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Error Propagation, Regression and Experimental Design
Last Updated: 2026-02-05 15:10:04
Abstract
Multivariate statistical methods are used to study the propagation of measurement errors through computational procedures, to fit mathematical models to experimental data, predict the outcome of experiments, design experiments that yielding optimal information or distinguish between model structures. The lecture introduces to linear and nonlinear regression methodology.
Content
A central task in any Simulation project is model validation, i.e. to check if the model describes the real system sufficiently well. An established and consistent methodology to achieve this goal is available by regression analysis. It requires a basic understanding of multivariate statistics and the theory of error propagation in linear and nonlinear computational procedures. The following questions can be answered with the methods introduced in the lecture: - How precise are computational results calculated on the basis of imprecise measurements? - Which tools and algorithms are available to facilitate error propagation analysis? - How are parametrized models fitted to measurement data? - How precise are the results of a model fit? - Can the fitted model be used to make meaningful predictions? - How can expensive (lab and simulation) experiments be designed in order to obtain maximal information with minimal effort? - If several models are available: What is the best model to describe the data? - How can experiments be designed for model selection? - What are the limitations, pitfalls and drawbacks of standard regression methodology? The lecture is accompanied by MATLAB exercises to train the introduced concepts and methods immediately when they are introduced.
Resources
Literature
Accompanying lecture materials on www.simtec.mb.uni-siegen.de (see Lehre->Materialien), log-in password available directly from [email protected]
General Information
- Language
- English
Examination
- Type
- end-of-semester examination
Course Components
| Type | Title | Time & Place | Hours |
|---|---|---|---|
| lecture with exercise |
Error Propagation, Regression and Experimental Design
8 blocks at 4 hours each!
|
|
3 h weekly |