Vladimir Ezhela, Institute for High Energy Physics, Russia


Eleven years ago the famous ISO GUM [1] appeared as the first official international document to focus metrologists and all practitioners working with measured data on the creation of an exhaustive and internationally acceptable standard on the expression of uncertainty in measurement.

Unfortunately the ISO GUM is applicable only to the case of one measurand and is self-contradictory in some places due to this limitation. That is why the intensive work on the extensions of the ISO GUM have been started in a couple of years after publication of the GUM and is still in progress [2], [3].

In this report we present:

1) A critical overview of the bad practice on presentation of correlated data in the physics literature and in scientific and technological data bases. Majority of incorrect presentations are inspired by the incorrect applications of the GUM recommendations and examples valid for the scalar case to the multivariate cases (even inside the GUM).

2) The derivation of the symple rules to calculate the rounding thresholds to preserve the positive definiteness of the covariance and correlation matrices as well as the rounding thresholds for the components of the mean vector to save it inside the unrounded scatter region.

3) We show also that in the multivariate case there are the strong limitations on the applicability of the linear differential low of uncertainty propagation and give the explicit formula in terms of number of input random variables, number of output variables and the order of Taylor polinomials sufficient to preserve the self consistent numerical presentation of the mean value of the vector function and its covariance matrix.
 
We claime that the original GUM should be corrected in places where the rounding rules for correlated data are discussed and used.

WE propose to include into the GUM_supplement_2 our suggestions on the safe rounding thresholds for correlation matrix and for the mean values.

We propose to include into the GUM_supplement_2 our rule to find the order N of the Taylor polynomials sufficient to construct the self consistent estimates of the n-dimentional vector function depending upon m-random variables and specification of its n-dimensional scatter region.

References
 
1. BIPM, IEC, IFCC, ISO, IUPAC, IUPAP, OIML, "Guide to the Expression of Uncertainty in Measurement", 2nd edn. ISBN 92-67-10188-9  (1995)
2. M.Cox and P.Harris, "The GUM and its planned supplemental guides" Accred Qual Assur 8 (2003) 375
3. M.G.Cox and P.M.Harris, "Measurement uncertainty and traceability" Meas. Sci. Technol. 17 (2006) 533

Keywords: multivariate uncertainty expression, multivariate uncertainty propagation, nonlinear differential uncertainty propagation low