Dark uncertainty in key comparisons in the gas analysis area

Abstract

CCQM-K118 natural gas is among the first key comparisons in the gas analysis area where a model was chosen to fit the data that considered possible overdispersion (‘dark uncertainty’) of the submitted results. As the key comparison was operated with as many travelling standards as there were participants, a Bayesian hierarchical model was developed that also took into account the (small) differences between the measurands across the suite of standards. As there was no independent reference value, such as from static gravimetry, the key comparison was evaluated using a consensus value. In this paper, we assess the performance of the model used in CCQM-K118 using the data from two previous key comparisons about the natural gas composition, CCQM-K23 and CCQM-K16. These key comparisons were operated with independent reference values and showed different levels of dispersion and agreement in the results. From the re-evaluation of the data, we conclude that the model developed for CCQM-K118 is fit for purpose and captures aptly the differences across the measurands for the different travelling standards and the overdispersion of the data. We also conclude that if there is no overdispersion of the data, this is reflected in the posterior probability distribution of the excess standard deviation. The representative value (e.g. median) of this standard deviation becomes then small if not negligible in comparison to the uncertainties stated by the participants.