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Erschienen in:
2009 | OriginalPaper | Buchkapitel
An Inverse Problem Statistical Methodology Summary
verfasst von : H. Thomas Banks, Marie Davidian, John R. Samuels Jr., Karyn L. Sutton
Erschienen in: Mathematical and Statistical Estimation Approaches in Epidemiology
Verlag: Springer Netherlands
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We discuss statistical and computational aspects of inverse or parameter estimation problems for deterministic dynamical systems based on Ordinary Least Squares and Generalized Least Squares with appropriate corresponding data noise assumptions of constant variance and nonconstant variance (relative error), respectively. Among the topics included here are mathematical model, statistical model and data assumptions, and some techniques (residual plots, sensitivity analysis, model comparison tests) for verifying these. The ideas are illustrated throughout with the popular logistic growth model of Verhulst and Pearl as well as with a recently developed population level model of pneumococcal disease spread.