dc.contributor.author Kahle, Thomas dc.contributor.author Rauh, Johannes dc.contributor.author Sullivant, Seth dc.date.accessioned 2016-10-12T07:37:40Z dc.date.available 2016-10-12T07:37:40Z dc.date.issued 2012 dc.identifier.uri http://publications.mfo.de/handle/mfo/1251 dc.description OWLF 2011 en_US dc.description.abstract We study random walks on contingency tables with fixed marginals, corresponding to a (log-linear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that are not connected. We study linear conditions on the values of the marginals that ensure that all tables in a given fiber are connected. We show that many graphical models have the positive margins property, which says that all fibers with strictly positive marginals are connected by the quadratic moves that correspond to conditional independence statements. The property persists under natural operations such as gluing along cliques, but we also construct examples of graphical models not enjoying this property. Our analysis of the positive margins property depends on computing the primary decomposition of the associated conditional independence ideal. The main technical results of the paper are primary decompositions of the conditional independence ideals of graphical models of the $N$-cycle and the complete bipartite graph $K_{2,N2-2}$, with various restrictions on the size of the nodes. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2012,06 dc.subject Algebraic statistics en_US dc.subject Markov basis en_US dc.subject Connectivity of fibers en_US dc.subject Binomial primary decomposition en_US dc.title Positive Margins and Primary Decomposition en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2012-06 local.scientificprogram OWLF 2011 en_US local.series.id OWP-2012-06 local.subject.msc 13 local.subject.msc 52 local.subject.msc 11 local.subject.msc 60 local.subject.msc 62 local.subject.msc 05 dc.identifier.urn urn:nbn:de:101:1-201204249311 dc.identifier.ppn 165145793X
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