Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex Rank Tests and Semigraphoids   Convex rank tests are 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. Each class consists of
the linear extensions of a partially ordered set specified by data. Our methods
refine existing rank tests of non-parametric statistics, such as the sign test
and the runs test, and are useful for exploratory analysis of ordinal data. We
establish a bijection between convex rank tests and probabilistic conditional
independence structures known as semigraphoids. The subclass of submodular rank
tests is derived from faces of the cone of submodular functions, or from
Minkowski summands of the permutohedron. We enumerate all small instances of
such rank tests. Of particular interest are graphical tests, which correspond
to both graphical models and to graph associahedra.

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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int