Overview
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 (GUM) 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 Supplement 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.
Research
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.
Software
Publications
Publication single view
Article
Title: | Analytical derivation of the reference prior by sequential maximization of Shannon's mutual information in the multi-group parameter case |
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Author(s): | O. Bodnar and C. Elster |
Journal: | Journal of Statistical Planning and Inference |
Year: | 2014 |
Volume: | 147 |
Pages: | 106--116 |
DOI: | 10.1016/j.jspi.2013.11.003 |
ISSN: | 03783758 |
Web URL: | http://www.sciencedirect.com/science/article/pii/S0378375813002802 |
Keywords: | Bayes,Reference prior,Shannon's mutual information,statistics |
Tags: | 8.42, Unsicherheit |
Abstract: | We provide an analytical derivation of a non-informative prior by sequential maximization of Shannon's mutual information in the multi-group parameter case assuming reasonable regularity conditions. We show that the derived prior coincides with the reference prior proposed by Berger and Bernardo, and that it can be considered as a useful alternative expression for the calculation of the reference prior. In using this expression we discuss the conditions under which an improper reference prior can be uniquely defined, i.e. when it does not depend on the particular choice of nested sequences of compact subsets of the parameter space needed for its construction. We also present the conditions under which the reference prior coincides with Jeffreys' prior. |