O'Hagan, A; Cox, M (2023) Simple informative prior distributions for Type A uncertainty evaluation in metrology. Metrologia, 60 (2). 025003

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Abstract

The result of a measurement, including the expression of uncertainty in the measurement, should represent a carefully considered opinion based on the metrologist’s experience and expertise, as well as on the data and other information sources. This is the position of the Guide to the expression of uncertainty in measurement (GUM), and the requirement for such judgement is clear in the case of Type B evaluation. However, when making Type A evaluations, involving statistical analysis of data, the GUM and its various supplements implicitly consider the data to be the only relevant information. This is unfortunate, and arguably unscientific, when, as is frequently the case, the metrologist could bring other relevant information to bear.

Bayesian statistical methods allow the use of prior information in addition to the data in Type A evaluation, and have been advocated by several authors. However, prior information is in principle subjective; another metrologist may bring different prior information to the analysis, leading to a different measurement result. As in other fields, there is some resistance in the metrology community to embrace Bayesian methods using substantive, subjective prior probability distributions.
We identify four desiderata — justification, simplicity, sufficient benefit and verification — that a Bayesian method employing prior information should satisfy. We present two prior distributions for use in the most basic of all Type A evaluations, where the data comprise a sample of indications assumed to be normally distributed. They represent prior information about the variance of the normal errors, in a simple form that is readily justified in practice. We show the benefit of these prior distributions, both in the single Type A evaluation and in a more complex measurement model, and resent simple guidance for verifying their validity.

Item Type:	Article
Keywords:	Uncertainty evaluation; GUM; Type A evaluation; simple informative prior;
Subjects:	Mathematics and Scientific Computing > Measurement Uncertainties
Divisions:	Data Science
Identification number/DOI:	10.1088/1681-7575/acb93d
Last Modified:	02 May 2023 09:28
URI:	https://eprintspublications.npl.co.uk/id/eprint/9690