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Bayesian estimation in multivariate inter-laboratory studies with unknown covariance matrices
Örebro University, Örebro University School of Business. National Institute of Standards and Technology, Gaithersburg, USA; Unit of Statistics, School of Business, Örebro University, Örebro, Sweden .ORCID iD: 0000-0003-1359-3311
Department of Mathematics, Stockholm University, Stockholm, Sweden .ORCID iD: 0000-0001-7855-8221
2023 (English)In: Metrologia, ISSN 0026-1394, E-ISSN 1681-7575, Vol. 60, no 5, article id 054003Article in journal (Refereed) Published
Abstract [en]

In the paper we present Bayesian inference procedures for the parameters of multivariate random effects model, which is used as a quantitative tool for performing multivariate key comparisons and multivariate inter-laboratory studies. The developed new approach does not require that the reported covariance matrices of participating laboratories are known and, as such, it can be used when they are estimated from the measurement results. The Bayesian inference procedures are based on samples generated from the derived posterior distribution when the Berger and Bernardo reference prior and the Jeffreys prior are assigned to the model parameter. Three numerical algorithms for the construction of Markov chains are provided and implemented in the CCAUV.V-K1 key comparisons. All three approaches yield similar Bayesian estimators with wider credible intervals when the Berger and Bernardo reference prior is used. Also, the Bayesian estimators for the elements of the inter-laboratory covariance matrix are larger under this prior than for the Jeffreys prior. Finally, the constructed joint credible sets for the components of the overall mean vector indicate the presence of linear dependence between them which cannot be captured when only univariate key comparisons are performed.

Place, publisher, year, edition, pages
IOP Publishing Ltd , 2023. Vol. 60, no 5, article id 054003
Keywords [en]
multivariate inter-laboratory studies, key comparisons, multivariate random effects model, objective Bayesian inference, rank plot, R<^> estimates
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:oru:diva-108144DOI: 10.1088/1681-7575/acee03ISI: 001053270100001Scopus ID: 2-s2.0-85169582291OAI: oai:DiVA.org:oru-108144DiVA, id: diva2:1797328
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Örebro UniversityAvailable from: 2023-09-14 Created: 2023-09-14 Last updated: 2023-09-14Bibliographically approved

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Bodnar, Olha

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