Commutative Algebra of Statistical Ranking

A model for statistical ranking is a family of probability distributions whose states are orderings of a xed nite set of items. We represent the orderings as maximal chains in a graded poset. The most widely used ranking models are parameterized by rational function in the model parameters, so they dene algebraic varieties. We study these varieties from the perspective of combinatorial commutative algebra. One of our models, the Plackett-Luce model, is non-toric. Five others are toric: the Birkho model, the ascending model, the Csiszár model, the inversion model, and the Bradley-Terry model. For these models we examine the toric algebra, its lattice polytope, and its Markov basis.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Bernd Sturmfels, Volkmar Welker
• Keywords: Combinatorial Commutative Algebra, CORR 2011, Education, Model, Model Parameters