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Probability in Metrology

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Data Modeling for Metrology and Testing in Measurement Science

Summary

The relationship is investigated between probability and metrology, here intended as the science of measurement. Metrology is shown to have historically participated in the development of statistic–probabilistic disciplines, not only adopting principles and methods, but also contributing with new and influential ideas. Two mainstreams of studies are identified in the science of measurement. The former starts with the classical theory of errors and ends with the contemporary debate on uncertainty; the latter originates from the development of a formal theory of measurement and it has attained recent results that make a systematic use of probability an appropriate logic for measurement. It is suggested that these two mainstreams may ultimately converge in a unique theory of measurement, formulated in a probabilistic language and applicable to all domains of science.

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References

  1. Bayes, T.: An essay towards solving a problem in the doctrine of chances. Phil. Trans. R. Soc. London, 53, 370-418 (1763)

    Google Scholar 

  2. Laplace, P. S.: Mémoire sur la probabilité des causes par les évenemens. Mem. Acad. R Sci. , 6, 621-656 (1774)

    Google Scholar 

  3. Gauss, C. F.: Theoria motus corporum coelestium in sectionibus conicis solem ambientium. Hamburg (1809) English translation by Davis, C. H., Dover (1963) reprinted 2004

    Google Scholar 

  4. Laplace, P.S.: Theorie analytique des probabilités, Courcier, Paris, (1812) In: Oeuvres Complétes de Laplace. Gauthier-Villars, Paris, vol. VII

    Google Scholar 

  5. Gauss, C. F.: Theoria combinationis observationum erroribus minimis obnoxiae. Gottingen, (1823) English translation by Stewart, G.W., SIAM, Philadelphia (1995)

    Google Scholar 

  6. von Helmholtz, H.: Zählen und Messen Erkenntnis theoretisch betrachtet, Philosophische Aufsätze Eduard Zeller gewidmet. Fuess, Leipzig (1887)

    Google Scholar 

  7. Campbell, N. R.: Physics - The elements. (1920) Representations as Foundations of science. Dover, New York (1957)

    Google Scholar 

  8. Fisher, R. A.: Statistical methods for research workers. Oliver and Boyd, Edinburg (1925)

    Google Scholar 

  9. Ferguson, A., Myers, C. S., Bartlett, R. J.: Qualitative estimates of sensory events. Final Report – British Association for the Advancement of Science, 2, 331-349 (1940)

    Google Scholar 

  10. Stevens, S. S.: On the theory of scales and measurement. Science, 103, 667-680 (1946)

    Article  Google Scholar 

  11. Fisher, R. A.: Statistical methods and scientific inference. Oliver and Boyd, Edinburg (1956)

    MATH  Google Scholar 

  12. Mandel, J.: The statistical analysis of experimental data. Wiley (1964) Repr. Dover (1984)

    Google Scholar 

  13. Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A.: Foundations of Measurement. Vol 1–3, Academic Press, New York (1971–1990)

    Google Scholar 

  14. Sheynin, O. B.: Laplace’s theory of errors. Archive for history of exact sciences, 17, 1-61 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sheynin, O. B.: C. F. Gauss and the theory of errors. Archive for history of exact sciences, 20, 21–72 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  16. Roberts, F.S.: Measurement theory. Addison-Wesley, Reading, MA (1979)

    MATH  Google Scholar 

  17. Falmagne, J.C.: A probabilistic theory of extensive measurement. Philosophy of Science, 47, 277–296 (1980)

    Article  MathSciNet  Google Scholar 

  18. Leaning M.S., Finkelstein, L.: A probabilistic treatment of measurement uncertainty in the formal theory of measurement. In: Streker, G. (ed) ACTA IMEKO 1979. Elsevier, Amsterdam (1980)

    Google Scholar 

  19. Finkelstein, L., Leaning, M.S.: A review of the fundamental concepts of measurement. Measurement, 2, 25–34 (1984)

    Article  Google Scholar 

  20. Narens, L.: Abstract measurement theory. MIT Press, Cambridge (1985)

    MATH  Google Scholar 

  21. Gonella, L.: Measuring instruments and theory of measurement. In:Proc. XI IMEKO World Congress, Houston, (1988)

    Google Scholar 

  22. Press, S.J.: Bayesian statistics. Wiley, New York (1989)

    MATH  Google Scholar 

  23. Costantini, D., Garibaldi, U., Penco, M. A.: Introduzione alla statistica- I fondamenti dell’argomentazione incerta. Muzzio, Padova (1992)

    Google Scholar 

  24. Weise, K., Wöger, W.: A Bayesian theory of measurement uncertainty. Measurement Science and Technology, 4, 1–11 (1993)

    Article  Google Scholar 

  25. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML: International Vocabulary of Basic and general terms in Metrology. Second Edition (1994) and current revision, Draft

    Google Scholar 

  26. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML: Guide to the Expression of Uncertainty in Measurement. ISO, Geneva (1995)

    Google Scholar 

  27. Michelini, R.C., Rossi, G.B.: Measurement uncertainty: a probabilistic theory for intensive entities. Measurement, 15, 143–157 (1995)

    Article  Google Scholar 

  28. Regenwetter, M.: Random utility representations of finite m-ary relations. Journal of Mathematical Psychology, 40, 219–234 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  29. Mari, L.: Beyond the representational viewpoint: a new formalization of measurement. Measurement, 27, 71–84 (2000)

    Article  Google Scholar 

  30. Monti, C. M., Pierobon, G.: Teoria della probabilitá. Zanichelli, Bologna (2000)

    Google Scholar 

  31. Hacking, I.: An introduction to probability and inductive logic. Cambridge Press, Cambridge (2001) Italian edition: Il Saggiatore, Milano (2005)

    Google Scholar 

  32. Regenwetter, M., Marley, A.A.J.: Random relations, random utilities, and random functions. Journal of Mathematical Psychology, 45, 864–912 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  33. Luce, R.D., Suppes, P.: Representational measurement theory. In: Stevens’ Handbook of Experimental Psychophysics. Vol. 4, Wiley, (2002)

    Google Scholar 

  34. Lira, I.: Evaluating the measurement uncertainty. IOP, Bristol (2002)

    Google Scholar 

  35. Rossi, G.B.: A probabilistic model for measurement processes. Measurement, 34, 85–99 (2003)

    Article  Google Scholar 

  36. Costantini, D.: I fondamenti storico-filosofici delle discipline statistico probabilistiche. Bollati Boringhieri, Torino (2004)

    Google Scholar 

  37. Rossi, G.B., Crenna, F., Panero, M.: Panel or jury testing methods in a metrological perspective. Metrologia, 42, 97–109 (2005)

    Article  Google Scholar 

  38. Rossi, G.B.: A probabilistic theory of measurement, Measurement, 39, 34–50 (2006)

    Article  Google Scholar 

  39. Rossi G.B., Crenna F., Cox M.G., Harris P.M.: Combining direct calculation and the Monte Carlo Method for the probabilistic expression of measurement results. In: Ciarlini, P., Filipe, E., Forbes, A.B., Pavese, F., Richter, D. (eds) Advanced Mathematical and Computational Tools in Metrology VII, World Scientific, Singapore (2006)

    Google Scholar 

  40. Rossi, G.B., Crenna F.,: A probabilistic approach to measurement-based decisions. Measurement, 39, 101–119 (2006)

    Article  Google Scholar 

  41. Rossi, G.B.: Measurability. Measurement, 40, 545–562 (2007)

    Article  Google Scholar 

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Authors and Affiliations

  1. Universitá degli Studi di Genova, DIMEC, Via All’Opera Pia 15 A, 16145, Genova, Italy

    Giovanni B. Rossi

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  1. Giovanni B. Rossi
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Correspondence to Giovanni B. Rossi .

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Editors and Affiliations

  1. Metrologica (INRIM), Divisione Termodinamica, Istituto Nazionale di Ricerca, Strada delle Cacce 73, Torino, 10135, Italy

    Franco Pavese

  2. MSC , Module 13 , National Physics Laboratory , Hampton Road, Teddington, Middlesex, TW11 0LW, United Kingdom

    Alistair B. Forbes

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© 2009 Birkhäuser Boston

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Rossi, G.B. (2009). Probability in Metrology. In: Pavese, F., Forbes, A. (eds) Data Modeling for Metrology and Testing in Measurement Science. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4804-6_2

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