Simple Guide for Evaluating and Expressing the Uncertainty of NIST Measurement Results

Abstract

Measurement is an informative assignment of value to quantitative or qualitative properties involving comparison with a standard (§2). Property values that are imperfectly known are modeled as random variables whose probability distributions describe states of knowledge about their true values (§3). Procedure (1) Measurand & Measurement Model. Define the measurand (property intended to be measured, §2), and formulate the measurement model (§4) that relates the value of the measurand (output) to the values of inputs (quantitative or qualitative) that determine or influence its value. Measurement models may be: • Measurement equations (§6) that express the measurand as a function of inputs for which estimates and uncertainty evaluations are available (Example E3); • Observation equations (§7) that express the measurand as a function of the pa rameters of the probability distributions of the inputs (Examples E2 and E14). (2) Inputs. Observe or estimate values for the inputs, and characterize associated uncer tainties in ways that are fit for purpose: at a minimum, by standard uncertainties or similar summary characterizations; ideally, by assigning fully specified probability dis tributions to them, taking correlations between them into account (§5). (3) Uncertainty Evaluation. Select either a bottom-up approach starting from an uncer tainty budget (or, uncertainty analysis), as in TN1297 and in the GUM, or a top-down approach, say, involving a proficiency test (§3f). The former typically uses a measure ment equation, the latter an observation equation. (3a) If the measurement model is a measurement equation, and • The inputs and the output are scalar (that is, real-valued) quantities: use the NIST Uncertainty Machine (NUM, uncertainty.nist.gov) (§6); • The inputs are scalar quantities and the output is a vectorial quantity: use the results of the Monte Carlo method produced by the NUM as illustrated in Example E15, and reduce them using suitable statistical analysis software (§6); • Either the output or some of the inputs are qualitative: use a custom version of the Monte Carlo method (Example E6). (3b) If the measurement model is an observation equation: use an appropriate statistical method, ideally selected and applied in collaboration with a statistician (§7). (4) Measurement Result. Provide an estimate of the measurand and report an evaluation of the associated uncertainty, comprising one or more of the following (§8): • Standard uncertainty (for scalar measurands), or an analogous summary of the dispersion of values that are attributable to the measurand (for non-scalar measurands); • Coverage region: set of possible values for the measurand that, with specified probability, is believed to include the true value of the measurand; • Probability distribution for the value of the measurand, characterized either analytically (exactly or approximately) or by a suitably large sample drawn from it.

Likelihood Ratio as Weight of Forensic Evidence: A Closer Look

“…From the perspective of metrology, the hybrid LR framework asks a forensic expert to measure the weight of evidence on behalf of the DM and report its value for subsequent use in Bayes' formula. As a measurement, any provided LR value would require an accompanying uncertainty statement (JCGM [53]; Possolo [54]) characterizing the analyst's belief regarding its deviation from the "true value," which the Bayesian paradigm defnes as the LR value a given DM would arrive at following careful review of the complete body of evidence considered by the expert. Overlooking or dismissing the relevant uncertainty would treat the value obtained by an expert as though it is a perfect measurement of weight of evidence, universally and exactly accurate.…”

Invited Article: Concepts and tools for the evaluation of measurement uncertainty

“…Our approach to the evaluation of measurement uncertainty is model-based, and so are the approaches described in the gum, by Taylor and Kuyatt in 1994 for nist, 6,7 and by EURACHEM 81 (a network of European organizations aiming to establish a system for the international traceability of chemical measurements and the promotion of good quality practices, www.eurachem.org), among many others. Therefore, we begin by reviewing the roles that models play in measurement, generally inspired by Tal.…”

“…V). [5][6][7] In this article, we focus on the measurement of properties of interest to the physical sciences and to derivative technologies and their applications, including physics, chemistry, biology, engineering, agriculture, manufacturing, etc. We do not discuss measurements of psychological or sensory properties of living organisms, like intelligence, preference, taste, or smell, nor measurements of properties of human or animal populations or of their economic or social interactions.…”

“…When the measurement equation involves some qualitative inputs, or when the output is qualitative, then uncertainty evaluation and propagation cannot be done using the technology in the gum, but may be practicable instead using a customized version of the Monte Carlo method, as in Example E6 (dna Sequencing) of the Simple Guide. 7 The uncertainty evaluation hinges on modeling the inputs and the output as random variables, with the understanding that any quantity value surrounded by uncertainty may be so modeled regardless of its intrinsic nature (for example, whether it is "fixed" or "variable," in any senses of these words). The gum explains (in Note 1 of 4.1.1) that "the same symbol is used for the physical quantity [.…”

Interpreting and propagating the uncertainty of the standard atomic weights (IUPAC Technical Report)

“…Measurement uncertainty characterizes a state of knowledge about the value of a quantity [28,29]. This state of knowledge may pertain to a particular person or to a group of persons, typically a scientific community.…”