Göteborgs universitet, Naturvetenskapliga fakulteten, Institutionen för matematiska vetenskaper, Gothenburg University, Faculty of Sciences, Department of Mathematical Sciences, Fallat, Shaun, Lauritzen, Steffen, Sadeghi, Kayvan, Uhler, Caroline, Wermuth, Nanny, and Zwiernik, Piotr
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.