TY - GEN

T1 - Geometry of rank tests

AU - Morton, Jason

AU - Pachter, Lior

AU - Shiu, Anne

AU - Sturmfels, Bernd

AU - Wienand, Oliver

N1 - Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:70449534423

SN - 8086742148

SN - 9788086742144

T3 - Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006

SP - 207

EP - 214

BT - Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006

T2 - 3rd European Workshop on Probabilistic Graphical Models, PGM 2006

Y2 - 12 September 2006 through 15 September 2006

ER -