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Robust Bayesian Linear Regression with Application to an Analysis of the CODATA Values for the Planck Constant
Physikalisch-Technische Bundesanstalt, Braunschweig and Berlin, Germany.
Physikalisch-Technische Bundesanstalt, Braunschweig and Berlin, Germany.ORCID iD: 0000-0003-1359-3311
Physikalisch-Technische Bundesanstalt, Braunschweig and Berlin, Germany.
2018 (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.

Place, publisher, year, edition, pages
Institute of Physics Publishing (IOPP), 2018. Vol. 55, no 1, p. 20-28
Keywords [en]
linear regression, Birge ratio, Bayesian inference, Planck constant
National Category
Probability Theory and Statistics Other Physics Topics
Identifiers
URN: urn:nbn:se:oru:diva-76694DOI: 10.1088/1681-7575/aa98aaISI: 000417910600003Scopus ID: 2-s2.0-85041168714OAI: oai:DiVA.org:oru-76694DiVA, id: diva2:1354047
Available from: 2019-09-24 Created: 2019-09-24 Last updated: 2019-10-25Bibliographically approved

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Bodnar, Olha

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