Next: Bibliography Up: Asymmetric Uncertainties: Sources, Treatment Previous: Some rules of thumb

# Conclusions

Asymmetric uncertainties do exist and there is no way to remove them artificially. If they are not properly treated, i.e. using prescriptions that do not have a theoretical ground but are more or less rooted in the physics community, the published result is biased. Instead, if they are properly treated using probability theory, in most cases of interest the final result is practically symmetric and approximately Gaussian, with expected value and standard deviations which take into account the several shifts due to individual asymmetric contributions. Note that some of the simplified methods to make statistical analyses had a raison d'être many years ago, when the computation was a serious limitation. Now it is not any longer a problem to evaluate, analytically or numerically, integrals of the kind of those appearing e.g. in Eqs.(1), (13) and (14).

In the case the final uncertainty remains asymmetric, the authors should provide detailed information about the `shape of the uncertainty', giving also most probable value, probability intervals, and so on. But the best estimate of the expected value and standard deviation should be always given (see also the ISO Guide [14]).

To conclude, I would like to leave the final word to my preferred quotation with whom I like to end seminars and courses on probability theory applied to the evaluation and the expression of uncertainty in measurements:

``Although this
Guide
provides a framework for assessing uncertainty, it cannot substitute for critical thinking, intellectual honesty, and professional skill. The evaluation of uncertainty is neither a routine task nor a purely mathematical one; it depends on detailed knowledge of the nature of the measurand and of the measurement. The quality and utility of the uncertainty quoted for the result of a measurement therefore ultimately depend on the understanding, critical analysis, and integrity of those who contribute to the assignment of its value.''[14]

It is a pleasure to thank Superfaber (Fabrizio Fabbri in hepnames) for helpful discussions on the subject and for his supervision of the manuscript.

Next: Bibliography Up: Asymmetric Uncertainties: Sources, Treatment Previous: Some rules of thumb
Giulio D'Agostini 2004-04-27