Simultaneous statistical inference is concerned with addressing several inferential problems under one and the same statistical model, i. e., based on one and the same dataset. One important example is the problem of multiple testing, meaning that m > 1 statistical hypotheses are tested on the basis of one and the same dataset.
Multivariate multiple test procedures have received growing attention recently. This is due to the fact that data generated by modern applications typically are high-dimensional, but exhibit pronounced dependencies due to the technical mechanisms involved in the experiments. Hence, it is possible and often necessary to exploit these dependencies in order to achieve reasonable statistical power.
We will give an overview of some multivariate approaches to multiple testing and their applications.
From the mathematical perspective, they rely on higher-order probability bounds, copula theory, and extreme value theory.

Einladung von Prof. Jens Rademacher