Journal of Statistical Theory and Practice

, Volume 6, Issue 1, pp 147–161 | Cite as

Design and Analysis of Fractional Factorial Experiments From the Viewpoint of Computational Algebraic Statistics

  • Satoshi Aoki
  • Akimichi TakemuraEmail author


We give an expository review of applications of computational algebraic statistics to design and analysis of fractional factorial experiments based on our recent works. For the purpose of design, the techniques of Gröbner bases and indicator functions allow us to treat fractional factorial designs without distinction between regular designs and nonregular designs. For the purpose of analysis of data from fractional factorial designs, the techniques of Markov bases allow us to handle discrete observations. Thus the approach of computational algebraic statistics greatly enlarges the scope of fractional factorial designs.

AMS Subject Classification



Gröbner bases Indicator function Nonregular designs 


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Copyright information

© Grace Scientific Publishing 2012

Authors and Affiliations

  1. 1.Graduate School of Science and EngineeringKagoshima UniversityKagoshimaJapan
  2. 2.CRESTJapan Science and Technology AgencyTokyoJapan
  3. 3.Department of Mathematical Informatics, Graduate School of Information Science and TechnologyUniversity of TokyoTokyoJapan

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