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Total positivity in Markov structures
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 2doi:10.1214/16-aos1478 fatcat:vnxcaff5kbdotfjwhzaslcgjai