Seminar: Sensitivity analysis: from variance analysis to Cramer-von Mises statistics
 Agnes Lagnoux, Math. Inst. Toulous

10:00, 24-11-2018, F206

Sensitivity analysis: from variance analysis to Cramer-von Mises statistics


A classical problem in the study of computer code experiments is the evaluation of the relative influence of the input variables on some numerical result obtained by a computer code. In this context, the output is seen as a function f of random inputs (generally assumed independent) and a sensitivity analysis is performed using the so-called Hoeffding decomposition. In this functional decomposition, f is expanded as an L²-sum of uncorrelated functions involving only a part of the random inputs. This leads to the Sobol index that measures the amount of randomness (the part of the variance) of the output due to one or more input variables. It remains then to estimate these Sobol indices to rank the variables with respect to their influence on the output. Nevertheless, the Sobol indices and their Monte-Carlo estimation are order two methods: thus they are well adapted to measure the contribution of an input on the deviation around the output mean and it seems very intuitive that the sensitivity of an extreme quantile of the output could depend on sets of variables that cannot be captured using only the variances.  One may generalize them with higher order methods. Indices based on contrast functions depending on the quantity of interest is a nice alternative when one considers quantiles or medians. Another promising possibility consists in defining indices depending on the whole distribution of the output conditioned by the input whose influence must be quantified.

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The 11th HCMUS Scientific Conference (9--10/11/2018)



Program file

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SL-STEM 2018 Conference
Further detail:

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