by Manuel Rodriguez Higuero
The Guide to the Expression of Uncertainty in Measurement (GUM) [1] and its Supplement 1 based on Monte Carlo propagation (GUM-S1) [2] currently coexist as two conceptual frameworks that are partially compatible but not equivalent. This work analyzes an operational discrepancy that appears when Type A uncertainty contributions are represented by Student’s t distributions with finite degrees of freedom in Monte Carlo simulations. It is shown that the usual parametrization adopted in the Monte Carlo supplement implicitly breaks the classical interpretation of the combined standard uncertainty as the true RMS standard deviation of the propagated distribution. Based on this observation, a renormalization of the Student’s t distribution is proposed that simultaneously preserves: (i) the heavy-tail structure associated with finite degrees of freedom, (ii) the interpretation of the combined standard uncertainty as the RMS-equivalent standard deviation, and (iii) the operational consistency of Monte Carlo propagation of uncertainties between laboratories.
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