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Approximate Bayesian evaluations of measurement uncertainty
Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik. (MAM)
National Institute of Standards and Technology, USA.
2018 (engelsk)Inngår i: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, s. 147-157Artikkel i tidsskrift (Fagfellevurdert) 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.

sted, utgiver, år, opplag, sider
2018. Vol. 55, s. 147-157
Emneord [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
HSV kategori
Forskningsprogram
matematik/tillämpad matematik
Identifikatorer
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
Tilgjengelig fra: 2018-09-28 Laget: 2018-09-28 Sist oppdatert: 2018-12-03bibliografisk kontrollert

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