Invited talk by Emiliano Torre
Events
Emiliano Torre gives an invited talk at the Institute of Neuroscience and Medicine (Forschungszentrum Jülich) titled "Vine copula modeling of high-dimensional inputs in uncertainty quantification problems".
Abstract
The quantification of uncertainty (UQ) in the response of a system to stochastic input requires to build a map of the input-output relationship, and to study how the components/parameters of the input influence the output.
Advanced UQ methods based on spectral decomposition, such as polynomial chaos expansions (PCE), accomplish this task under the assumption that the components of the input are statistically independent, or that they can be mapped onto independent variables by means of isoprobabilistic transformations like Rosenblatt or Nataf. Such transformations, however, are in general difficult to compute, both analytically and numerically, especially in large dimensions. Thus, these methods are not applicable in the most general setting of dependent inputs.
In this contribution we propose an effective approach to model the input's dependence structure (copula) via vine copulas. Vine copulas consist of a factorization of a joint copula into pair copulas of its components. The advantage of this approach is two-fold: it grants great
flexibility in modeling the pairwise dependencies of the data, while at the same time providing a map of those onto independent data via the Rosenblatt transform. The independent data can be used to build a map of the input-output relationship describing the system by, e.g., PCE.