Marginalization and conditioning for LWF chain graphs
Copyright policy )Marginalization and conditioning for LWF chain graphs
In this paper, we deal with the problem of marginalization over and conditioning on two disjoint subsets of the node set of chain graphs (CGs) with the LWF Markov property. For this purpose, we define the class of chain mixed graphs (CMGs) with three types of edges and, for this class, provide a separation criterion under which the class of CMGs is stable under marginalization and conditioning and contains the class of LWF CGs as its subclass. We provide a method for generating such graphs after marginalization and conditioning for a given CMG or a given LWF CG. We then define and study the class of anterial graphs, which is also stable under marginalization and conditioning and contains LWF CGs, but has a simpler structure than CMGs.
48 pages, 9 figures, 2 tables
- University of Cambridge United Kingdom
- University of Cambridge
- University College London United Kingdom
- UNIVERSITY OF CAMBRIDGE
- UNIVERSITY OF CAMBRIDGE
FOS: Computer and information sciences, 62A99, LWF Markov property, Other Statistics (stat.OT), c-separation criterion, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), Foundational topics in statistics, mixed graph, $m$-separation, $c$-separation criterion, Statistics - Other Statistics, Multivariate analysis, m-separation, marginalization and conditioning, Statistics - Machine Learning, chain graph, independence model, FOS: Mathematics, 62H99
FOS: Computer and information sciences, 62A99, LWF Markov property, Other Statistics (stat.OT), c-separation criterion, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), Foundational topics in statistics, mixed graph, $m$-separation, $c$-separation criterion, Statistics - Other Statistics, Multivariate analysis, m-separation, marginalization and conditioning, Statistics - Machine Learning, chain graph, independence model, FOS: Mathematics, 62H99
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