The GUM, Bayesian inference and the observation and measurement equations

Measurement: Journal of the International Measurement Confederation

Volumn 44, Issue 8, 2011, Pages 1422-1435

  Forbes, A B ^a   Sousa, J A ^b  

^a NATIONAL PHYSICAL LABORATORY   (United Kingdom)

^b Lab Regional de Engenharia Civil   (Portugal)

Author keywords

Bayesian inference; Measurement equation; Measurement uncertainty; Observation equation

Indexed keywords

BAYESIAN INFERENCE; HIGHLY NONLINEAR; KNOWLEDGE DISTRIBUTION; MEASURAND; MEASUREMENT EQUATION; MEASUREMENT EQUATIONS; MEASUREMENT UNCERTAINTY; MEASURING SYSTEMS; OBSERVATION AND MEASUREMENT; OBSERVATION EQUATION; UNCERTAINTY EVALUATION;

BAYESIAN NETWORKS; INFERENCE ENGINES; MEASUREMENTS; NONLINEAR EQUATIONS;

UNCERTAINTY ANALYSIS;

EID: 79960173299     PISSN: 02632241     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.measurement.2011.05.007     Document Type: Article

References (21)

1. J.O. Berger Statistical Decision Theory and Bayesian Analysis 2nd ed. 1985 Springer New York
2. J.O. Berger, J.M. Bernardo, and D. Sun The formal definition of reference priors Annals of Statistics 37 2009 905 938
3. J.M. Bernardo, and A.F.M. Smith Bayesian Theory 1994 Wiley New York
4. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Evaluation of measurement data - guide to the expression of uncertainty in measurement. Joint Committee for Guides in Metrology, JCGM 100:2008.
5. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP, and OIML. Evaluation of measurement data - supplement 1 to the "Guide to the expression of uncertainty in measurement" - propagation of distributions using a Monte Carlo method. Joint Committee for Guides in Metrology, JCGM 101:2008.
6. G.E.P. Box, and G.C. Tiao Bayesian inference in statistical analysis 1973 Wiley New York (Wiley Classics Library Edition 1992 edition)
7. M.G. Cox, A.B. Forbes, P.M. Harris, I.M. Smith. Uncertainty evaluation associated with calibration functions, in: IMEKO XIX World Congress, September 6-11, 2009, Lisbon, 2009.
8. M.G. Cox, G.B. Rossi, P.M. Harris, and A. Forbes A probabilistic approach to the analysis of measurement processes Metrologia 45 5 2008 493 502
9. C. Elster, and B. Toman Bayesian uncertainty analysis under prior ignorance of the measurand versus analysis using the supplement 1 to the guide: a comparison Metrologia 46 2009 261 266
10. A.B. Forbes, J.A. Sousa. The GUM, Bayesian inference and forward and inverse uncertainty evaluation, in: SPMet, October 3-4, 2007, Funchal, 2007.
11. A. Gelman, J.B. Carlin, H.S. Stern, and D.B. Rubin Bayesian Data Analysis second ed. 2004 Chapman & Hall/CRC Boca Raton, FL
12. G.R. Grimmett, and D.R. Stirzaker Probability and Random Processes third ed. 2001 Oxford University Press
13. L. Hogben Handbook of Linear Algebra 2007 Chapman & Hall/CRC Boca Raton, FL
14. E.T. Jaynes Probability Theory: The Logic of Science 2003 Cambridge University Press Cambridge
15. R.N. Kacker, and A. Jones On the use of Bayesian statistics to make the guide to the expression of uncertainty in measurement consistent Metrologia 40 2003 235 248
16. I. Lira, and D. Grientschnig Equivalence of alternative Bayesian procedures for evaluating measurement uncertainty Metrologia 47 2010 334 336
17. A.H. Maslow The Psychology of Science: A Reconnaissance 2002 Maurice Bassett Publishing Chapel Hill, NC (e-book from original publication in 1966 edition)
18. H.S. Migon, and D. Gamerman Statistical Inference: An Integrated Approach 1999 Arnold London
19. A. Possolo, and B. Toman Assessment of measurement uncertainty via observation equations Metrologia 44 2007 464 475 (Pubitemid 350212282)
20. D.S. Sivia Data Analysis: A Bayesian Tutorial 1996 Clarendon Press Oxford
21. K. Weise, and W. Woeger A Bayesian theory of measurement uncertainty Measurement Science and Technology 4 1 1993 1 11