Семинар Теорија вероватноћа и математичка статистика, 7. новембар 2018.

• 02. Новембар, 2018
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Наредни састанак Семинара биће одржан у среду, 7. новембра 2018. у сали 843 Математичког факултета са почетком у 15 часова.

Предавач: Невена Марић, University of Missouri – St. Louis

Наслов предавања: CORRELATIONS AND POLYTOPES

Апстракт: Every correlation matrix belongs En, the set of symmetric positive semi-definite matrices with all diagonal elements equal to 1. For Gaussian marginals, the entirety of En can be realized, but this is the only nontrivial set of marginals for which the question has been settled. Surprisingly enough, for other common distributions very little is known. A notable partially explored example is that of copulas, for n<10. I will present our recent contribution in this subject, a complete characterization of the correlations of n-variate symmetric Bernoulli distributions (for any n) as a polytope, by explicitly identifying its vertices. The polytope is bijectively related to the well-known CUT(n) polytope defined as the convex hull of the cut vectors in a complete graph with vertex set {1,...,n}. This characterization leads also to an explicit method to verify if a correlation structure is admissible or not, and also in some cases can be used to simulate from other distributions with prescribed marginals and correlations