Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals

Satoshi Aoki; Takayuki Hibi; Hidefumi Ohsugi

Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals

Statistics Theory 2014-05-15 v1 Commutative Algebra Statistics Theory

Authors: Satoshi Aoki , Takayuki Hibi , Hidefumi Ohsugi

Abstract

It is known that a Markov basis of the binary graph model of a graph $G$ corresponds to a set of binomial generators of cut ideals $I_{\widehat{G}}$ of the suspension $\widehat{G}$ of $G$ . In this paper, we give another application of cut ideals to statistics. We show that a set of binomial generators of cut ideals is a Markov basis of some regular two-level fractional factorial design. As application, we give a Markov basis of degree 2 for designs defined by at most two relations.

Keywords

Markov chain Monte Carlo fractional factorial designs cut ideals Markov basis binary graph model binomial generators

Cite

@article{arxiv.1302.2882,
  title  = {Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals},
  author = {Satoshi Aoki and Takayuki Hibi and Hidefumi Ohsugi},
  journal= {arXiv preprint arXiv:1302.2882},
  year   = {2014}
}

Comments

24 pages. arXiv admin note: text overlap with arXiv:1302.2408

Markov chain Monte Carlo methods for the regular two-level fractional factorial designs and cut ideals

Abstract

Keywords

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