Bayesian framework for proficiency tests using auxiliary information on laboratories
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In this paper, we propose a Bayesian framework to analyse proficiency tests results that allows to combine prior information on laboratories and prior knowledge on the consensus value when no measurement uncertainties nor replicates are reported. For these proficiency tests, where the reported data is reduced to its minimum, we advocate that each piece of information related to the measurement process is valuable and can lead to a more reliable estimation of the consensus value and its associated uncertainty. The resulting marginal posterior distribution of the consensus value relies on the management of expert knowledge used to build prior distributions on the consensus value and the laboratory effects. The choices of priors are discussed to promote the method when the required auxiliary information is available. This new approach is applied on a simulated data set and on a real-life environmental proficiency test.
KeywordsBayesian statistics Proficiency test Monte Carlo method Expert knowledge
The authors are grateful to BIPEA (Bureau InterProfessionnel d’Etudes Analytiques, http://www.bipea.org/) for the active collaboration on the environmental case study. They thank Véronique Le Diouron and Béatrice Lalere from the Department of Organic Chemistry of LNE for providing the reference value for the environmental case study. The research within this EURAMET joint research project received funding from the European Communitys Seventh Framework Programme, ERANET Plus, under Grant Agreement No. 217257. This work was part of a Joint Research Project within the European Metrology Research Programme EMRP under Grant Agreement No. 912/2009/EC.
- 2.CCQM Guidance note (2013) Estimation of a consensus KCRV and associated degrees of equivalence. Version 10Google Scholar
- 3.Demeyer S (2011) Approche bayésienne de l’évaluation de l’incertitude de mesure : application aux comparaisons interlaboratoires. PhD thesis, Conservatoire National des Arts et Métiers, https://tel.archives-ouvertes.fr/tel-00585727
- 4.Demeyer S, Foulley JL, Fischer N, Saporta G (2012) Bayesian analysis of structural equation models using parameter expansion. In: Summa M, Bottou L, Goldfarb B, Murtagh F, Pardoux A, Touati M (eds) Statistical learning and data science. Chapman&Hall/CRC, Boca Raton, pp 135–145Google Scholar
- 5.Ellison SLR (2014) metRology: Support for metrological applications. R package version 0.9-17. http://CRAN.R-project.org/package=metRology
- 6.Gelman A, Carlin JB, Stern HS, Rubin DB (2014) Bayesian data analysis. Chapman & Hall/CRC, Boca RatonGoogle Scholar
- 7.ISO/IEC 13528 (2015) Statistical methods for use in proficiency testing by interlaboratory comparisons. International Organization for Standardization (ISO), Geneva, SwitzerlandGoogle Scholar
- 8.ISO/IEC 17043 (2010) Conformity assessment - General requirements for proficiency testing. International Organization for Standardization (ISO), Geneva, SwitzerlandGoogle Scholar
- 9.JCGM 200-2012 (2012) International vocabulary of metrology—basic and general concepts and associated terms (VIM). International Organization for Standardization (ISO), Geneva, SwitzerlandGoogle Scholar
- 10.R Core Team (2014) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/
- 11.Schiel D, Rienitz O (2011) Final report on CCQM-K70: Determination of Hg in natural water at a concentration level required by the European environmental quality standard (EQS). Metrologia 48(1A):08011. http://stacks.iop.org/0026-1394/48/i=1A/a=08011