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Chain graph models: topological sorting of meta-arrows and efficient construction of $${\mathcal{B}}$$ -essential graphs

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Chain graph models: topological sorting of meta-arrows and efficient construction of $${\mathcal{B}}$$ -essential graphs

Content Provider	Springer Nature Link
Author	Rocca, Luca Roverato, Alberto
Copyright Year	2007
Abstract	Essential graphs and largest chain graphs are well-established graphical representations of equivalence classes of directed acyclic graphs and chain graphs respectively, especially useful in the context of model selection. Recently, the notion of a labelled block ordering of vertices $${\mathcal{B}}$$ was introduced as a flexible tool for specifying subfamilies of chain graphs. In particular, both the family of directed acyclic graphs and the family of “unconstrained” chain graphs can be specified in this way, for the appropriate choice of $${\mathcal{B}}$$ . The family of chain graphs identified by a labelled block ordering of vertices $${\mathcal{B}}$$ is partitioned into equivalence classes each represented by means of a $${\mathcal{B}}$$ -essential graph. In this paper, we introduce a topological ordering of meta-arrows and use this concept to devise an efficient procedure for the construction of $${\mathcal{B}}$$ -essential graphs. In this way we also provide an efficient procedure for the construction of both largest chain graphs and essential graphs. The key feature of the proposed procedure is that every meta-arrow needs to be processed only once.
Starting Page	73
Ending Page	83
Page Count	11
File Format	PDF
ISSN	16182510
Journal	Statistical Methods and Applications
Volume Number	17
Issue Number	1
e-ISSN	1613981X
Language	English
Publisher	Springer-Verlag
Publisher Date	2007-04-03
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Conditional independence Graphical model Labelled block ordering Markov equivalence Markov property Partial ordering Well-ordering Economic Theory Statistics for Business/Economics/Mathematical Finance/Insurance Statistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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