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Error propagation: Difference between revisions
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Proper reporting of experimental measurements requires the calculation of error bars or "confidence intervals". The appropriate and satisfactory calibration of data and analysis of errors is essential to be able to judge the relevance of observed trends. Below, a brief definition of the main concepts and a discussion of generic ways to obtain error estimates is provided. | Proper reporting of experimental measurements requires the calculation of error bars or "confidence intervals". The appropriate and satisfactory calibration of data and analysis of errors is essential to be able to judge the relevance of observed trends. Below, a brief definition of the main concepts and a discussion of generic ways to obtain error estimates is provided. | ||
<ref>[http://www.nrbook.com/ W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in FORTRAN (Cambridge University Press, 1992), 2nd ed.]</ref> | <ref>[http://www.nrbook.com/ W. Press, S. Teukolsky, W. Vetterling, and B. Flannery, Numerical Recipes in FORTRAN (Cambridge University Press, 1992), 2nd ed.]</ref> | ||
<ref>P. Bevington and D. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, UK, 2003), 3rd ed. ISBN 978-0072472271</ref> | <ref>P. Bevington and D. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, UK, 2003), 3rd ed. {{ISBN|978-0072472271}}</ref> | ||
Of course, any particular measuring device generally requires specific techniques. | Of course, any particular measuring device generally requires specific techniques. | ||
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The simplest case is when the physically interesting phenomenon is slowly varying in time. | The simplest case is when the physically interesting phenomenon is slowly varying in time. | ||
Random noise is usually characterised by a high frequency, so that a filter in frequency space can then separate signal and noise neatly. | Random noise is usually characterised by a high frequency, so that a filter in frequency space can then separate signal and noise neatly. | ||
<ref>D. Newland, An Introduction to Random Vibrations, Spectral and Wavelet Analysis (Dover, New York, 1993) ISBN 0486442748</ref> | <ref>D. Newland, An Introduction to Random Vibrations, Spectral and Wavelet Analysis (Dover, New York, 1993) {{ISBN|0486442748}}</ref> | ||
However, when the physically interesting information is fluctuating, this signal-noise separation by frequency is not feasible, and much care is needed when analysing data. | However, when the physically interesting information is fluctuating, this signal-noise separation by frequency is not feasible, and much care is needed when analysing data. | ||
The application of a set of techniques is required to understand such signals (cross correlation, conditional averaging, spectral analysis, [[Bicoherence|bi-spectral analysis]], | The application of a set of techniques is required to understand such signals (cross correlation, conditional averaging, spectral analysis, [[Bicoherence|bi-spectral analysis]], | ||
<ref>J. van den Berg, ed., Wavelets in Physics (Cambridge University Press, 1999) ISBN 978-0521593113</ref>, [[Biorthogonal decomposition]], | <ref>J. van den Berg, ed., Wavelets in Physics (Cambridge University Press, 1999) {{ISBN|978-0521593113}}</ref>, [[Biorthogonal decomposition]], | ||
determination of fractal dimension, mutual information, reconstruction of chaotic attractor, | determination of fractal dimension, mutual information, reconstruction of chaotic attractor, | ||
<ref>H. Abarbanel, R. Brown, J. Sidorowich, and L. S. Tsimring, [[doi:10.1103/RevModPhys.65.1331|Rev. Mod. Phys. 65, 1331 (1993)]]</ref> ...). | <ref>H. Abarbanel, R. Brown, J. Sidorowich, and L. S. Tsimring, [[doi:10.1103/RevModPhys.65.1331|Rev. Mod. Phys. 65, 1331 (1993)]]</ref> ...). | ||