The Principle of Maximum Entropy Applied in the Evaluation of the Measurement Uncertainty

The maximum entropy approach is a flexible and powerful tool for assigning a probability distribution to a measurable quantity treated as a random variable subjected to known moment constraints. The aim of this paper is to describe how the principle of maximum entropy may be used to transform information about the value of a quantity into a probability density function (pdf) that reflects exactly that information and nothing else. This principle will be applied to common cases of metrological interest, where different kinds of information are available. The derivation of the pdf is given in each case, and two practical examples with numerical results are reported to demonstrate the efficiency of the maximum entropy method.