Details:
Title  Markov bases and designed experiments.  Author(s)  Satoshi Aoki, Akimichi Takemura  Type  Book, Chapter in Book, Conference Proceeding  Abstract  Markov bases first appeared in a 1998 work by Diaconis and Sturmfels (Ann Stat 26:363–397, 1998). In this paper, they considered the problem of estimating the p values for conditional tests for data summarized in contingency tables by Markov chain Monte Carlo methods; this is one of the fundamental problems in applied statistics. In this setting, it is necessary to have an appropriate connected Markov chain over the given finite sample space. Diaconis and Sturmfels formulated this problem with the idea of a Markov basis, and they showed that it corresponds to the set of generators of a wellspecified toric ideal. Their work is very attractive because the theory of a Gröbner basis, a concept of pure mathematics, can be used in actual problems in applied statistics. In fact, their work became one of the origins of the relatively new field, computational algebraic statistics. In this chapter, we first introduce their work along with the necessary background in statistics. After that, we use the theory of Gröbner bases to solve actual applied statistical problems in experimental design.  ISBN  9784431545736/hbk; 97844 
URL 
http://link.springer.com/chapter/10.1007%2F9784431545743_4 
Language  English  Pages  165221  Publisher  Tokyo: Springer  Year  2013  Edition  0  Translation 
No  Refereed 
No 
