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  1. Bernd R. L. Siebert1,
  2. Klaus-Dieter Sommer2

Published Online: 15 MAR 2011

DOI: 10.1002/3527600434.eap705

Encyclopedia of Applied Physics

Encyclopedia of Applied Physics

How to Cite

Siebert, B. R. L. and Sommer, K.-D. 2011. Uncertainty. Encyclopedia of Applied Physics. 415–462.

Author Information

  1. 1

    Physikalisch-Technische Bundesanstalt, Braunschweig, Germany

  2. 2

    Physikalisch-Technische Bundesanstalt, Braunschweig und Berlin, Germany

Publication History

  1. Published Online: 15 MAR 2011


On the basis of the modern uncertainty approach represented by the “Guide to the Expression of Uncertainty in Measurement” (GUM), a first supplement to the GUM and related publications of members of the Joint Committee for Guides in Metrology (JCGM), the chapter explains the basic ideas and provides guidance on uncertainty evaluation. The standard GUM procedure for evaluating uncertainty is explicated in detail as an appropriate method for linear or nearly linear problems. A Monte Carlo method (MCM) is introduced as the tool of choice for all problems that cannot be treated properly with that standard procedure. The procedures presented are in essence based on Bayesian probability theory. The so-called error approach is briefly summarized in an Appendix. An extensive glossary lists the most often used symbols, acronyms, and scientific terms.


  • uncertainty evaluation;
  • Bayesian approach;
  • error approach;
  • GUM;
  • Monte Carlo methods;
  • propagation of probability density functions