The GUM, Bayesian inference and the observation and measurement equations

In this paper, we compare uncertainty evaluation procedures based on the measurement and observation equation approaches applied to a class of models covering many practical measuring systems. We derive general conditions for when the two approaches give the same distributions associated with the measurand and give examples of how and where they differ. We argue that while it is possible to interpret the measurement equation approach as determining a state of knowledge distribution for the measurand, for some problems there are conceptual, and for highly nonlinear models, practical difficulties with this interpretation. These conceptual difficulties do not arise if the measurement equation approach is interpreted as characterising the behaviour of a measuring system. The discussion presented here is relevant to the revision of the GUM, currently being undertaken by the Joint Committee for Guides in Metrology.