Open Access
Issue
Int. J. Metrol. Qual. Eng.
Volume 15, 2024
Article Number 14
Number of page(s) 17
DOI https://doi.org/10.1051/ijmqe/2024010
Published online 13 August 2024
  1. Joint Committee for Guides in Metrology, Evaluation of measurement data — Supplement 1 to the Guide to the expression of uncertainty in measurement — Propagation of distributions using a Monte Carlo method. Sèvres, France: International Bureau of Weights and Measures (BIPM), 2008, BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML, JCGM 101:2008. [Online]. Available: http://www.bipm.org/en/publications/guides/gum.html [Google Scholar]
  2. D.V. Lindley, The probability approach to the treatment of uncertainty in artificial intelligence and expert systems, Stat. Sci. 17–24 (1987) [Google Scholar]
  3. C.P. Robert, G. Casella, G. Casella, Monte Carlo statistical methods (Springer, 1999), vol. 2 [Google Scholar]
  4. K. Klauenberg, C. Elster, Markov chain Monte Carlo methods: an introductory example, Metrologia 53, S32 (2016) [CrossRef] [Google Scholar]
  5. E.T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106, 620 (1957) [CrossRef] [MathSciNet] [Google Scholar]
  6. R.E. Kass, L. Wasserman, The selection of prior distributions by formal rules, J. Am. Stat. Assoc. 91, 1343–1370 (1996) [CrossRef] [Google Scholar]
  7. K. Chaloner, Elicitation of prior distributions, Bayesian Biostat. 141, 156 (1996) [Google Scholar]
  8. A. O'Hagan, C.E. Buck, A. Daneshkhah, J.R. Eiser, P.H. Garthwaite, D.J. Jenkinson, J.E. Oakley, T. Rakow, Uncertain judgements: eliciting experts' probabilities (John Wiley & Sons, 2006) [CrossRef] [Google Scholar]
  9. G.A. Kyriazis, Comparison of GUM Supplement 1 and Bayesian analysis using a simple linear calibration model, Metrologia 45, L9 (2008) [CrossRef] [Google Scholar]
  10. C. Elster, B. Toman, Bayesian uncertainty analysis under prior ignorance of the measurand versus analysis using the Supplement 1 to the Guide: a comparison, Metrologia 46, 261 (2009) [CrossRef] [Google Scholar]
  11. I. Lira, D. Grientschnig, Equivalence of alternative Bayesian procedures for evaluating measurement uncertainty, Metrologia 47, 334 (2010) [CrossRef] [Google Scholar]
  12. A. Forbes, J. Sousa, The GUM, Bayesian inference and the observation and measurement equations, Measurement 44, 1422–1435 (2011) [CrossRef] [Google Scholar]
  13. J. Berger, The case for objective Bayesian analysis, Bayesian Anal. 1, 385–402 (2006) [Google Scholar]
  14. N. Giaquinto, L. Fabbiano, Examples of S1 coverage intervals with very good and very bad long-run success rate, Metrologia 53, S65 (2016) [CrossRef] [Google Scholar]
  15. G. Wübbeler, C. Elster, On the transferability of the GUM-S1 type A uncertainty, Metrologia 57, 015005 (2020) [CrossRef] [Google Scholar]
  16. M. Marschall, G. Wübbeler, C. Elster, Rejection sampling for Bayesian uncertainty evaluation using the Monte Carlo techniques of GUM-S1,Metrologia 59, 015004 (2021) [Google Scholar]
  17. A. O'Hagan, M. Cox, Simple informative prior distributions for Type A uncertainty evaluation in metrology, Metrologia 60, 025003 (2023) [CrossRef] [Google Scholar]
  18. J. Meija, O. Bodnar, A. Possolo, Ode to bayesian methods in metrology, Metrologia 60, 052001 (2023) [CrossRef] [Google Scholar]
  19. M. Evans, N. Hastings, B. Peacock, C. Forbes, Statistical distributions (John Wiley & Sons, 2011) [Google Scholar]
  20. V. Barnett, Probability plotting methods and order statistics, J. Royal Stat. Soc.: Ser. C (Applied Statistics) 24, 95–108 (1975) [Google Scholar]
  21. G. Wübbeler, M. Marschall, C. Elster, A simple method for Bayesian uncertainty evaluation in linear models, Metrologia 57, 065010 (2020) [CrossRef] [Google Scholar]
  22. EA Laboratory Committee and others, Expression of the Uncertainty of Measurement in Calibration, ” European Co-Operation for Accreditation, Paris, France, ReportNo. EA-4/02 M: 2013 (2013). Available: http://www.european-accreditation.org/publication/ea-4-02-m-rev01-september-2013 [Google Scholar]
  23. S. Demeyer, N. Fischer, C. Elster, Guidance on Bayesian uncertainty evaluation for a class of GUM measurement models, Metrologia 58, 014001 (2020) [Google Scholar]
  24. A. Gelman, J. Carlin, H. Stern, D. Rubin, Bayesian Data Analysis (Chapman andS Hall-CRC, 2003) [CrossRef] [Google Scholar]
  25. A. O'Hagan, J. Forster, Kendall's Advanced Theory of Statistics, volume 2B, Bayesian Inference (Arnold, 2004) [Google Scholar]
  26. A. van der Veen, Bayesian inference in r and rstan, in Good Practice in Evaluating Measurement Uncertainty − Compendium of examples (2021), pp. 21–28. Available: http://empir.npl.co.uk/emue/wp-content/uploads/sites/49/2021/07/Compendium_ M36.pdf [Google Scholar]
  27. I. Lira, Analysis and comparison of Bayesian methods for type A uncertainty evaluation with prior knowledge, Ukrainian Metrolog. J. 4, 3–6 (2022) [CrossRef] [Google Scholar]
  28. D. Foreman-Mackey, D.W. Hogg, D. Lang, J. Goodman, “emcee: the MCMC hammer,” Publications of the Astronomical Society of the Pacific 125, no. 925 (2013) p. 306 [CrossRef] [Google Scholar]
  29. C.F. Carobbi, M. Cati, L.M. Millanta, Using the log-normal distribution in the statistical treatment of experimental data affected by large dispersion, in 2003 IEEE Symposium on Electromagnetic Compatibility. Symposium Record (Cat. No. 03CH37446) 2. IEEE (2003) pp. 812–816 [CrossRef] [Google Scholar]
  30. W.R. Ott, A physical explanation of the lognormality of pollutant concentrations, J. Air Waste Manag. Assoc. 40, 1378–1383 (1990) [CrossRef] [PubMed] [Google Scholar]
  31. ISO, 11929: Determination of the Characteristic Limits (Decision Threshold, Detection Limit and Limits of the Confidence Interval) for Measurements of Ionizing Radiation: Fundamentals and Application (International Organization for Standardization, 2010) [Google Scholar]
  32. O. Bodnar, R. Behrens, C. Elster, Bayesian inference for measurements of ionizing radiation under partial information, Metrologia 54, S29 (2017) [CrossRef] [Google Scholar]
  33. O. Bodnar, G. Wübbeler, C. Elster, On the application of Supplement 1 to the GUM to non-linear problems, Metrologia 48, 333 (2011) [CrossRef] [Google Scholar]

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