Displaying similar documents to “On the moments of random variables uniformly distributed over a polytope.”

Marginalization like a projection.

Juan Francisco Verdegay-López, Serafín Moral (2001)

Mathware and Soft Computing


This paper studies the problem of marginalizing convex polytopes of probabilities represented by a set of constraints. This marginalization is obtained as a special case of projection on a specific subspace. An algorithm that projects a convex polytope on any subspace has been built and the expression of the subspace, where the projection must be made for obtaining the marginalization, has been calculated.

Hierarchical models, marginal polytopes, and linear codes

Thomas Kahle, Walter Wenzel, Nihat Ay (2009)



In this paper, we explore a connection between binary hierarchical models, their marginal polytopes, and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.

Recent Results on Random Polytopes

Rolf Schneider (2008)

Bollettino dell'Unione Matematica Italiana


This is a survey over recent asymptotic results on random polytopes in d-dimensional Euclidean space. Three ways of generating a random polytope are considered: convex hulls of finitely many random points, projections of a fixed high-dimensional polytope into a random d-dimensional subspace, intersections of random closed halfspaces. The type of problems for which asymptotic results are described is different in each case.