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

Published

Author(s)

Raghu N. Kacker

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

Keywords

Behrens-Fisher distribution, measurement uncertainty, t-distribution, variance components

Citation

Kacker, R. (2006), Bayesian Alternative to the Guide's Use of the Welch-Satterthwaite Formula, Metrologia, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150900 (Accessed April 12, 2024)
Created January 3, 2006, Updated February 19, 2017