Grabe, M: Generalized Gaussian Error Calculus
(Sprache: Englisch)
This book addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. It integrates mathematics and its applications to physical measurements, and serves as a text for graduate students and a reference for researchers.
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This book addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. It integrates mathematics and its applications to physical measurements, and serves as a text for graduate students and a reference for researchers.
Klappentext zu „Grabe, M: Generalized Gaussian Error Calculus “
For the first time in 200 years Generalized Gaussian Error Calculus addresses a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large.
The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. Beyond, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions.
The approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence interval as put down by Student, and a contribution due to unknown systematic errors, as expressed by an appropriate worst case estimation.
The proposed book Generalized Gaussian Error Calculus addresses for the first time since 200 years a rigorous, complete and self-consistent revision of the Gaussian error calculus. Since experimentalists realized that measurements in general are burdened by unknown systematic errors, the classical, widespread used evaluation procedures scrutinizing the consequences of random errors alone turned out to be obsolete. As a matter of course, the error calculus to-be, treating random and unknown systematic errors side by side, should ensure the consistency and traceability of physical units, physical constants and physical quantities at large.
The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. What's more, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions.
This approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence interval as put down by Student, and a contribution due to unknown systematic errors, as expressed by an appropriate worst case estimation.
The generalized Gaussian error calculus considers unknown systematic errors to spawn biased estimators. What's more, random errors are asked to conform to the idea of what the author calls well-defined measuring conditions.
This approach features the properties of a building kit: any overall uncertainty turns out to be the sum of a contribution due to random errors, to be taken from a confidence interval as put down by Student, and a contribution due to unknown systematic errors, as expressed by an appropriate worst case estimation.
Inhaltsverzeichnis zu „Grabe, M: Generalized Gaussian Error Calculus “
Basics of Metrology.- True Values and Traceability.- Models and Approaches.- Generalized Gaussian Error Calculus.- The New Uncertainties.- Treatment of Random Errors.- Treatment of Systematic Errors.- Error Propagation.- Means and Means of Means.- Functions of Erroneous Variables.- Method of Least Squares.- Essence of Metrology.- Dissemination of Units.- Multiples and Sub-multiples.- Founding Pillars.- Fitting of Straight Lines.- Preliminaries.- Straight Lines: Case (i).- Straight Lines: Case (ii).- Straight Lines: Case (iii).- Fitting of Planes.- Preliminaries.- Planes: Case (i).- Planes: Case (ii).- Planes: Case (iii).- Fitting of Parabolas.- Preliminaries.- Parabolas: Case (i).- Parabolas: Case (ii).- Parabolas: Case (iii).- Non-Linear Fitting.- Series Truncation.- Transformation.
Autoren-Porträt von Michael Grabe
1967 Graduation in Physics at the Technical University of Stuttgart1970 Doctorate at the Technical University of Braunschweig
1970 - 1975 Scientific assistant and lecturer at the Technical University of Braunschweig
1975 - 2004 Member of Staff at the Physikalische Technischer Bundesanstalt Braunschweig, commissioned to legal metrology, computerized interferometric measurment of length, measurement uncertainties and the adjustment of physical constants
Bibliographische Angaben
- Autor: Michael Grabe
- 2010, 301 Seiten, 5 farbige Abbildungen, 50 Schwarz-Weiß-Abbildungen, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer
- ISBN-10: 3642033040
- ISBN-13: 9783642033049
- Erscheinungsdatum: 26.02.2010
Sprache:
Englisch
Rezension zu „Grabe, M: Generalized Gaussian Error Calculus “
From the reviews: "This book is aimed at the metrology community. ... The approach elaborated in this book assesses unknown systematic errors via intervals of estimated lengths. ... the author proposes the generalized Gaussian approach presented here as one which produces reliable measurement uncertainties meeting the demands of traceability." (Rainer Schlittgen, Zentralblatt MATH, Vol. 1210, 2011)
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