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An Inverse Problem Statistical Methodology Summary

In: Mathematical and Statistical Estimation Approaches in Epidemiology

Author

Listed:
  • H. Thomas Banks

    (North Carolina State University, Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine)

  • Marie Davidian

    (North Carolina State University, Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine)

  • John R. Samuels Jr.

    (North Carolina State University, Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine)

  • Karyn L. Sutton

    (North Carolina State University, Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine)

Abstract

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.

Suggested Citation

  • H. Thomas Banks & Marie Davidian & John R. Samuels Jr. & Karyn L. Sutton, 2009. "An Inverse Problem Statistical Methodology Summary," Springer Books, in: Gerardo Chowell & James M. Hyman & Luís M. A. Bettencourt & Carlos Castillo-Chavez (ed.), Mathematical and Statistical Estimation Approaches in Epidemiology, pages 249-302, Springer.
    • Handle: RePEc:spr:sprchp:978-90-481-2313-1_11
    DOI: 10.1007/978-90-481-2313-1_11
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