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The Set of Moves Connecting Specific Fibers

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Markov Bases in Algebraic Statistics

Part of the book series: Springer Series in Statistics ((SSS,volume 199))

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Abstract

So far we have not assumed any restrictions on fibers or cell counts of contingency tables. In some problems, however, we have to impose some conditions on fibers or contingency tables. In such cases we need to find a set of moves connecting restricted fibers or restricted tables. In some cases only a subset of a minimal Markov basis is required to connect restricted fibers. In other cases, however, no minimal Markov basis connects every restricted fiber. In the present chapter, we study two such problems. The first one is to find a set of moves connecting every fiber with positive marginals for the discrete logistic regression model. The second one is the case where cell counts are restricted to be zero or one.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science Graduate School of Science and Engineering, Kagoshima University, Kagoshima, Japan

    Satoshi Aoki

  2. Faculty of Economics, Niigata University, Niigata, Japan

    Hisayuki Hara

  3. Department of Mathematical Informatics Graduate School of Information Science and Technology, University of Tokyo, Tokyo, Japan

    Akimichi Takemura

Authors
  1. Satoshi Aoki
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  2. Hisayuki Hara
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  3. Akimichi Takemura
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Aoki, S., Hara, H., Takemura, A. (2012). The Set of Moves Connecting Specific Fibers. In: Markov Bases in Algebraic Statistics. Springer Series in Statistics, vol 199. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3719-2_13

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