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Rank transformations are frequently employed in numerical experiments involving a computational model, especially in the context of sensitivity and uncertainty analyses. Ranks can cope with nonlinear (albeit monotonic) input output distributions, allowing the use of linear regression techniques. Rank transformed statistics are more robust, and provide a useful solution in the presence of long tailed input and output distributions (Saltelli and Homma, 1992). Care must be employed when interpreting the results of such analyses, as any conclusion drawn for the ranked model does not translate easily to the original model. In the present note an heuristic approach is taken, exploring, by way of practical examples, the differences between the original and the ranked models. This is done employing sensitivity indices, whereby the total variance of the model output is decomposed into a sum of terms of increasing dimensionality. The sensitivity indices were developed by Sobol (1990, 1993), and have conceptual similarities with the Fourier Amplitude Sensitivity Test (FAST). Both methods allow the total model variance D to be written as the sum of terms of different dimension. The sensitivity indices have much in common with the importance measure discussed by other investigators.

Additional information

Authors: SALTELLI A, JRC Ispra (IT)
Bibliographic Reference: Paper presented: SAMO 95, Belgirate (IT), September 25-27, 1995
Availability: Available from (1) as Paper EN 39584 ORA
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