The conceptual and technical framework of probability theory and the data-analytic tools from statistical science are enabling technologies for measurement science. This overview is a refresher or a primer on these technologies that support normative and prescriptive accounts of the analysis of measurement uncertainty, including the GUM and its Supplements: and it assumes no more knowledge of mathematics, probability, or statistics than undergraduate curricula in the sciences or engineering typically provide. The different meanings of probability, the rules that govern the combination of probabilities, and the concepts of probability distribution, independence, and exchangeability, are the basis for the expression, calculation, and interpretation of measurement uncertainty. Both measurement nist-equations and observation nist-equations are presented as instances of measurement models, and the conditions are discussed when one, or the other, may offer the most advantageous starting point for uncertainty analysis. Direct methods, either based on Taylor approximations or on analytical or Monte Carlo propagation of distributions, solve the problems that the GUM addresses, where the uncertainty of input quantities is propagated to an output quantity that the input quantities do not, in turn, depend upon. Inverse methods are best suited to situations where initial focus ought best be placed on the data rather than on the measurand: in such cases, the inversion of viewpoint whereby it finally focuses on the measurand is accomplished by the same probabilistic mechanism that extracts the relevant information from the data and blends it with any pre-existing information about the measurand.
JCGM WG1 Internal Document GUM Supplement 0
Error Propagation, Measurement Equation, Measurement uncertainty, Metrology, Monte Carlo, Observation Equation, Probability