Uncertainty assessments based on observation and measurement equations

At least two main approaches to the assessment of uncertainty in measurement have been proposed. One of them makes use of a measurement equation as stated in the GUM and its supplements to represent the model adopted for the measurement. The other approach, essentially the Bayesian inference, bases the assessment on an observation equation. It is shown here that the latter allows one to take prior knowledge about the measurand into account. It also allows measurement information to be used for updating knowledge about other non-observable quantitities. In addition, the transferability requirement of the GUM is satisfied. In contrast, the assessment based on a measurement equation hinders our learning process from measurement information.