Graphical representation of independence structures
Sadeghi, Kayvan
Lauritzen, Steffen
Statistics
Discrete mathematics (statistics)
Combinatorics
Computer science (mathematics)
ancestral graph
bidirected graph
chain graph
composition property
directed acyclic graph
global and pairwise Markov property
graphoid
independence model
marginalisation and conditioning
maximality
MC graph
separation criterion
summary graph
undirected graph
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 independence structure for LMGs and pairwise and global Markov properties
for RGs, discuss their maximality, and, in particular, prove the equivalence of
pairwise and global Markov properties for graphoids defined over the nodes of
RGs. Three subclasses of LMGs (MC, summary, and ancestral graphs) capture
the modified independence model after marginalisation over unobserved variables
and conditioning on selection variables of variables satisfying independence restrictions
represented by a directed acyclic graph (DAG). We derive algorithms
to generate these graphs from a given DAG or from a graph of a specific subclass,
and we study the relationships between these classes of graphs. Finally, a manual
and codes are provided that explain methods and functions in R for implementing
and generating various graphs studied in this thesis.
This thesis is not currently available via ORA.
2012
text
thesis
born digital
ora:6540
en
urn:uuid:86ff6155-a6b9-48f9-9dac-1ab791748072