TY - JOUR AB - 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 semigraphoid which is upward-stable and singleton-transitive. 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. AU - Fallat, Shaun AU - Lauritzen, Steffen AU - Sadeghi, Kayvan AU - Uhler, Caroline AU - Wermuth, Nanny AU - Zwiernik, Piotr ID - 1089 IS - 3 JF - Annals of Statistics SN - 00905364 TI - Total positivity in Markov structures VL - 45 ER -