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MiS Preprint

Mode Poset Probability Polytopes

Guido Montúfar and Johannes Rauh


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.

Mar 24, 2015
Mar 26, 2015
order polytope, modes, implicitization

Related publications

2015 Repository Open Access
Guido Montúfar and Johannes Rauh

Mode poset probability polytopes

In: Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech Republic, September 16-19, 2015 / Václav Kratochvíl (ed.)
Praha : Oeconomica, 2015. - pp. 147-154
2016 Journal Open Access
Guido Montúfar and Johannes Rauh

Mode poset probability polytopes

In: Journal of algebraic statistics, 7 (2016) 1, pp. 1-13