Geometry of rank tests

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

Geometry of rank tests

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

Mathematics

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 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 language	English (US)
Title of host publication	Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006
Pages	207-214
Number of pages	8
State	Published - 2006
Event	3rd European Workshop on Probabilistic Graphical Models, PGM 2006 - Prague, Czech Republic Duration: Sep 12 2006 → Sep 15 2006

Publication series

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

Other

Other	3rd European Workshop on Probabilistic Graphical Models, PGM 2006
Country/Territory	Czech Republic
City	Prague
Period	9/12/06 → 9/15/06

All Science Journal Classification (ASJC) codes

Statistics and Probability

Cite this

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title = "Geometry of rank tests",

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.",

author = "Jason Morton and Lior Pachter and Anne Shiu and Bernd Sturmfels and Oliver Wienand",

year = "2006",

language = "English (US)",

isbn = "8086742148",

series = "Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006",

pages = "207--214",

booktitle = "Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006",

}

Morton, J, Pachter, L, Shiu, A, Sturmfels, B & Wienand, O 2006, Geometry of rank tests. in Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006. Proceedings of the 3rd European Workshop on Probabilistic Graphical Models, PGM 2006, pp. 207-214, 3rd European Workshop on Probabilistic Graphical Models, PGM 2006, Prague, Czech Republic, 9/12/06.

TY - GEN

T1 - Geometry of rank tests

AU - Morton, Jason

AU - Pachter, Lior

AU - Shiu, Anne

AU - Sturmfels, Bernd

AU - Wienand, Oliver

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.

UR - http://www.scopus.com/inward/record.url?scp=70449534423&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449534423&partnerID=8YFLogxK

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 -

Geometry of rank tests

Abstract

Publication series

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All Science Journal Classification (ASJC) codes

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