We will have two talks:
A tradeoff between explorations and repetitions in global sensitivity analysis for stochastic computer models
Global sensitivity analysis often accompanies computer modeling to understand what are the important factors of a model of interest. In particular, Sobol indices, naturally estimated by Monte-Carlo methods, permit to quantify the contribution of the inputs to the variability of the output. However, stochastic computer models raise difficulties. There is no unique definition of Sobol indices and their estimation is difficult because a good balance between repetitions of the computer code and explorations of the input space must be found. The problem of finding an optimal tradeoff between explorations and repetitions is addressed. Two Sobol indices are considered, their estimators constructed and their asymptotic properties established. To find an optimal tradeoff between repetitions and explorations, a tractable error criterion, which is small when the inputs of the model are ranked correctly, is built and minimized under a fixed computing budget. Then, Sobol estimates based on the balance found beforehand are produced. Convergence rates are given and it is shown that this method is asymptotically oracle. Numerical tests and a sensitivity analysis of a Susceptible-Infectious-Recovered (SIR) model are performed.
Meta-model of a large credit risk portfolio in the Gaussian copula model
We design a meta-model for the loss distribution of a large credit portfolio in the Gaussian copula model. Using both the Wiener chaos expansion on the systemic economic factor and a Gaussian approximation on the associated truncated loss, we significantly reduce the computational time needed for sampling the loss and therefore estimating risk measures on the loss distribution. The accuracy of our method is confirmed by many numerical examples.
Joint work with Florian Bourgey and Clément Rey.
Organizers: Julien Bect (L2S) and Fernando Lopez Caballero (MSSMAT).
No registration is needed, but an email would be appreciated if you intend to come.