EMUE-D1-2-BayesianMassCalibration

S. Demeyer; N. Fischer; M. G. Cox; A. M. H. van der Veen; O. Pellegrino; J. Sousa; A. Bošnjaković; V. Karahodžić; C. Elster

doi:10.5281/zenodo.3726908

Published March 25, 2020 | Version 1.0

Dataset Open

EMUE-D1-2-BayesianMassCalibration

1. LNE
2. NPL
3. VSL
4. IPQ
5. IMBiH
6. PTB

This example describes the calibration of a conventional mass of a weight W against a reference weight R with a nominal mass of 100 g. The example builds on that given in JCGM 101:2008. This time a Bayesian evaluation of the measurement is performed. A Bayesian approach differs from the Monte Carlo method (MCM) of JCGM 101:2008 and the law of propagation of uncertainty (LPU) in JCGM 100:2008 in that it combines prior knowledge about the measurand with the data obtained during calibration. From the joint posterior probability density function which is obtained from this combination, a value and a coverage interval for the measurand are obtained.

Files contained in the dataset are:

- EMUEActivity113_MassCalibration.pdf: report “Bayesian approach applied to the mass calibration example in JCGM 101:2008”;

- EMUEActivity113_MassCalibration.tex: LaTeX source file to be compiled in order to produce EMUEActivity113_MassCalibration.pdf;

- Compendium.bib: bibliography file;

- conjugateBayesKnownV.pdf: image contained in the report;

- MCMvsBayesNI.pdf: image contained in the report;

- JCGM101_Mass_calibration_code.R : R code to run the example from the report.

Notes

The report relies on the following publications: - BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Supplement 1 to the 'Guide to the Expression of Uncertainty in Measurement' – Propagation of distributions using a Monte Carlo method, JCGM 101:2008. BIPM, 2008. - A. Gelman, J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin. Bayesian Data Analysis, 3rd edition. Chapman and Hall/CRC, 2013. - G.E.P. Box and G.C. Tiao. Bayesian Inference in Statistical Analysis. Wiley, 1992. - C. Elster. Bayesian uncertainty analysis compared with the application of the GUM and its supplements. Metrologia, 51:S159–S166, 2014. - BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Guide to the Expression of Uncertainty in Measurement, JCGM 100:2008, GUM 1995 with minor corrections. BIPM, 2008. - J. A. Sousa, A. B. Forbes, A. S. Ribeiro, P. M. Harris, F. Carvalho, and L. Bacelar. The evaluation of uncertainty in mass calibration: possible approaches in a comparison study. Journal of Physics: Conference Series, 459:012033, sep 2013. - S. Chib and E. Greenberg. Understanding the metropolis-hastings algorithm. The American Statistician, 49(4):327–335, 1995.

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