Revisiting the problem of the evaluation of the uncertainty associated with a single measurement

By international accord, the standard uncertainty of a directly measured quantity is taken as the square root of the variance of its probability density function (pdf). The pdf can be inferred from the dispersion of unbiased observations obtained by repeatedly measuring the quantity involved. If the quantity is not repeatedly measured, the apparent scarcity of experimental data may require consideration of information other than experimental data to assign the pdf and to evaluate the uncertainty; in this context, an evaluator tends intuitively to consider information linked with his experience. In this work, we report on a method, based on the theorem of Bayes, to assign the pdf and to evaluate the uncertainty of a quantity measured only once. This method allows us to include in the uncertainty evaluation the information concerning the evaluator's experience. It gives theoretical support to the intuition since it satisfies the formalities of statistical inference. Two examples are presented.