Markov properties for mixed graphs
Copyright policy )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 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.
Published in at http://dx.doi.org/10.3150/12-BEJ502 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)
- University College London United Kingdom
- Carnegie Mellon University United States
- University of Oxford United Kingdom
FOS: Computer and information sciences, Statistics & Probability, CONDITIONAL-INDEPENDENCE, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), composition property, global Markov property, m-separation, pairwise Markov property, CAUSAL-MODELS, SYSTEMS, Statistics - Machine Learning, maximality, FOS: Mathematics, Science & Technology, Other Statistics (stat.OT), $m$-separation, Statistics - Other Statistics, graphoid, CHAIN GRAPHS, Physical Sciences, independence model, Mathematics
FOS: Computer and information sciences, Statistics & Probability, CONDITIONAL-INDEPENDENCE, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), composition property, global Markov property, m-separation, pairwise Markov property, CAUSAL-MODELS, SYSTEMS, Statistics - Machine Learning, maximality, FOS: Mathematics, Science & Technology, Other Statistics (stat.OT), $m$-separation, Statistics - Other Statistics, graphoid, CHAIN GRAPHS, Physical Sciences, independence model, Mathematics
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).35 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!