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Title: Generalized Fréchet Bounds for Cell Entries in Multidimensional Contingency Tables, Special Volume in honor of memory of S.E.Fienberg
Creator: Richards, Donald, Uhler, Caroline
Description: We consider the lattice, L, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and...
Show moreWe consider the lattice, L, of all subsets of a multidimensional contingency table and establish the properties of monotonicity and supermodularity for the marginalization function, n(·), on L. We derive from the supermodularity of n(·) some generalized Fr ́echet inequalities comple- menting and extending inequalities of Dobra and Fienberg. Further, we construct new monotonic and supermodular functions from n(·), and we remark on the connection between supermodularity and some correlation inequalities for probability distributions on lattices. We also apply an inequal- ity of Ky Fan to derive a new approach to Fr ́echet inequalities for multidimensional contingency tables.
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Collection: Journal of Algebraic Statistics

Title: Maximal Length Projections in Group Algebras with Applications to Linear Rank Tests of Uniformity
Creator: Bargagliotti, Anna E., Orrison, Michael
Description: Let G be a finite group, let CG be the complex group algebra of G, and let p ∈ CG. In this paper, we show how to construct submodules S of CG...
Show moreLet G be a finite group, let CG be the complex group algebra of G, and let p ∈ CG. In this paper, we show how to construct submodules S of CG of a fixed dimension with the property that the orthogonal projection of p onto S has maximal length. We then provide an example of how such submodules for the symmetric group Sn can be used to create new linear rank tests of uniformity in statistics for survey data that arises when respondents are asked to give a complete ranking of n items.
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Collection: Journal of Algebraic Statistics

Title: Connectivity for 3 x 3 x K contingency tables
Creator: Sumi, Toshio, 2012
Description: We consider an exact sequential conditional test for three-way conditional test of no interaction. At each time τ, the test uses as the...
Show moreWe consider an exact sequential conditional test for three-way conditional test of no interaction. At each time τ, the test uses as the conditional inference frame the set F(Hτ) of all tables with the same three two-way marginal tables as the obtained table Hτ . For 3 × 3 × K tables, we propose a method to construct F(Hτ) from F(Hτ−1). This enables us to perform efficiently the sequential exact conditional test. The subset Sτ of F (Hτ ) consisting of s + Hτ − Hτ −1 for s ∈ F(Hτ−1) contains Hτ , where the operations + and − are defined elementwise. Our argument is based on the minimal Markov basis for 3 × 3 × K contingency tables and we give a minimal subset M of some Markov basis which has the property that F (Hτ ) = {s − m | s ∈ Sτ , m ∈ M}.
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Collection: Journal of Algebraic Statistics

Title: Matrix Completion for the Independence Model
Creator: Kubjas, Kaie, Rosen, Zvi
Description: We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex ∆mn−1. The motivation for studying this...
Show moreWe investigate the problem of completing partial matrices to rank-one matrices in the standard simplex ∆mn−1. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for partial observations to come from the independence model. For each pattern of specified entries, we give equations and inequalities which are satisfied if and only if an eligible completion exists. We also describe the set of valid completions, and we optimize over this set.
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Collection: Journal of Algebraic Statistics

Title: One example of general unidentifiable tensors
Creator: Chiantini, Luca, Mella, Massimiliano, Ottaviani, Giorgio
Description: Abstract. Theidentifiabilityofparametersinaprobabilisticmodelisacrucialnotioninstatistical inference. We prove that a general tensor of rank 8...
Show moreAbstract. Theidentifiabilityofparametersinaprobabilisticmodelisacrucialnotioninstatistical inference. We prove that a general tensor of rank 8 in C3 ⊗ C6 ⊗ C6 has at least 6 decompositions as sum of simple tensors, so it is not 8-identifiable. This is the highest known example of balanced tensors of dimension 3, which are not k-identifiable, when k is smaller than the generic rank.
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Collection: Journal of Algebraic Statistics

Title: Hilbert Polynomial of the Kimura 3-Parameter Model, AS2012 Special Volume, part 1: This issue includes a second series of papers from talks, posters and collaborations resulting from and inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July 2012.
Creator: Kubjas, Kaie, inspired by the Algebraic Statistics in the Alleghenies Conference at Penn State, which took place in July
Description: In [2] Buczyn ́ska and Wi ́sniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on...
Show moreIn [2] Buczyn ́ska and Wi ́sniewski showed that the Hilbert polynomial of the algebraic variety associated to the Jukes-Cantor binary model on a trivalent tree depends only on the number of leaves of the tree and not on its shape. We ask if this can be generalized to other group-based models. The Jukes-Cantor binary model has Z2 as the underlying group. We consider the Kimura 3-parameter model with Z2 × Z2 as the underlying group. We show that the generalization of the statement about the Hilbert polynomials to the Kimura 3-parameter model is not possible as the Hilbert polynomial depends on the shape of a trivalent tree.
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Collection: Journal of Algebraic Statistics

Title: Stephen Fienberg's influence on algebraic statistics, Special Volume in honor of memory of S.E.Fienberg
Creator: Petrović, Sonja, Slavkovic, Aleksandra, Yoshida, Ruriko
Date: 2019, 2019-04-12
Description: Stephen (Steve) E. Fienberg (1942-2016) was an eminent statistician, whose impact on research, education and the practice of statistics, and...
Show moreStephen (Steve) E. Fienberg (1942-2016) was an eminent statistician, whose impact on research, education and the practice of statistics, and many other fields is astonishing in its breadth. He was a visionary when it came to linking many different areas to address real scientific issues. He professed the importance of statistics in many disciplines, but recognized that true interdisciplinary work requires joining of the expertise across different areas, and it is in this spirit that he helped steer algebraic statistics toward becoming a thriving subject. Many of his favorite topics in the area are covered in this special issue. We are grateful to all authors for contributing to this volume to honor him and his influence on the field. During the preparation of this issue, we learned about the tragic killing of his widow, Joyce Fienberg, during the Tree of Life Synagogue massacre in Pittsburgh, PA on October 27, 2018. This issue is dedicated to their memory.
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Collection: Journal of Algebraic Statistics

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