Contribution to a conversation about the Supplement 1 to the GUM

Abstract

A recent contribution to this journal describes a particular situation of uncertainty assessment where probabilistically symmetric coverage intervals, produced in accordance with the Supplement 1 to the GUM, cover the measurand with frequency much smaller than their nominal coverage probability, in a long sequence of simulated repetitions of the measurement process and corresponding uncertainty assessment, in each of which the value of the measurand is assumed known.These findings motivate our contribution to the ongoing, accelerating discussion of that Supplement, which began years before its publication, and has only gained momentum with the recent release of its final form.We begin by suggesting that the coverage intervals whose frequentist performance has been found to be poor, indeed are coverage intervals for a quantity different from the measurand that is the focus of attention, and we offer a fresh viewpoint wherefrom to appreciate the situation.Next, we point out that the Monte Carlo method for uncertainty propagation that is the core contribution of Supplement 1 is valid under very general conditions, indeed much more general than the conditions Supplement 1 lists as sufficient for its valid application.To produce a coverage interval according to the Supplement 1 involves two steps: generating a sample of values of the measurand via a Monte Carlo procedure and then summarizing this sample into a coverage interval. Although the Supplement favours probabilistically symmetric intervals, it also states explicitly that other prescriptions are tenable. With this in mind, finally we explain that the choice of summarization can be interpreted as reflecting a priori beliefs about the measurand.In the particular case under consideration in the motivating contribution, where the measurand is known to be non-negative, the choice of either a probabilistically symmetric interval or an interval whose left endpoint is 0 would correspond to two quite different prior beliefs. Considering this lesson, we suggest that, in all cases, the best course of action is to adopt a Bayesian approach that naturally reveals all participating assumptions and beliefs openly, and makes all of them accessible to examination and criticism, as befits every scientific procedure.

Use of Pooled Standard Deviation of Paired Samples in Calculating the Measurement Uncertainty by the Monte Carlo Method

“…In case of using the standard deviation obtained from a sample, one degree of freedom was attributed to v. When using the pooled standard deviation, degrees of freedom attributed to v were equal to 19. The sensitivity coefficients are calculated according to equations (11) to (14). An example of calculating the measurement uncertainty, evaluated from a single sample, is shown in Figure 9.…”

“…According Possolo [11] and Suzuki et al [12], the MCM, differently from GUM Framework, uses the concept of probability distributions propagation of the input quantities and not only the propagation of the standard uncertainties, as recommended by the traditional method. That is, the probability distribution of each source of uncertainty is propagated through the measurement equation.…”

Prospects of industrial consumption embedded final emissions: a revision on Chinese household embodied industrial emissions

“…This simulation method has several advantages over the conventional measures of uncertainties 48 . The 'GUM supplement 1' provides the general provisions for the 'propagation' of uncertainties under this approach 49 . Under MCS, 'pseudorandom' numbers are produced using algorithms; afterwards these numbers are imposed to follow a set 'probability distribution' .…”

Deriving PDFs for Interrelated Quantities: What to Do If There Is “More Than Enough” Information?

“…Here, the symbol ξ b designates the set of variables that represent the possible values of the quantities X b . In these circumstances, the PDF for the quantities in any other parameterization X p can be obtained by means of the change-of-variables theorem (CVT) [7]- [9] …”