Evaluating the Uncertainty of Input Quantities in Measurement Models
Antonio M. Possolo
The Guide to the Expression of Uncertainty in Measurement gives guidance about how values and uncertainties should be assigned to the input quantities that appear in measurement models. This contribution offers a concrete proposal for how that guidance may be updated in light of the advances in the evaluation and expression of measurement uncertainty that were made in the course of the twenty years that have elapsed since the publication of that Guide, and also considering situations that the Guide does not contemplate. Our motivation is the ongoing conversation about a new edition of the Guide. While generally we favor a Bayesian approach, we also recognize the value that other approaches occasionally may bring to the problems considered here, and focus on methods that are widely applicable, including to cases that the Guide could not address. Besides Bayesian methods, we discuss maximum likelihood estimation, robust statistical methods, and measurement models where values of nominal properties play the same role that input quantities play in traditional models. We illustrate these general purpose techniques in concrete examples, employing data sets that are realistic but that also are of conveniently small sizes. The supplementary material available online lists the R computer code that we have used to produce these examples. Although we strive to stay close to Clause 4 of the GUM, we depart from it as we review the class of measurement models that we believe are generally useful in contemporary measurement science. We also greatly expand and update the treatment that the Guide gives to Type B evaluations of uncertainty: reviewing the state-of-the-art, disciplined approach to the elicitation of expert knowledge, and its encapsulation in probability distributions that are usable in uncertainty propagation exercises.
GUM, input quantities, uncertainty evaluation, elicitation, nominal properties, logit, probit, probability distributions, robust statistical methods, Bayesian methods, maximum likelihood, time series, AIC, measurement model, measurement equation, observation equation, Weibull, dental materials, Type A, Type B, Poisson counts, Poisson rates.