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Contributions à l'analyse de sensibilité et à l'analyse discriminante généralisée

Abstract : Two topics are studied in this thesis: sensitivity analysis and generalized discriminant analysis.

Global sensitivity analysis of a mathematical model studies how the output variables of this last react to variations of its inputs. The methods based on the study of the variance quantify the part of variance of the response of the model due to each input variable and each subset of input variables. The first subject of this thesis is the impact of a model uncertainty on results of a sensitivity analysis. Two particular forms of uncertainty are studied: that due to a change of the model of reference, and that due to the use of a simplified model with the place of the model of reference. A second problem was studied during this thesis, that of models with correlated inputs. Indeed, classical sensitivity indices not having significance (from an interpretation point of view) in the presence of correlation of the inputs, we propose a multidimensional approach consisting in expressing the sensitivity of the output of the model to groups of correlated variables. Applications in the field of nuclear engineering illustrate this work.

Generalized discriminant analysis consists in classifying the individuals of a test sample in groups, by using information contained in a training sample, when these two samples do not come from the same population. This work extends existing methods in a Gaussian context to the case of binary data. An application in public health illustrates the utility of generalized discrimination models thus defined.
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Contributor : Julien Jacques Connect in order to contact the contributor
Submitted on : Monday, January 2, 2006 - 3:43:57 PM
Last modification on : Friday, April 15, 2022 - 3:00:03 PM
Long-term archiving on: : Monday, September 20, 2010 - 1:21:16 PM


  • HAL Id : tel-00011169, version 2



Julien Jacques. Contributions à l'analyse de sensibilité et à l'analyse discriminante généralisée. Mathématiques [math]. Université Joseph-Fourier - Grenoble I, 2005. Français. ⟨tel-00011169v2⟩



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