This is an interesting discussion.
Some years ago, I stumbled over the “Error” values in the EDAX TEAM EBSD/EDS Software. The only information I found (2019-10-02 [1]) was:
“I asked EDAX and here's the answer (roughly): The estimated error is based on all random (usually 1 sigma) and systematically sources (Processing of spectra, models etc.) available.
The TEAM software includes full calculation of analytical uncertainty plus an estimation of error propagation.” [1]
Later I saw results from Oxford software containing also columns “Wt%” and “Wt% Sigma”.
I don’t know if the formalism is described somewhere.
For a physicist, a concentration given as c_X = (-0.02 ± 0.05) would mean: “The concentration of element X is zero within the confidence level.”
The same would hold for c_X = (0.00 ± 0.05).
We have to discuss two cases:
(1) What is the effect of negative intensities?
If intensity_value < 0 transfers not only into negative number of atoms, but also into negative values for contributions of the yet to be determined average sample Z, backscattering, adsorption, fluorescence, a.s.o. this would be definitely non-physical, but the effect may be small, because only a small number of atoms will be treated this way.
(2) Where are the negative counts from? IMHO negative counts are the result of peak fitting and/or background subtraction.
Linear least squares fit (of spectra) one could do (i) with the constraint that the intensity of the fitted spectra must be non-negative [2], or (ii) using the fit results of our preferred software
AND take their confidence intervals into account.
The confidence intervals for the fitting parameters are easily calculated by modern software (e.g. polyfit, polyval in Matlab/Octave; regression tool in Excel).
Method (i) will yield always non-negative intensities.
Using method (ii) any intensity_value < confidence_value should be set to 0. Here the statistics of the input data (counting noise) is taken into consideration.
I don’t know what option is used in the commercial programs.
[1]
https://www.researchgate.net/post/Whats_the_meaning_of_the_Error_value_in_EDAXs_TEAM_EBSD_EDS_Software[2] J. A. Taillon, An Open Evaluation of Hyperspectral Unmixing Strategies for EDS Analysis, Microscopy and Microanalysis, 24(S1), 752-753, doi:10.1017/S1431927618004257