Graphical representation of independence structures

Thesis

In this thesis we describe subclasses of a class of graphs with three types of edges, called loopless mixed graphs (LMGs). The class of LMGs contains almost all known classes of graphs used in the literature of graphical Markov models. We focus in particular on the subclass of ribbonless graphs (RGs), which as special cases include undirected graphs, bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and summary graphs. We define a unifying interpretation of independe...

Expand abstract

Authors: Sadeghi, K

• Publication date: 2012
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: Oxford University, UK
• Language: English
• Keywords: MC graph; bidirected graph; composition property; graphoid; independence model; summary graph; global and pairwise Markov property; chain graph; ancestral graph; directed acyclic graph; separation criterion; undirected graph; maximality; marginalisation and conditioning
• Subjects: Combinatorics; Computer science (mathematics); Statistics; Discrete mathematics (statistics)