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dc.contributor.authorFallat, Sen
dc.contributor.authorLauritzen, Sen
dc.contributor.authorSadeghi, Kayvanen
dc.contributor.authorUhler, Cen
dc.contributor.authorWermuth, Nen
dc.contributor.authorZwiernik, Ken
dc.date.accessioned2017-05-03T14:26:49Z
dc.date.available2017-05-03T14:26:49Z
dc.date.issued2017-06en
dc.identifier.issn0090-5364
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/263999
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.description.sponsorshipSF was supported in part by an NSERC Discovery Research Grant, KS by grant #FA9550-12-1-0392 from the U.S. Air Force Office of Scientic Research (AFOSR) and the Defense Advanced Research Projects Agency (DARPA), CU by the Austrian Science Fund (FWF) Y 903-N35, and PZ by the European Union Seventh Framework Programme PIOF-GA-2011-300975.
dc.languageengen
dc.language.isoenen
dc.publisherInstitute of Mathematical Statistics
dc.subjectassociationen
dc.subjectconcentration graphen
dc.subjectconditional Gaussian distributionen
dc.subjectfaithfulnessen
dc.subjectgraphical modelsen
dc.subjectlog-linear interactionsen
dc.subjectMarkov propertyen
dc.subjectpositive dependenceen
dc.titleTotal Positivity in Markov Structuresen
dc.typeArticle
prism.endingPage1184
prism.issueIdentifier3en
prism.publicationDate2017en
prism.publicationNameAnnals of Statisticsen
prism.startingPage1152
prism.volume45en
dc.identifier.doi10.17863/CAM.9360
dcterms.dateAccepted2016-05-18en
rioxxterms.versionofrecord10.1214/16-AOS1478en
rioxxterms.versionAMen
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2017-06en
rioxxterms.typeJournal Article/Reviewen
cam.issuedOnline2017-06-13en
cam.orpheus.successThu Jan 30 12:53:35 GMT 2020 - The item has an open VoR version.*
rioxxterms.freetoread.startdate2100-01-01


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