Mode Poset Probability Polytopes

  • Guido Francisco Montufar Max Planck Institute for Mathematics in the Sciences
  • Johannes Rauh York University

Abstract

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 of a probability 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.

Author Biographies

Guido Francisco Montufar, Max Planck Institute for Mathematics in the Sciences
Postdoc
Johannes Rauh, York University
Postdoc
Published
2016-07-12
How to Cite
MONTUFAR, Guido Francisco; RAUH, Johannes. Mode Poset Probability Polytopes. Journal of Algebraic Statistics, [S.l.], v. 7, n. 1, july 2016. ISSN 1309-3452. Available at: <http://216.47.136.110/jalgstat/article/view/41>. Date accessed: 23 oct. 2017. doi: https://doi.org/10.18409/jas.v7i1.41.
Section
AS2015 Special Issue articles

Keywords

order polytope, partial order, implicitization, mode