When performing multiple testing, adjusting the distribution of the null hypotheses is ubiquitous in applications. However, the effect of such an operation remains largely unknown, especially in terms of false discovery proportion (FDP) and true discovery proportion (TDP). In this talk, we explore this issue in the most classical case where the null distributions are Gaussian with an unknown rescaling parameters (mean and variance) and where the Benjamini-Hochberg (BH) procedure is applied after a datarescaling step.[-]

Multivariate extreme value distributions are a common choice for modelling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate extreme value distributions into a Markov random field with respect to a tree. Although in general not an extreme value distribution itself, this Markov tree is attracted by a multivariate extreme value distribution. The latter serves as a tree-based approximation to an unknown extreme value distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim's algorithm with estimated pairwise upper tail dependence coefficients or Kendall's tau values as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree-structured extreme value distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin.[-]

Consider a sample of points drawn from some unknown density on $R^d$. Assume the only information we have about the sample are the $k$-nearest neighbor relationships: we know who is among the $k$-nearest neighors of whom, but we do not know any distances between points, nor the point coordinates themselves. We prove that as the sample size goes to infinty, it is possible to reconstruct the underlying density p and the distances of the points (up to a multiplicative constant).

$k$-nearest neighbor graph - random geometric graph - ordinal embedding[-]