Title: Path weights in concentration graph models
Authors: Alberto Roverato - University of Padova (Italy) [presenting]
Abstract: Statistical models associated with a graph, called graphical models, are of significant interest in many modern applications and have become a popular tool for representing network structures in applied contexts such as genetic and brain network analysis. A graph is represented as a set of nodes, also called vertices, interconnected by a set of edges. A path in a graph is a finite sequence of distinct vertices with the property that each vertex in the sequence is adjacent to the vertex next to it. In graphical models, paths joining vertices of the graph play a central role because they determine the specification of the association structure of the variables highlighting the role played by intermediate variables. In models for continuous acyclic directed graphs, the well-established theory of path analysis provides a method that aims at quantifying the relative importance of causal relationships represented by directed paths. On the other hand, in undirected graphs a theory concerning the analysis of the strength of the association encoded by paths has been introduced only more recently. We consider concentration graph models and show how weights associated with undirected paths can be applied in the analysis of the graph structure and in the computation of betweenness centrality measures.