Sensitivity Analysis for Uncertainty Quantification in Mathematical Models

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.

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