.
"Sadeghi, Kayvan" .
"Combinatorics" .
"graphoid" .
.
"en" .
.
"text" .
"MC graph" .
"In this thesis we describe subclasses of a class of graphs with three types of\nedges, called loopless mixed graphs (LMGs). The class of LMGs contains almost\nall known classes of graphs used in the literature of graphical Markov models. We\nfocus in particular on the subclass of ribbonless graphs (RGs), which as special\ncases include undirected graphs, bidirected graphs, and directed acyclic graphs, as\nwell as ancestral graphs and summary graphs. We define a unifying interpretation\nof independence structure for LMGs and pairwise and global Markov properties\nfor RGs, discuss their maximality, and, in particular, prove the equivalence of\npairwise and global Markov properties for graphoids defined over the nodes of\nRGs. Three subclasses of LMGs (MC, summary, and ancestral graphs) capture\nthe modified independence model after marginalisation over unobserved variables\nand conditioning on selection variables of variables satisfying independence restrictions\nrepresented by a directed acyclic graph (DAG). We derive algorithms\nto generate these graphs from a given DAG or from a graph of a specific subclass,\nand we study the relationships between these classes of graphs. Finally, a manual\nand codes are provided that explain methods and functions in R for implementing\nand generating various graphs studied in this thesis." .
"undirected graph" .
"directed acyclic graph" .
"Statistics" .
.
"maximality" .
.
"Discrete mathematics (statistics)" .
.
"independence model" .
"Lauritzen, Steffen" .
.
"ora:6540" .
.
"2014-02-05T00:50:33.377000+00:00"^^ .
"summary graph" .
"Graphical representation of independence structures" .
"fedoraAdmin" .
.
.
"composition property" .
"Computer science (mathematics)" .
.
"bidirected graph" .
"2012" .
"2012-11-02T09:05:02.908000+00:00"^^ .
"separation criterion" .
"ora:6540" .
"ancestral graph" .
"global and pairwise Markov property" .
.
"This thesis is not currently available via ORA." .
"born digital" .
"urn:uuid:86ff6155-a6b9-48f9-9dac-1ab791748072" .
"marginalisation and conditioning" .
.
"thesis" .
"chain graph" .