition (). But does it really matter if the limit is 0.0782, rather than 0.0780, or 0.0800? As stated in Sections and , the limits have to be considered in the same way as the uncertainty. Nobody cares if the uncertainty of the uncertainty is 10 or 20%, and nobody would redo a MACRO-like experiment to lower the monopole limit by 20%. Simply translating this argument to the case under study, it may give the impression that one significant digit would be enough (0.08), but this is not true, if we stick to presenting the result under the condition that is smaller than . In fact, what really matters, is not the absolute mass, but the mass difference with respect to the kinematical limit. If the experiment ran with infinite statistics and found `nothing', there is no interest in providing a detailed study for the limit: it will be exactly the same as the kinematical limit. Therefore, the interesting piece of information that the experimenter should provide is how far the lower bound is from the kinematical limit, i.e. what really matters is not the absolute mass scale, but rather the mass difference. In our case we have