Probability distributions and coverage probability in GUM, JCGM documents, and statistical inference

• JCGM documents have distorted the operational view of GUM.
• JCGM views of probability distribution and coverage probability diverge from GUM.
• Standard deviation of JCGM probability distribution disagrees with GUM uncertainty.
• JCGM coverage interval and coverage probability are not well-defined.
• Bayesian interpretation is not relevant because measurands do not have unique values.

We discuss the interpretations of a probability distribution to express the state of knowledge about a quantity and the resulting coverage probability in the 1993 Guide to the Expression of Uncertainty in Measurement (GUM) and the subsequent JCGM documents: JCGM 101:2008, JCGM 104:2009, and JCGM 200:2008. The JCGM 101:2008 is titled ‘Supplement 1 to the GUM’ and the JCGM 104:2009 is titled ‘Introduction to the GUM and related documents’. It is reasonable to expect that they would have followed the GUM definitions of probability distribution and coverage probability. We submit that such is not the case. We submit that a connection between the standard deviation of a JCGM probability distribution and the GUM standard uncertainty is obscure. The JCGM interpretation of a probability distribution is seemingly based on Bayesian statistics. Also coverage probability has a well-established meaning in conventional statistics. Therefore we discuss the meanings of probability distribution and coverage probability in conventional and Bayesian statistical inference.