Probabilistic and least-squares inference of the parameters of a straight-line model

Metrologia

Volumn 44, Issue 5, 2007, Pages 379-384

  Lira, Ignacio ^a   Elster, Clemens ^b   Wöger, Wolfgang ^b,c  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b PHYSIKALISCH TECHNISCHE BUNDESANSTALT   (Germany)

^c NONE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COVARIANCE MATRIX; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION;

PROBABILISTIC METHOD; STRAIGHT-LINE MODEL; TRUE VALUES;

MEASUREMENT THEORY;

EID: 38549133857     PISSN: 00261394     EISSN: 16817575     Source Type: Journal    
DOI: 10.1088/0026-1394/44/5/014     Document Type: Article

References (24)

1. Legendre A M 1805 Nouvelles Méthodes pour la Détermination des Orbites des Comètes (Paris: F Didot)
2. Gauss C F 1823 Theoria Combinationis Obsevationum Erroribus Minimis Obnoxiae vol 4 (Göttingen, Germany: Werke)
3. Adcock R J 1878 A problem in least squares Analyst 5 53-4
4. Pearson K 1901 On lines and planes of closest fit to systems of points in space Phil. Mag. 2 559-72
5. Deming W E 1943 Statistical Adjustment of Data (New York: Wiley) reprinted 1984
6. Bartlett M S 1949 The fitting of straight lines if both variables are subject to error Biometrika 5 207-42
7. York D 1966 Least-squares fitting of a straight line Can. J. Phys. 44 1079-86
8. Williamson J H 1968 Least-squares fitting of a straight line Can. J. Phys. 46 1845-7
9. Barker D R and Diana L M 1974 Simple method for fitting data when both variables have uncertainties Am. J. Phys. 42 224-7
10. Orear J 1982 Least squares when both variables have uncertainties Am. J. Phys. 50 912-6
11. Neri F, Saitta G and Chiofalo S 1989 An accurate and straightforward approach to line regression analysis of error-affected experimental data J. Phys. E: Sci. Instrum. 22 215-7
12. Cecchi G C 1991 Error analysis of the parameters of a least-squares determined curve when both variables have uncertainties Meas. Sci. Technol. 2 1127-8
13. Cecchi G C 1993 Error analysis of the parameters of a least-squares determined curve when both variables have uncertainties Meas. Sci. Technol. 4 906 (erratum)
14. Macdonald J R and Thompson W J 1992 Least-squares fitting when both variables contain errors: pitfalls and possibilities Am. J. Phys. 69 66-73
15. Cameron Reed B 1992 Linear least-squares fits with errors in both coordinates: II. Comments on parameter variances Am. J. Phys. 60 59-62
16. Kalantar A H 1992 Straight-line parameters' errors propagated from the errors in both coordinates Meas. Sci. Technol. 3 1113
17. Moreno C and Bruzzone H 1993 Parameters' variances of a least-squares determined straight line with errors in both coordinates Meas. Sci. Technol. 4 635-6
18. Bruzzone H and Moreno C 1998 When errors in both coordinates make a difference in the fitting of straight lines by least squares Meas. Sci. Technol. 9 2007-11
19. Jaynes E T 1957 Information theory and statistical mechanics Phys. Rev. 106 620-30
20. Wöger W 1987 Probability assignment to systematic deviations by the principle of maximum entropy IEEE Trans. Instrum. Meas. 36 655-8
21. Lira I 2000 Curve adjustment by the least-squares method Metrologia 37 677-81
22. Weise K 1986 Treatment of uncertainties in precision measurements IEEE Trans. Instrum. Meas. 36 642-5
23. Elster C, Wöger W and Cox M G 2007 Draft GUM Supplement 1 and Bayesian analysis Metrologia 44 L31-2
24. Lira I 2002 Evaluating the Measurement Uncertainty. Fundamentals and Practical Guidance (Bristol: Institute of Physics Publishing)