Non-linear models and best estimates in the GUM

Abstract

A non-linear function of a sample average is different from the average of that function evaluated for each element of the sample. However, in the Guide to the Expression of Uncertainty in Measurement (GUM) the second approach to calculating an average is considered potentially preferable to the first in order to obtain a measurand estimate. In this paper the issue is discussed, and it is shown that the second approach is inconsistent with the GUM framework. However, it is indeed preferable for input quantities having an intrinsically random behaviour. We comment on the approach adopted in this respect in Supplement 1 of the GUM and show that it is consistent with the first method.

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