What can we learn from the GUM of 1995?

• Recommendation INC-1 intended that systematic errors be given frequentist variances.
• It was misunderstood, the result being a mixture of frequentist and Bayesian ideas.
• The GUM is being revised to follow ‘objective Bayesian’ statistics.
• Logical problems arise with ‘objective Bayesian’ statistics in metrology.
• An alternative approach true to Recommendation INC-1 is proposed.

The Guide to the Expression of Uncertainty in Measurement (GUM) of 1995 is known to be flawed in aspects of it statistical theory and is now undergoing revision. This article considers three controversies faced in the development of such a document, namely (i) the acceptance of the existence of ‘true values’, (ii) the association of variances with systematic influences and (ii) the representation of fixed but unknown quantities by probability distributions, which is a step that separates Bayesian statistics from frequentist, i.e. classical, statistics. Particular attention is paid to Recommendation INC-1 of 1980, which is said to be the foundation of the GUM. This advocates that variances be associated with systematic effects in a manner according with frequentist statistics. However, the revision of the GUM is being carried out along Bayesian lines. A number of difficulties are identified with this approach.