statistics

Course description Interest in the geometrical approach to statistical inference has been growing in the last decades. Starting from the seminal works of Rao (1945) and then Amari and Chentsov in the 80s, the inter-disciplinary field of Information Geometry (IG) is now well-established with few dedicated conferences and a journal Information Geometry.

Many real systems (social groups, the brain, economic and transportation networks) display a particular organization of their hubs (nodes with a lot of connections): they are more densely connected among them than expected by chance. In other words, these rich nodes form clubs, called 'rich clubs'. How do these (structural) rich clubs reflect on dynamical processes taking place on the network? It depends on many aspects: of course, it depends on the dynamics, so here we focus on diffusion dynamics modelled through continuous-time random walks. Then, it also depends on which other types of structures are present in the network, and on their hierarchical relations. In brief: the presence of a strong structural does not imply the existence a strong functional rich club (easier diffusion among rich nodes). The vice versa is also true: functional rich clubs do not translate directly into denser connectivity among hubs. For more detail, and cool plots, see the paper!

Abstract A statistical data depth $d(x, \mathbb{P})$ is a measure of depth or outlyingness of a sample $x \in \mathbb{R}^p$ with respect to its underlying distribution $\mathbb{P}$ and it provides a centre-outward ordering of sample points.