Version 1
: Received: 29 November 2023 / Approved: 29 November 2023 / Online: 30 November 2023 (09:16:25 CET)
How to cite:
Feistel, R.; Lovell-Smith, J. Uncertainty Propagation using Dispersion Matrices Accounting for Systematic Error in Least‐Squares Regression. Preprints2023, 2023111917. https://doi.org/10.20944/preprints202311.1917.v1
Feistel, R.; Lovell-Smith, J. Uncertainty Propagation using Dispersion Matrices Accounting for Systematic Error in Least‐Squares Regression. Preprints 2023, 2023111917. https://doi.org/10.20944/preprints202311.1917.v1
Feistel, R.; Lovell-Smith, J. Uncertainty Propagation using Dispersion Matrices Accounting for Systematic Error in Least‐Squares Regression. Preprints2023, 2023111917. https://doi.org/10.20944/preprints202311.1917.v1
APA Style
Feistel, R., & Lovell-Smith, J. (2023). Uncertainty Propagation using Dispersion Matrices Accounting for Systematic Error in Least‐Squares Regression. Preprints. https://doi.org/10.20944/preprints202311.1917.v1
Chicago/Turabian Style
Feistel, R. and Jeremy Lovell-Smith. 2023 "Uncertainty Propagation using Dispersion Matrices Accounting for Systematic Error in Least‐Squares Regression" Preprints. https://doi.org/10.20944/preprints202311.1917.v1
Abstract
Empirical equations representing, interpolating and smoothing groups of measurement results by regression methods are in widespread use in metrology and other fields of science and engineering. Standard equations for the propagation of measurement uncertainties to values computed from such equations are available but suffer from a lack of general acceptance and are only infrequently applied in practice. One reason for the slow uptake is the lack of clear methods to account for systematic error. In this paper, uncertainty propagation equations in terms of covariance matrices are generalized to allow for systematic errors in least-squares regression, and effects of the resulting uncertainties are investigated analytically. A stochastic ensemble model of systematic error is proposed for the computation of the non-diagonal elements of the weight matrix of the Generalized Least-Squares method (GLS) from the measurement uncertainty. A GLS projector formalism is described which separates the effects of measurement scatter on values calculated by the equation from those on the related “residuals”, i.e., the residual errors in the fitted data. The same projectors act similarly on the associated uncertainties and covariance matrices and permit the effects of systematic errors on the simulation covariance to be quantified. It is demonstrated that, in order to include systematic errors in the uncertainty estimates of GLS, covariance matrices may be substituted by novel, specifically defined dispersion matrices that are not specified yet by the GUM[1]. Systematic measurement errors may be estimated from various sources; a particularly easy way suggested here involves analyzing the structure in the regression residuals. It is demonstrated that GLS projectors exhibit inherent features of “error blindness” also with respect to systematic errors. [1] GUM: Guide to the Expression of Uncertainty in Measurement, http://www.bipm.org/en/publications/guides
Computer Science and Mathematics, Probability and Statistics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
