Markov properties for mixed graphs
In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids. We focus in particular on...
| Asıl Yazarlar: | , |
|---|---|
| Materyal Türü: | Journal article |
| Dil: | English |
| Baskı/Yayın Bilgisi: |
International Statistical Institute
2011
|
| _version_ | 1826278975645679616 |
|---|---|
| author | Sadeghi, K Lauritzen, S |
| author_facet | Sadeghi, K Lauritzen, S |
| author_sort | Sadeghi, K |
| collection | OXFORD |
| description | In this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids. We focus in particular on the subclass of ribbonless graphs which as special cases include undirected graphs, bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and summary graphs. We define maximality of such graphs as well as a pairwise and a global Markov property. We prove that the global and pairwise Markov properties of a maximal ribbonless graph are equivalent for any independence model that is a compositional graphoid. |
| first_indexed | 2024-03-06T23:51:56Z |
| format | Journal article |
| id | oxford-uuid:72e6b348-88e1-417b-a77a-bd8bf4ca7edb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T23:51:56Z |
| publishDate | 2011 |
| publisher | International Statistical Institute |
| record_format | dspace |
| spelling | oxford-uuid:72e6b348-88e1-417b-a77a-bd8bf4ca7edb2022-03-26T19:53:02ZMarkov properties for mixed graphsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:72e6b348-88e1-417b-a77a-bd8bf4ca7edbEnglishSymplectic Elements at OxfordInternational Statistical Institute2011Sadeghi, KLauritzen, SIn this paper, we unify the Markov theory of a variety of different types of graphs used in graphical Markov models by introducing the class of loopless mixed graphs, and show that all independence models induced by $m$-separation on such graphs are compositional graphoids. We focus in particular on the subclass of ribbonless graphs which as special cases include undirected graphs, bidirected graphs, and directed acyclic graphs, as well as ancestral graphs and summary graphs. We define maximality of such graphs as well as a pairwise and a global Markov property. We prove that the global and pairwise Markov properties of a maximal ribbonless graph are equivalent for any independence model that is a compositional graphoid. |
| spellingShingle | Sadeghi, K Lauritzen, S Markov properties for mixed graphs |
| title | Markov properties for mixed graphs |
| title_full | Markov properties for mixed graphs |
| title_fullStr | Markov properties for mixed graphs |
| title_full_unstemmed | Markov properties for mixed graphs |
| title_short | Markov properties for mixed graphs |
| title_sort | markov properties for mixed graphs |
| work_keys_str_mv | AT sadeghik markovpropertiesformixedgraphs AT lauritzens markovpropertiesformixedgraphs |