Article2014

On the adjustment of inconsistent data using the Birge ratio

45 citations0/0 files storedMetrologia

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Scientific Measurement and Uncertainty Evaluation Statistical Methods and Bayesian Inference Statistical and numerical algorithms

Abstract

The Birge ratio is applied in metrology to enlarge quoted uncertainties when combining inconsistent measurement results on the same measurand. We discuss the statistical model underlying such a procedure and argue that the resulting uncertainty associated with the adjusted value is underrated. We provide a simple modification of this uncertainty on the basis of an objective Bayesian inference. While the proposed uncertainty approaches that obtained by the conventional procedure for a large number n of combined measurement results, differences are significant for small n . For example, for n = 4 we get an increase of 73% in the standard uncertainty associated with the adjusted value, and for n = 10 the increase is still 13%. We derive the posterior distribution for the adjusted value in closed form, including a 95% credible interval. In addition, we show that our results do not only hold when the distribution of the measurement results is assumed to be Gaussian, but for a whole family of (elliptically contoured) location-scale distributions. We illustrate the modified Birge method by its application to data from the 2002 adjustment of the Newtonian constant of gravitation.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 45 citations exist upstream.

References

2006GUIDE TO THE EXPRESSION OF UNCERTAINTY IN MEASUREMENT 2008Evaluation of measurement data — Guide to the expression of uncertainty in measurement 2012CODATA recommended values of the fundamental physical constants: 2010 2005CODATA recommended values of the fundamental physical constants: 2002 2012Measurement Science and Technology: a historical perspective 2009Laboratory effects models for interlaboratory comparisons 2004Combining information from interlaboratory evaluations using a random effects model 2010Redefinition of the kilogram and the impact on its future dissemination

Cited by

2017The parameter uncertainty inflation fallacy 2015A tutorial on Bayesian Normal linear regression 2016Evaluation of uncertainty in the adjustment of fundamental constants 2017Evaluation of the accuracy, consistency, and stability of measurements of the Planck constant used in the redefinition of the international system of units

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.