Geometry of rank tests

Jason Morton, Lior Pachter, Anne Shiu, Bernd Sturmfels, Oliver Wienand

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We study partitions of the symmetric group which have desirable geometric properties. The statistical tests defined by such partitions involve counting all permutations in the equivalence classes. These permutations are the linear extensions of partially ordered sets specified by the data. Our methods refine rank tests of non-parametric statistics, such as the sign test and the runs test, and are useful for the exploratory analysis of ordinal data. Convex rank tests correspond to probabilistic conditional independence structures known as semi-graphoids. Submodular rank tests are classified by the faces of the cone of submodular functions, or by Minkowski summands of the permutohedron. We enumerate all small instances of such rank tests. Graphical tests correspond to both graphical models and to graph associahedra, and they have excellent statistical and algorithmic properties.

Original languageEnglish (US)
Title of host publicationProceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006
Pages207-214
Number of pages8
StatePublished - 2006
Event3rd European Workshop on Probabilistic Graphical Models, PGM 2006 - Prague, Czech Republic
Duration: Sep 12 2006Sep 15 2006

Publication series

NameProceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006

Other

Other3rd European Workshop on Probabilistic Graphical Models, PGM 2006
CountryCzech Republic
CityPrague
Period9/12/069/15/06

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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