You are here

Mode Poset Probability Polytopes

Journal Name:

Publication Year:

Author NameUniversity of Author
Abstract (2. Language): 
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 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.
1
13

JEL Codes:

REFERENCES

References: 

[1] Elizabeth S. Allman, John A. Rhodes, and Amelia Taylor. A semialgebraic description
of the general Markov model on phylogenetic trees. SIAM Journal on Discrete
Mathematics, 28:736{755, 2014. http://dx.doi.org/10.1137/120901568.
[2] Graham Brightwell and Peter Winkler. Counting linear extensions. Order, 8(3):225{
242, 1991. http://dx.doi.org/10.1007/BF00383444.
[3] Mara Angelica Cueto, Enrique A. Tobis, and Josephine Yu. An implicitization challenge
for binary factor analysis. Journal of Symbolic Computation, 45(12):1296{1315,
2010. http://dx.doi.org/10.1016/j.jsc.2010.06.011.
[4] Mathias Drton, Bernd Sturmfels, and Seth Sullivant. Lectures on algebraic statistics.
Oberwolfach Seminars, volume 39, Birkhauser, Basel-Boston-Berlin, 2009. http:
//dx.doi.org/10.1007/978-3-7643-8905-5.
[5] Jir Matousek. Lectures on Discrete Geometry. Springer-Verlag New York, Inc.,
Secaucus, NJ, USA, 2002. http://dx.doi.org/10.1007/978-1-4613-0039-7.
[6] Guido Montufar. Mixture decompositions of exponential families using a decomposition
of their sample spaces. Kybernetika, 49(1):23{39, 2013. http://www.
kybernetika.cz/content/2013/1/23.
REFERENCES 13
[7] Guido Montufar and Jason Morton. When does a mixture of products contain a
product of mixtures? SIAM Journal on Discrete Mathematics, 29(1):321{347, 2015.
http://dx.doi.org/10.1137/140957081.
[8] Richard P. Stanley. Two poset polytopes. Discrete & Computational Geometry,
1(1):9{23, 1986. http://dx.doi.org/10.1007/BF02187680.
[9] Gunter M. Ziegler. Lectures on Polytopes, volume 152 of Graduate Texts in Mathe-
matics. Springer Verlag, 1995. http://dx.doi.org/10.1007/978-1-4613-8431-1.
[10] Piotr Zwiernik and Jim Q. Smith. Implicit inequality constraints in a binary tree
model. Electron. J. Statist., 5:1276{1312, 2011. http://dx.doi.org/10.1214/
11-EJS640.

Thank you for copying data from http://www.arastirmax.com