Abstract

Contrary to the claims put forward in “Evaluation of measurement data – Guide to the expression of uncertainty in measurement”, issued by the Joint Committee for Guides in Metrology, the error concept and the uncertainty concept are the same. Arguments in favour of the contrary have been analyzed and were found not compelling. Neither was any evidence presented in this document that “errors” and “uncertainties” define a different relation between the measured and the true value of the variable of interest, nor does this document refer to a Bayesian account of uncertainty beyond the mere endorsement of a degree-of-belief-type conception of probability.

Highlights

  • For more than 200 years, error estimation used a more or less unified terminology where the 10 term ‘error’ was used, with some caveats, for designating a statistical estimate of the expected difference between the measured and the true value of a measurand (Gauss, 1809, 1816; Pearson, 1920; Fisher, 1925; Rodgers, 1990; Mayo, 1996; Rodgers, 2000, just to name a few)

  • The Joint Committee for Guides in Metrology (JCGM), on request of the Bureau International de Poids et Mesures (BIPM) presented a contrasting definition how we have to conceive 15 the term ‘error’ and have stipulated a new terminology, where the term ‘measurement uncertainty’ is used in situations where one would have said ‘measurement error’ before (Joint Committee for Guides in Metrology (JCGM), 2008, this source is referenced as GUM08)

  • Supplementary material in the context of GUM is found in Joint Committee for Guides in Metrology (JCGM) (2012) and several supplements to GUM08, that are found on the BIPM website 20

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Summary

Introduction

For more than 200 years, error estimation used a more or less unified terminology where the 10 term ‘error’ was used, with some caveats, for designating a statistical estimate of the expected difference between the measured and the true value of a measurand (Gauss, 1809, 1816; Pearson, 1920; Fisher, 1925; Rodgers, 1990; Mayo, 1996; Rodgers, 2000, just to name a few). Third we scrutinize the claim that there will always be unknown sources of uncertainty and that it is impossible to relate the 60 measured value along with its uncertainty estimate to the true value (Section 5.4) After these more general considerations we critically discuss the applicability of the GUM08 concept to indirect measurements of atmospheric state variables (Section 6). There we discuss the problems of measurands that are not well-defined in the sense of GUM08 (Section 6.1), if it is really adequate to report the combined error only (Section 6.2) and if the measurement equation as presented in GUM08 does 65 optimally support the uncertainty assessment in atmospheric remote sensing (Section 6.3) In this context, we investigate whether the difference between the traditional concept of error analysis and the uncertainty concept might be linked to a Bayesian versus a frequentist conception of probability. The availability of F−1 allows to statistically estimate the effect of measurement noise and systematic effects in b or F−1 on x (Rodgers, 1990, 2000; von Clarmann et al, 2020)

The connotation of the term ‘error’
The operational definition
Likelihood, probability, and the base rate fallacy
Nonlinearity issues
Incompleteness of the error budget
What if the measurand is not well-defined?
The combined error
The causal arrow
Bayesian versus non-Bayesian
Conclusions
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