Mode Poset Probability Polytopes
Combinatorics
2015-03-03 v1 Probability
Abstract
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.
Keywords
Cite
@article{arxiv.1503.00572,
title = {Mode Poset Probability Polytopes},
author = {Guido Montufar and Johannes Rauh},
journal= {arXiv preprint arXiv:1503.00572},
year = {2015}
}
Comments
8 pages, 1 figure