Mode Poset Probability Polytopes
Guido Montúfar and Johannes Rauh
Contact the author: Please use for correspondence this email.
Submission date: 24. Mar. 2015
published in: Journal of algebraic statistics, 7 (2016) 1, p. 1-13
DOI number (of the published article): 10.18409/jas.v7i1.41
Keywords and phrases: order polytope, modes, implicitization
Download full preprint: PDF (313 kB)
A mode of a probability vector is a local maximum with respect to some vicinity structure on the set of elementary events. The mode inequalities cut out a polytope from the simplex of probability vectors. Related to this is the concept of strong modes. A strong mode of a distribution 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.