# Total positivity in Markov structures

@article{Fallat2015TotalPI, title={Total positivity in Markov structures}, author={Shaun M. Fallat and Steffen Lauritzen and Kayvan Sadeghi and C. Uhler and N. Wermuth and Piotr Zwiernik}, journal={arXiv: Statistics Theory}, year={2015} }

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… CONTINUE READING

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