Bayesian approach of measurement uncertainty evaluation

For the purposes of this article, it is assumed that the fundamental steps of specifying the measurand and analyzing the measurement process—which lead to a list of influencing quantities—have already been completed. Indeed, these steps are common to any measurement uncertainty assessment and determine the scope of the uncertainty assessment performed. It should also be noted that the model used to represent the relationships between quantities (a measurement model or statistical model, as explained below) is not unique and is developed by combining the metrologist’s expertise and knowledge to address a specific need or requirement.

The Bayesian approach is attracting growing interest in metrology, where it is now recognized as one of the methods for evaluating uncertainty within the framework of the "Guide to the Expression of Measurement Uncertainty" (see JCGM GUM 6 ). Its popularity stems from its ability to model uncertainty, incorporate prior knowledge, and enable the analysis of complex data within a unified probabilistic framework, thereby increasing the reliability of results and associated decision-making. According to Lindley , the Bayesian framework is, by its very nature, the only one suitable for representing measurement uncertainty. Furthermore, metrologists appreciate being able to rely on the existing links between the Bayesian approach and the traditional methods of JCGM 100 and JCGM 101. This allows them, on the one hand, to maintain consistency with previous uncertainty evaluations, and on the other hand, to explore the potential offered by the Bayesian approach for specific applications. It is thus common for a traditional uncertainty calculation to have been performed before embarking on a fully Bayesian approach.

Unlike the classical frequentist framework, the Bayesian framework holds that every parameter of a statistical model can be represented...