Articlehybrid2021

The GUM perspective on straight-line errors-in-variables regression

Katy Klauenberg · Steffen Martens · Alen Bošnjaković · M G Cox · Adriaan M. H. van der Veen · Clemens Elster

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Scientific Measurement and Uncertainty Evaluation Advanced Statistical Methods and Models Statistical and numerical algorithms

Abstract

Following the Guide to the expression of uncertainty in measurement (GUM), the slope and intercept in straight-line regression tasks can be estimated and their uncertainty evaluated by defining a measurement model. Minimizing the weighted total least-squares functional appropriately defines such a model when both regression input quantities (X and Y) are uncertain. This paper compares the uncertainty of the straight line evaluated by propagating distributions and by the law of propagation of uncertainty (LPU). The latter is in turn often approximated because the non-linear measurement model does not have closed form. We reason that the uncertainty recommended in the dedicated technical specification ISO/TS 28037:2010 does not fully implement the LPU (as intended) and can understate the uncertainty. A systematic simulation study quantifies this understatement and the circumstances where it becomes relevant. In contrast, the LPU uncertainty may often be appropriate. As a result, it is planned to revise ISO/TS 28037:2010.

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References

2006GUIDE TO THE EXPRESSION OF UNCERTAINTY IN MEASUREMENT 2008Evaluation of measurement data — Guide to the expression of uncertainty in measurement 2008Evaluation of measurement data — Supplement 1 to the “Guide to the expression of uncertainty in measurement” — Propagation of distributions using a Monte Carlo method 2011Evaluation of measurement data – Supplement 2 to the “Guide to the expression of uncertainty in measurement” – Extension to any number of output quantities 2007Assessment of measurement uncertainty via observation equations 2020Guide to the expression of uncertainty in measurement — Part 6: Developing and using measurement models 2006Implementation of a generalized least-squares method for determining calibration curves from data with general uncertainty structures 2014Bayesian uncertainty analysis compared with the application of the GUM and its supplements

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