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An Inverse Problem Statistical Methodology Summary

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Book cover Mathematical and Statistical Estimation Approaches in Epidemiology

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.

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Author information

Authors and Affiliations

  1. Center for Research in Scientific Computation and Center for Quantitative Sciences in Biomedicine, North Carolina State University, Raleigh, NC 27695-8212, USA

    H. Thomas Banks, Marie Davidian, John R. Samuels Jr. & Karyn L. Sutton

Authors
  1. H. Thomas Banks
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  2. Marie Davidian
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  3. John R. Samuels Jr.
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  4. Karyn L. Sutton
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Editor information

Editors and Affiliations

  1. Arizona State University School of Human Evolution & Social Change, Tempe, AZ 85287-2402, USA

    Gerardo Chowell

  2. Los Alamos National Laboratory, Mail Stop B284, Los Alamos, NM 87545, USA

    James M. Hyman  & Luís M. A. Bettencourt  & 

  3. Dept. Mathematics & Statistics, Arizona State University, P.O.Box 871804, Tempe, AZ 85287, USA

    Carlos Castillo-Chavez

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© 2009 Springer Science+Business Media B.V.

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Banks, H.T., Davidian, M., Samuels, J.R., Sutton, K.L. (2009). An Inverse Problem Statistical Methodology Summary. In: Chowell, G., Hyman, J.M., Bettencourt, L.M.A., Castillo-Chavez, C. (eds) Mathematical and Statistical Estimation Approaches in Epidemiology. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2313-1_11

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