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Total Positivity in Markov Structures

dc.creatorFallat, S
dc.creatorLauritzen, S
dc.creatorSadeghi, Kayvan
dc.creatorUhler, C
dc.creatorWermuth, N
dc.creatorZwiernik, K
dc.date.accessioned2016-05-18
dc.date.accessioned2018-11-24T23:27:08Z
dc.date.available2017-05-03T14:26:49Z
dc.date.available2018-11-24T23:27:08Z
dc.date.issued2017-06
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/263999
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3955
dc.description.abstractWe discuss properties of distributions that are multivariate totally positive of order two (MTP$_{2}$) related to conditional independence. In particular, we show that any independence model generated by an MTP$_{2}$ distribution is a compositional semigraphoid which is upward-stable and singleton-transitive. In addition, we prove that any MTP$_{2}$ distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP$_{2}$ distributions and discuss ways of constructing MTP$_{2}$ distributions; in particular we give conditions on the log-linear parameters of a discrete distribution which ensure MTP$_{2}$ and characterize conditional Gaussian distributions which satisfy MTP$_{2}$.
dc.languageen
dc.publisherInstitute of Mathematical Statistics
dc.publisherAnnals of Statistics
dc.subjectassociation
dc.subjectconcentration graph
dc.subjectconditional Gaussian distribution
dc.subjectfaithfulness
dc.subjectgraphical models
dc.subjectlog-linear interactions
dc.subjectMarkov property
dc.subjectpositive dependence
dc.titleTotal Positivity in Markov Structures
dc.typeArticle


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