Mode Poset Probability Polytopes

Guido Montúfar and Johannes Rauh

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Submission date: 24. Mar. 2015
Pages: 10
published as: Mode poset probability polytopes.
In: Journal of algebraic statistics, 7 (2016) 1, p. 1-13 
DOI number (of the published article): 10.18409/jas.v7i1.41
published as: Mode poset probability polytopes.
In: Proceedings of the 10th workshop on uncertainty processing WUPES '15, Moninec, Czech Republic, September 16-19, 2015 / V. Kratochvíl (ed.)
Praha : Oeconomica, 2015. - P. 147 - 154 
Bibtex
Keywords and phrases: order polytope, modes, implicitization
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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.