On the role of probability in science, analytical measurement and QUAM

Recently, it has been shown that a probability distribution attributed to a constant, e.g. the true concentration of an analyte, cannot be used to accurately describe an objective set of information about the constant (Measurement Sensors 24, 2022, 100416;  Accreditation and Quality Assurance 29, 2024, 189–192). In this paper, that result is extended to show that such a distribution cannot always accurately describe subjective belief about it either. These results suggest that a logical system of uncertainty analysis in measurement can only be based on classical principles in which probability distributions describe patterns of measurements and errors under repetition. They call into question the premise underlying the approach to the evaluation of measurement uncertainty promoted in the supplements to the Guide to the Expression of Uncertainty in Measurement. The relevance of these results to the Eurachem/CITAC Guide Quantifying Uncertainty in Analytical Measurement (QUAM) is discussed, and QUAM is shown to be largely free of the problematic idea.