Total positivity in Markov structures
Author(s)
Fallat, Shaun; Lauritzen, Steffen; Sadeghi, Kayvan; Uhler, Caroline; Wermuth, Nanny; Zwiernik, Piotr; ... Show more Show less
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We discuss properties of distributions that are multivariate totally positive of order two (MTP2) related to conditional independence. In particular, we show that any independence model generated by an MTP2 distribution is a compositional semi-graphoid which is upward-stable and singletontransitive. In addition, we prove that any MTP2 distribution satisfying an appropriate support condition is faithful to its concentration graph. Finally, we analyze factorization properties of MTP2 distributions and discuss ways of constructing MTP2 distributions; in particular, we give conditions on the log-linear parameters of a discrete distribution which ensure MTP2 and characterize conditional Gaussian distributions which satisfy MTP2.
Date issued
2017Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Institute for Data, Systems, and SocietyJournal
The Annals of Statistics
Publisher
Institute of Mathematical Statistics