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Publication Citation: Bayesian Alternative to the Guide's Use of the Welch-Satterthwaite Formula

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Author(s): Raghu N. Kacker;
Title: Bayesian Alternative to the Guide's Use of the Welch-Satterthwaite Formula
Published: January 03, 2006
Abstract: The Guide to the Expression of Uncertainty in Measurement suggests that to account for the statistical uncertainty in a combined standard uncertainty that arises when one or more of its components are evaluated from a limited number of independent normally distributed measurements, the coverage factor may be determined from a scaled-and-shifted t-distribution with effective degrees of freedom obtained from the Welch-Satterthwaite formula. We propose, as an alternative, a normal distribution with standard deviation equal to a Bayesian combined standard uncertainty. A Bayesian combined standard uncertainty has no statistical uncertainty arising from limited numbers of measurements. Therefore, the proposed normal distribution with Bayesian combined standard uncertainty greatly simplifies the expression of uncertainty by eliminating the need of quantifying the statistical uncertainty in uncertainty arising from limited numbers of measurements.
Citation: Metrologia
Volume: 43
Pages: pp. 1 - 11
Keywords: Behrens-Fisher distribution;measurement uncertainty;t-distribution;variance components
Research Areas: Math, Statistics
PDF version: PDF Document Click here to retrieve PDF version of paper (171KB)