Total positivity in Markov structures

Shaun Fallat, Steffen Lauritzen, Kayvan Sadeghi, Caroline Uhler, Nanny Wermuth, Piotr Zwiernik
2017 Annals of Statistics  
We 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 semi-graphoid which is upward-stable and singletontransitive. 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
more » ... tions 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 .
doi:10.1214/16-aos1478 fatcat:vnxcaff5kbdotfjwhzaslcgjai