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Bodnar, Olha
Publications (5 of 5) Show all publications
Bodnar, O. & Possolo, A. (2018). Approximate Bayesian Evaluations of Measurement Uncertainty. In: : . Paper presented at XV International Scientific and Technical Seminar Measurement Uncertainty: Scientific, Normative, Applied and Methodical Aspects (pp. 4-4).
Open this publication in new window or tab >>Approximate Bayesian Evaluations of Measurement Uncertainty
2018 (English)Conference paper, Oral presentation with published abstract (Other academic)
Keywords
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:nbn:se:mdh:diva-41059 (URN)
Conference
XV International Scientific and Technical Seminar Measurement Uncertainty: Scientific, Normative, Applied and Methodical Aspects
Available from: 2018-09-28 Created: 2018-09-28 Last updated: 2018-10-01Bibliographically approved
Bodnar, O. & Possolo, A. (2018). Approximate Bayesian evaluations of measurement uncertainty. Metrologia, 55, 147-157
Open this publication in new window or tab >>Approximate Bayesian evaluations of measurement uncertainty
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.

Keywords
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:nbn:se:mdh:diva-41063 (URN)10.1088/1681-7575/aaa5be (DOI)2-s2.0-85045694539 (Scopus ID)
Available from: 2018-09-28 Created: 2018-09-28 Last updated: 2018-12-03Bibliographically approved
Possolo, A., Bodnar, O., Butler, T. A., Molloy, J. L. & Winchester, M. R. (2018). Value assignment and uncertainty evaluation for single-element reference solutions. Metrologia, 55(3), 404-413
Open this publication in new window or tab >>Value assignment and uncertainty evaluation for single-element reference solutions
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2018 (English)In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, no 3, p. 404-413Article in journal (Refereed) Published
Abstract [en]

A Bayesian statistical procedure is proposed for value assignment and uncertainty evaluation for the mass fraction of the elemental analytes in single-element solutions distributed as NIST standard reference materials. The principal novelty that we describe is the use of information about relative differences observed historically between the measured values obtained via gravimetry and via high-performance inductively coupled plasma optical emission spectrometry, to quantify the uncertainty component attributable to between-method differences. This information is encapsulated in a prior probability distribution for the between-method uncertainty component, and it is then used, together with the information provided by current measurement data, to produce a probability distribution for the value of the measurand from which an estimate and evaluation of uncertainty are extracted using established statistical procedures.

Place, publisher, year, edition, pages
IOP PUBLISHING LTD, 2018
National Category
Mathematics Probability Theory and Statistics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-39295 (URN)10.1088/1681-7575/aabd57 (DOI)000431827100002 ()2-s2.0-85048238027 (Scopus ID)
Available from: 2018-05-24 Created: 2018-05-24 Last updated: 2018-12-10Bibliographically approved
Bodnar, O., Elster, C. & Wübbeler, G. (2017). Robust Bayesian Linear Regression with Application to an Analysis of the CODATA Values for the Planck Constant. Metrologia, 55(1), 20-28
Open this publication in new window or tab >>Robust Bayesian Linear Regression with Application to an Analysis of the CODATA Values for the Planck Constant
2017 (English)In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 55, no 1, p. 20-28Article in journal (Refereed) Published
Abstract [en]

Weighted least-squares estimation is commonly applied in metrology to fit models to measurements that are accompanied with quoted uncertainties. The weights are chosen in dependence on the quoted uncertainties. However, when data and model are inconsistent in view of the quoted uncertainties, this procedure does not yield adequate results.

When it can be assumed that all uncertainties ought to be rescaled by a common factor, weighted least-squares estimation may still be used, provided that a simple correction of the uncertainty obtained for the estimated model is applied. We show that these uncertainties and credible intervals are robust, as they do not rely on the assumption of a Gaussian distribution of the data. Hence, common software for weighted least-squares estimation may still safely be employed in such a case, followed by a simple modification of the uncertainties obtained by that software. We also provide means of checking the assumptions of such an approach.

The Bayesian regression procedure is applied to analyze the CODATA values for the Planck constant published over the past decades in terms of three different models: a constant model, a straight line model and a spline model. Our results indicate that the CODATA values may not have yet stabilized

Keywords
Bayesian linear regression
National Category
Probability Theory and Statistics Other Physics Topics
Identifiers
urn:nbn:se:mdh:diva-41065 (URN)10.1088/1681-7575/aa98aa (DOI)
Available from: 2018-09-28 Created: 2018-09-28 Last updated: 2018-10-01Bibliographically approved
Bodnar, O. Analysis of Key Comparisons with Two Reference Standards: Extended Random Effects Meta-Analysis. In: Alistair B Forbes, Nien-Fan Zhang, Anna Chunovkina, Sascha Eichstädt (Ed.), Advanced Mathematical and Computational Tools in Metrology and Testing XI: . Singapore: World Scientific
Open this publication in new window or tab >>Analysis of Key Comparisons with Two Reference Standards: Extended Random Effects Meta-Analysis
(English)In: Advanced Mathematical and Computational Tools in Metrology and Testing XI / [ed] Alistair B Forbes, Nien-Fan Zhang, Anna Chunovkina, Sascha Eichstädt, Singapore: World ScientificChapter in book (Refereed)
Abstract [en]

We propose a statistical method for analyzing key comparisons with two transfer standards measured in two petals. The new approach is based on an extension of the established random effects model. A full Bayesian analysis based on the reference prior is developed and analytic expressions for the results are derived. One benefit of the suggested approach is that it provides a comprehensive assessment of the laboratory biases in terms of their posterior distributions. Another advantage is that it can easily be applied in practice. The approach is illustrated for the CCM.M-K7 key comparison data.

Place, publisher, year, edition, pages
Singapore: World Scientific
Keywords
extended random effects model, two transfer standards, reference analysis, CCM.M-K7
National Category
Probability Theory and Statistics Other Physics Topics
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-41060 (URN)9789813274297 (ISBN)
Available from: 2018-09-28 Created: 2018-09-28 Last updated: 2018-10-01Bibliographically approved
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