A formulation of the law of propagation of uncertainty to facilitate the treatment of shared influences

Abstract

The law of propagation of uncertainty requires the proper treatment of dependence between the estimates of quantities influencing the measurement. Sometimes these estimates are themselves obtained in previous separate measurements, and the correlation between these estimates is not recorded. In such a case, the corresponding correlation coefficient or covariance will wrongly be deemed to be zero. In other situations, the number of input or output quantities might be large and information about dependence might not be recorded because of the apparent need for the construction of a large matrix of covariances. This paper presents (i) a method whereby information about dependence is recorded in a table with, typically, fewer columns than the matrix and (ii) a corresponding re-expression of the law of propagation of uncertainty. Examples of the application of the method are given.

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