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dc.contributor.authorCaines, Peter
dc.contributor.authorMohammadi, Fatemeh
dc.contributor.authorSáenz-de-Cabezón, Eduardo
dc.contributor.authorWynn, Henry
dc.date.accessioned2023-01-10T12:03:03Z
dc.date.available2023-01-10T12:03:03Z
dc.date.issued2022-06-10
dc.description.abstractLattice conditional independence models [Andersson and Perlman, Lattice models for conditional independence in a multivariate normal distribution, Ann. Statist. 21 (1993), 1318–1358] are a class of models developed first for the Gaussian case in which a distributive lattice classifies all the conditional independence statements. The main result is that these models can equivalently be described via a transitive directed acyclic graph (TDAG) in which, as is normal for causal models, the conditional independence is in terms of conditioning on ancestors in the graph. We demonstrate that a parallel stream of research in algebra, the theory of Hibi ideals, not only maps directly to the lattice conditional independence models but gives a vehicle to generalise the theory from the linear Gaussian case. Given a distributive lattice (i) each conditional independence statement is associated with a Hibi relation defined on the lattice, (ii) the directed graph is given by chains in the lattice which correspond to chains of conditional independence, (iii) the elimination ideal of product terms in the chains gives the Hibi ideal and (iv) the TDAG can be recovered from a special bipartite graph constructed via the Alexander dual of the Hibi ideal. It is briefly demonstrated that there are natural applications to statistical log-linear models, time series and Shannon information flow.en_US
dc.identifier.citationCaines, Mohammadi, Sáenz-de-Cabezón, Wynn. Lattice conditional independence models and Hibi ideals. Transactions of the London Mathematical Society. 2022;9(1):1-19en_US
dc.identifier.cristinIDFRIDAID 2099180
dc.identifier.doi10.1112/tlm3.12041
dc.identifier.issn2052-4986
dc.identifier.urihttps://hdl.handle.net/10037/28115
dc.language.isoengen_US
dc.publisherWileyen_US
dc.relation.journalTransactions of the London Mathematical Society
dc.rights.accessRightsopenAccessen_US
dc.rights.holderCopyright 2022 The Author(s)en_US
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0en_US
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)en_US
dc.titleLattice conditional independence models and Hibi idealsen_US
dc.type.versionpublishedVersionen_US
dc.typeJournal articleen_US
dc.typeTidsskriftartikkelen_US
dc.typePeer revieweden_US


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Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Med mindre det står noe annet, er denne innførselens lisens beskrevet som Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)