Details:
Title  Some characterizations of minimal Markov basis for sampling from discrete conditional distributions.  Author(s)  Satoshi Aoki, Akimichi Takemura  Type  Article in Journal  Abstract  n this paper we given some basic characterizations of minimal Markov basis for a connected Markov chain, which is used for performing exact tests in discrete exponential families given a sufficient statistic. We also give a necessary and sufficient condition for uniqueness of minimal Markov basis. A general algebraic algorithm for constructing a connected Markov chain was given by Diaconis and Sturmfels (1998,The Annals of Statistics,26, 363–397). Their algorithm is based on computing Gröbner basis for a certain ideal in a polynomial ring, which can be carried out by using available computer algebra packages. However structure and interpretation of Gröbner basis produced by the packages are sometimes not clear, due to the lack of symmetry and minimality in Gröbner basis computation. Our approach clarifies partially ordered structure of minimal Markov basis.  Keywords  Contingency tables, exact tests, Markov chain, Monte Carlo  ISSN  00203157; 15729052/e 
URL 
http://link.springer.com/article/10.1007%2FBF02530522 
Language  English  Journal  Ann. Inst. Stat. Math.  Volume  56  Number  1  Pages  117  Publisher  Springer Japan, Tokyo  Year  2004  Edition  0  Translation 
No  Refereed 
No 
