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Geometry of rank tests

Morton, Jason and Pachter, Lior and Shiu, Anne and Sturmfels, Bernd and Wienand, Oliver (2006) Geometry of rank tests. In: Proceedings of the 3rd European Workshop on Probabilistic Graphical Models. Action M Agency , Prague, Czech Republic, Art. No.7. ISBN 9788086742144. https://resolver.caltech.edu/CaltechAUTHORS:20170307-095347077

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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.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://www.utia.cas.cz/files/mtr/pgm06/7_paper.pdfPublisherArticle
https://arxiv.org/abs/math/0605173arXivDiscussion Paper
http://www.utia.cas.cz/MTR/pgm06_proceedingsOrganizationConference Proceedings
ORCID:
AuthorORCID
Pachter, Lior0000-0002-9164-6231
Additional Information:This paper originated in discussions with Olivier Pourquié and Mary-Lee Dequéant in the DARPA Fundamental Laws of Biology Program, which supported Jason Morton, Lior Pachter, and Bernd Sturmfels. Anne Shiu was supported by a Lucent Technologies Bell Labs Graduate Research Fellowship. Oliver Wienand was supported by the Wipprecht foundation.
Funders:
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Lucent Technologies Bell LabsUNSPECIFIED
Wipprecht FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20170307-095347077
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20170307-095347077
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:74836
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:07 Mar 2017 17:59
Last Modified:24 Feb 2020 10:30

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