# Mathematical and Statistical Estimation Approaches in EpidemiologySensitivity Analysis for Uncertainty Quantification in Mathematical Models

Mathematical and Statistical Estimation Approaches in Epidemiology: Sensitivity Analysis for... [All mathematical models are approximate and their usefulness depends on our understanding the uncertainty inherent in the predictions. Uncertainties can affect the reliability of the results at every stage of computation; they may grow or even shrink as the solution of the model evolves. Often these inherent uncertainties cannot be made arbitrarily small by a more complex model or additional computation and we must understand how the uncertainty in the model parameters, the initial conditions, and the model itself, lead to uncertainties in the model predictions. This chapter is an introductory survey of sensitivity analysis and illustrates how to define the derivative of the model solution as a function of the model input and determine the relative importance of the model parameters on the model predictions.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Mathematical and Statistical Estimation Approaches in EpidemiologySensitivity Analysis for Uncertainty Quantification in Mathematical Models

Editors: Chowell, Gerardo; Hyman, James M.; Bettencourt, Luís M. A.; Castillo-Chavez, Carlos
52 pages

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# References (31)

Publisher
Springer Netherlands
ISBN
978-90-481-2312-4
Pages
195 –247
DOI
10.1007/978-90-481-2313-1_10
Publisher site
See Chapter on Publisher Site

### Abstract

[All mathematical models are approximate and their usefulness depends on our understanding the uncertainty inherent in the predictions. Uncertainties can affect the reliability of the results at every stage of computation; they may grow or even shrink as the solution of the model evolves. Often these inherent uncertainties cannot be made arbitrarily small by a more complex model or additional computation and we must understand how the uncertainty in the model parameters, the initial conditions, and the model itself, lead to uncertainties in the model predictions. This chapter is an introductory survey of sensitivity analysis and illustrates how to define the derivative of the model solution as a function of the model input and determine the relative importance of the model parameters on the model predictions.]

Published: Jan 1, 2009

Keywords: Linear Programming Problem; Sensitivity Index; Singular Vector; Initial Value Problem; Algorithmic Differentiation