14.05.2025 12:15 Luciana Dalla Valle (University of Torino, IT): Approximate Bayesian conditional copulas
According to Sklar’s theorem, any multidimensional absolutely continuous distribution function can be uniquely represented as a copula, which captures the dependence structure among the vector components. In real data applications, the interest of the analyses often lies on specific functionals of the dependence, which quantify aspects of it in a few numerical values. A broad literature exists on such functionals, however extensions to include covariates are still limited. This is mainly due to the lack of unbiased estimators of the conditional copula, especially when one does not have enough information to select the copula model. Several Bayesian methods to approximate the posterior distribution of functionals of the dependence varying according covariates are presented and compared; the main advantage of the investigated methods is that they use nonparametric models, avoiding the selection of the copula, which is usually a delicate aspect of copula modelling. These methods are compared in simulation studies and in two realistic applications, from civil engineering and astrophysics.
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21.05.2025 12:15 Michael Muma (TU Darmstadt): The T-Rex Selector: Fast High-Dimensional Variable Selection with False Discovery Rate Control
Providing guarantees on the reproducibility of discoveries is essential when drawing inferences from high-dimensional data. Such data is common in numerous scientific domains, for example, in biomedicine, it is imperative to reliably detect the genes that are truly associated with the survival time of patients diagnosed with a certain type of cancer, or in finance, one aims at determining a sparse portfolio to reliably perform index tracking. This talk introduces the Terminating-Random Experiments (T-Rex) selector, a fast multivariate variable selection framework for high-dimensional data. The T-Rex selector provably controls a user-defined target false discovery rate (FDR) while maximizing the number of selected variables. It scales to settings with millions of variables. Its computational complexity is linear in the number of variables, making it more than two orders of magnitude faster than, e.g., the existing model-X knockoff methods. An easy-to-use open-source R package that implements the TRexSelector is available on CRAN. The focus of this talk lies on high-dimensional linear regression models, but we also describe extensions to principal component analysis (PCA) and Gaussian graphical models (GGMs).
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