Some characterizations of minimal Markov basis for sampling from discrete conditional distributions
Some characterizations of minimal Markov basis for sampling from discrete conditional distributions
复制标题
DOI：
10.1007/bf02530522
复制
发表时间：
2004-03
影响因子：
1
通讯作者：
A. Takemura;S. Aoki
中科院分区：
文献类型：
--
作者：
A. Takemura;S. Aoki
本文给出了连通马氏链的极小马氏基的一些基本刻画，它可用于在给定充分统计量的情况下对离散指数族进行精确检验。给出了极小马氏基唯一的一个充要条件。Diaconis和Sturmfels（1998，The Annals of Statistics，26，363-397）给出了构造连通Markov链的通用代数算法。他们的算法是基于计算多项式环中某个理想的Gröbner基，这可以通过使用可用的计算机代数软件包来实现。然而，由于Gröbner基计算中缺乏对称性和极小性，由软件包产生的Gröbner基的结构和解释有时并不清楚。我们的方法澄清了最小马尔可夫基的偏序结构。
In 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.