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Approximate Bayesian evaluations of measurement uncertainty
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)
National Institute of Standards and Technology, USA.
2018 (English)In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, p. 147-157Article in journal (Refereed) Published
Abstract [en]

The Guide to the Expression of Uncertainty in Measurement (GUM) includes formulas that produce an estimate of a scalar output quantity that is a function of several input quantities, and an approximate evaluation of the associated standard uncertainty.

This contribution presents approximate, Bayesian counterparts of those formulas for the case where the output quantity is a parameter of the joint probability distribution of the input quantities, also taking into account any information about the value of the output quantity available prior to measurement expressed in the form of a probability distribution on the set of possible values for the measurand.

The approximate Bayesian estimates and uncertainty evaluations that we present have a long history and illustrious pedigree, and provide sufficiently accurate approximations in many applications, yet are very easy to implement in practice. Differently from exact Bayesian estimates, which involve either (analytical or numerical) integrations, or Markov Chain Monte Carlo sampling, the approximations that we describe involve only numerical optimization and simple algebra. Therefore, they make Bayesian methods widely accessible to metrologists.

We illustrate the application of the proposed techniques in several instances of measurement: isotopic ratio of silver in a commercial silver nitrate; odds of cryptosporidiosis in AIDS patients; height of a manometer column; mass fraction of chromium in a reference material; and potential-difference in a Zener voltage standard.

Place, publisher, year, edition, pages
2018. Vol. 55, p. 147-157
Keywords [en]
Laplace approximation, measurement uncertainty, Bayes rule, Gauss’s formula, ANOVA, random effects, Markov Chain Monte Carlo, homogeneity, cryptosporidiosis, manometer, reference material, between-bottle, within-bottle, Zener voltage standard
National Category
Probability Theory and Statistics Other Physics Topics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-41063DOI: 10.1088/1681-7575/aaa5beScopus ID: 2-s2.0-85045694539OAI: oai:DiVA.org:mdh-41063DiVA, id: diva2:1252008
Available from: 2018-09-28 Created: 2018-09-28 Last updated: 2018-12-03Bibliographically approved

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Bodnar, Olha

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CiteExportLink to record
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  • apa
  • ieee
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  • nn-NO
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