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====== What is Sensitivity Analysis ======

Sensitivity analysis (SA) is the study of how the variation in the output of a model (numerical or otherwise) can be apportioned, qualitatively or quantitatively, to different sources of variation, and how the given model depends upon the information fed into it. Reasons why modelers should carry out a sensitivity analysis are to determine:

<HTML><ol style="list-style-type: lower-alpha;"></HTML>
<HTML><li></HTML>if a model resembles the system or processes under study;<HTML></li></HTML>
<HTML><li></HTML>the parameters that mostly contribute to the output variability;<HTML></li></HTML>
<HTML><li></HTML>the model parameters (or parts of the model itself) that are insignificant;<HTML></li></HTML>
<HTML><li></HTML>if there is some region in the space of input parameters for which the model variation is maximal;<HTML></li></HTML>
<HTML><li></HTML>the optimal regions within the space of the parameters for use in a subsequent calibration study;<HTML></li></HTML>
<HTML><li></HTML>if and which (group of) parameters interact with each other.<HTML></li></HTML><HTML></ol></HTML>

//(Saltelli, 2000)//\\
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//Local and global sensitivity analysis//
 aims at determining how sensitive the model output is to changes in model inputs. When input parameters are relatively certain, we can look at the partial derivative of the output function with respect to the input parameters. This sensitivity measure can easily be computed numerically by performing multiple simulations varying input-parameters around a nominal value. We will find out the local impact of the parameters on the model output and therefore techniques like these are called local sensitivity analysis. For environmental and health risk assessments, input parameters will often be uncertain and therefore local sensitivity analysis techniques will not be usable for a quantitative analysis. We want to find out which of the uncertain input parameters are more important in determining the uncertainty in the output of interest. To find this we need to consider global sensitivity analysis, which are usually implemented using Monte Carlo (MC) simulation and are, therefore, called sampling-based methods.\\
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//Choice of an appropriate method//

Different sensitivity analysis techniques will do well on different types of model problems. At an initial phase, for models with a large amount of uncertain input parameters, a screening method could be used to qualitatively find out which the most important parameters are and which are not important. The screening method implemented in EIKOS is the Morris design //(Morris, 1991)//. A natural starting point in the analysis with sampling-based methods would be to examine scatter plots. With these, the modeller can graphically find out nonlinearities, nonmonotonicity and correlations between the inputoutput parameters.


//References//

Saltelli, 2000. Andrea Saltelli. What is sensitivity analysis? In Sensitivity analysis, Wiley Ser. Probab. Stat., pages 3–13. Wiley, Chichester, 2000.

Morris, 1991. Max D. Morris. Parameterial sampling plans for preliminary computational experiments. Technometrics, 33(2):161–174, May 1991.

**See also**

  * [[Sensitivity_analysis_toolbox_wiki|Sensitivity analysis toolbox Wiki]]
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