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Parameter Selection Methods in Inverse Problem Formulation

Part of the Lecture Notes in Mathematics book series (LNMBIOS,volume 2064)

Abstract

We discuss methods for a priori selection of parameters to be estimated in inverse problem formulations (such as Maximum Likelihood, Ordinary and Generalized Least Squares) for dynamical systems with numerous state variables and an even larger number of parameters. We illustrate the ideas with an in-host model for HIV dynamics which has been successfully validated with clinical data and used for prediction and a model for the reaction of the cardiovascular system to an ergometric workload.

Keywords

  • Ordinary Little Square
  • Parameter Vector
  • Fisher Information Matrix
  • Uncertainty Quantification
  • Sensitivity Matrix

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

This research was supported in part by Grant Number R01AI071915-07 from the National Institute of Allergy and Infectious Diseases and in part by the Air Force Office of Scientific Research under grant number FA9550-09-1-0226. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIAID, the NIH or the AFOSR.

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Banks, H.T., Cintrón-Arias, A., Kappel, F. (2013). Parameter Selection Methods in Inverse Problem Formulation. In: Batzel, J., Bachar, M., Kappel, F. (eds) Mathematical Modeling and Validation in Physiology. Lecture Notes in Mathematics(), vol 2064. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32882-4_3

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