2018 BFY III Abstract Detail Page
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| Abstract Title: |
The Covariance Matrix and Jacobian in Error Propagation |
| Abstract: |
The covariance matrix for a data set encodes the uncertainties in that data and possible correlations among their random variations. The Jacobian describes how small changes to the data set values will change the parameters derived from that set. The covariance matrix for the derived parameters is readily obtained from matrix formulas involving the input covariance matrix and a Jacobian. The formulas are demonstrated for data from our muon lifetime measurements and from our Balmer series spectroscopy measurements. The Microsoft Excel Solver program is used to determine the fitting parameters according to the maximum likelihood or least squares principle. Using only Excel's built-in array functions, the input covariance matrix and the Jacobian are constructed and used to determine the parameter covariance matrix. For the Balmer series experiment, the Rydberg uncertainty is calculated from the uncertainty in the measured diffraction angles for the spectral lines from a hydrogen source from reference sources used to calibrate the spectrometer. |
| Abstract Type: |
Poster
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Author/Organizer Information |
| Primary Contact: |
Robert DeSerio
University of Florida
Department of Physics
Gainesville, FL 32611-8440
Phone: (352) 392-1690
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