A Review of “A Unified Theory of Measurement Errors and Uncertainties” in the Context of Uncertainty Quantification in Nuclear Safeguards

A recent paper by H. Huang titled “A Unified Theory of Measurement Errors and Uncertainties” proposed modifications to the Guide to the Expression of Uncertainty in Measurements (GUM). Huang’s suggested modifications are non-Bayesian, in contrast to other recently-suggested Bayesian modifications to the GUM. Two of Huang’s key suggestions are: (1) to drop the use of the t-distribution that is used to estimate coverage intervals for the true measurand value (claiming that the t-distribution is a distorted transformation) and, (2) to use an unbiased estimate of the measurement error standard deviation. Regarding (1), the true measurand could, for example, be either a true mass or a true measurement error standard deviation. Regarding (2), the usual sample variance is unbiased for the true variance, but the usual sample standard deviation is biased low for the true standard deviation. This paper reviews these two suggestions in Huang’s paper in the context of both bottom-up (first-principles, using GUM or GUM-like measurement error variance propagation) and top-down (empirical, using, for example, inter-laboratory comparisons) uncertainty quantification (UQ) as used in nuclear safeguards. One point to emphasize is that there is very large uncertainty in any non-Bayesian estimate of a true standard deviation that is based on a small number of observations. This paper concludes with a brief review of the state of bottom-up and top-down UQ as currently practiced in many safeguards organizations