A Bayesian approach to information fusion for evaluating the measurement uncertainty |
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Authors: | Klaus-Dieter Sommer Olaf Kühn Fernando Puente León Bernd R.L. Siebert |
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Affiliation: | 1. Physikalisch-Technische Bundesanstalt (PTB), D-38116 Braunschweig, Germany;2. Thuringian State Bureau for Metrology and Verification (LMET), D-98693 Ilmenau, Germany;3. Universität Karlsruhe, Institut für Industrielle Informationstechnik, D-76128 Karlsruhe, Germany;1. Department of Mechanical Engineering, Technical University of Denmark (DTU), Produktionstorvet 425, 2800 Kgs. Lyngby, Denmark;2. Image Metrology A/S, Lyngsø Allé 3A, 2970 Hørsholm, Denmark;1. School of Physical Science and Technology, Southwest University, Chongqing 400715, China;2. Physique Nucléaire Théorique, Université Libre de Bruxelles, C.P. 229, B-1050 Bruxelles, Belgium |
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Abstract: | The Bayesian approach to uncertainty evaluation is a classical example of the fusion of information from different sources. Basically, it is founded on both the knowledge about the measurement process and the influencing quantities and parameters. The knowledge about the measurement process is primarily represented by the so-called model equation, which forms the basic relationship for the fusion of all involved quantities. The knowledge about the influencing quantities and parameters is expressed by their degree of belief, i.e. appropriate probability density functions that usually are obtained by utilizing the principle of maximum information entropy and the Bayes theorem. Practically, the Bayesian approach to uncertainty evaluation is put into effect by employing numerical integration techniques, preferably Monte-Carlo methods. Compared to the ISO-GUM procedure, the Bayesian approach does not have any restrictions with respect to nonlinearities and calculation of confidence intervals. |
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