Undesirable effects of covariance matrix techniques for error analysis

David Seibert

doi:10.1103/PhysRevD.49.6240

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Undesirable effects of covariance matrix techniques for error analysis

David Seibert^*

Theory Division, CERN, CH-1211 Geneva 23, Switzerland

^*Current address: Physics Department, Kent State University, Kent, OH 44242. Electronic address (internet): seibert@scorpio.kent.edu

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Phys. Rev. D 49, 6240 – Published 1 June, 1994

DOI: https://doi.org/10.1103/PhysRevD.49.6240

Abstract

Regression with $χ^{2}$ constructed from covariance matrices should not be used for some combinations of covariance matrices and fitting functions. Using the technique for unsuitable combinations can amplify systematic errors. This amplification is uncontrolled, and can produce arbitrarily inaccurate results that might not be ruled out by a $χ^{2}$ test. In addition, this technique can give incorrect (artificially small) errors for fit parameters. I give a test for this instability and a more robust (but computationally more intensive) method for fitting correlated data.

References (7)

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[c1] W.T. Eadie et al., Statistical Methods in Experimental Physics (North-Holland, Amsterdam, 1971), pp. 62-66

[c2] T.A. DeGrand, Phys. Rev. D 36, 176 (1987)

[c3] C. DeTar and J.B. Kogut, Phys. Rev. D 36, 2828 (1987)

[c4] S. Gottlieb et al., Phys. Rev. D 38, 2245 (1988)

[c5] P. Abreu et al., Phys. Lett. B 247, 137 (1990)

[c6] B. Wosiek, Acta Phys. Pol. B21, 1021 (1990)

[c7] D. Toussaint, in From Actions to Answers - Proceedings of the 1989 Theoretical Advanced Study Institute in Elementary Particle Physics, edited by T. DeGrand and D.Toussaint (World Scientific, Singapore, 1990)

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Undesirable effects of covariance matrix techniques for error analysis

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References (7)

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