Bayesian Uncertainty Analysis for a Regression Model Versus Application of GUM Supplement 1 to the Least-Squares Estimate

Published

May 5, 2011

Author(s)

Blaza Toman, Clemens Elster

Abstract

Application of least-squares as, for instance, in curve fitting is an important tool of data analysis in metrology. It is tempting to employ the supplement 1 to the GUM (GUM-S1) to evaluate the uncertainty associated with the resulting parameter estimates, albeit doing so is beyond the specified scope of GUM-S1. We compare the result of such a procedure to a Bayesian uncertainty analysis of the corresponding regression model. It is shown that under certain assumptions both analyses yield the same results but this is not true in general. Some simple examples are given which illustrate the similarities and differences between the two approaches.

Citation

Metrologia

Pub Type

Journals

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Keywords

Monte Carlo uncertainty analysis, GUM Supplement 1, Bayesian analysis, least squares estimation.

Citation

Toman, B. and Elster, C. (2011), Bayesian Uncertainty Analysis for a Regression Model Versus Application of GUM Supplement 1 to the Least-Squares Estimate, Metrologia, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=907685 (Accessed October 22, 2025)