Mode Poset Probability Polytopes AS2015 Special Issue articles: This issue includes a series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics Conference held in Genoa, Italy, in June 2015. Special issue guest editors: Piotr Zwiernik and Fabio Rapallo. order polytope partial order implicitization mode A mode of a probability distribution is an elementary event that has more probability mass than each of its direct neighbors, with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability distributions. Related to this is the concept of strong modes. A strong mode is an elementary event that has more probability mass than all its direct neighbors together. The set of probability distributions with a given set of strong modes is again a polytope. We study the vertices, the facets, and the volume of such polytopes depending on the sets of (strong) modes and the vicinity structures. Montúfar, Guido Rauh, Johannes 2016 2016-07-12 Article application/pdf islandora:1007803 http://hdl.handle.net/10560/islandora:1007803 MATH / Applied Mathematics Illinois Institute of Technology Journal of Algebraic Statistics en Open Access