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Measurement uncertainty

Working Group 8.42
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Comparison of measurement results, reliable decision-making and conformity assessment require the evaluation of uncertainties associated with measurement results. The ability to compare measurements made in different places and at different times underpins international metrology. The Guide to the Expression of Uncertainty in Measurement (Opens external link in new windowGUM) provides guidance for the evaluation of uncertainties, and it has been applied successfully in many applications throughout metrology.


Illustration of Monte Carlo method according to Opens external link in new windowSupplement 1 to the GUM.

In recent years metrology has expanded to support new fields to address societal challenges relating to energy and sustainability, climate and environmental monitoring, life sciences and health, using measurement modalities such as imaging, spectroscopy, earth observation and sensor networks. Reliable uncertainty evaluation is particularly important in these applications, e.g. to safeguard the diagnosis of a tumor in quantitative imaging or to reliably monitor air pollution. The GUM does not adequately address the challenges arising in these applications, and the development of statistical procedures for improved uncertainty evaluation is an urgent need.

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The focus of PTB’s Working Group 8.42 is on the development of Bayesian methods for the evaluation of uncertainties. The development is carried out within the context of different research areas of data analysis such as large-scale data analysis or deep learning. Bayesian inference procedures suitable for the extension of the current GUM methodology are also part of the current research in PTB’s Working Group 8.42. Examples include simple means to assign distributions representing the available prior knowledge, or procedures for the numerical calculation of results. Open source software support is provided to ease the application of the research results.

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Publication single view


Title: Quantitative magnetic resonance spectroscopy: semi-parametric modeling and determination of uncertainties
Author(s): C. Elster, F. Schubert, A. Link, M. Walzel, F. Seifert and H. Rinneberg
Journal: Magnetic resonance in medicine
Year: 2005
Volume: 53
Issue: 6
Pages: 1288--96
DOI: 10.1002/mrm.20500
ISSN: 0740-3194
Web URL: http://www.ncbi.nlm.nih.gov/pubmed/15906296
Keywords: Bayes Theorem,Brain Chemistry,Computer Simulation,Computer-Assisted,Humans,Least-Squares Analysis,Magnetic Resonance Spectroscopy,Magnetic Resonance Spectroscopy: methods,Models, Statistical,Regression,Signal Processing, Computer-Assisted,Statistical
Tags: 8.42, Unsicherheit, in-vivo
Abstract: A semi-parametric approach for the quantitative analysis of magnetic resonance (MR) spectra is proposed and an uncertainty analysis is given. Single resonances are described by parametric models or by parametrized in vitro spectra and the baseline is determined nonparametrically by regularization. By viewing baseline estimation in a reproducing kernel Hilbert space, an explicit parametric solution for the baseline is derived. A Bayesian point of view is adopted to derive uncertainties, and the many parameters associated with the baseline solution are treated as nuisance parameters. The derived uncertainties formally reduce to Cramér-Rao lower bounds for the parametric part of the model in the case of a vanishing baseline. The proposed uncertainty calculation was applied to simulated and measured MR spectra and the results were compared to Cramér-Rao lower bounds derived after the nonparametrically estimated baselines were subtracted from the spectra. In particular, for high SNR and strong baseline contributions the proposed procedure yields a more appropriate characterization of the accuracy of parameter estimates than Crémer-Rao lower bounds, which tend to overestimate accuracy.

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