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MiS Preprint
22/2015

Mode Poset Probability Polytopes

Guido Montúfar and Johannes Rauh

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.

Received:
Mar 24, 2015
Published:
Mar 26, 2015
Keywords:
order polytope, modes, implicitization

Related publications

inBook
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
inJournal
2016 Journal Open Access
Guido Montúfar and Johannes Rauh

Mode poset probability polytopes

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