标题： Segre-Veronese配置的马尔可夫基和Gröbner基用于检验组选择中的独立性 显示英文标题

标题： Markov basis and Groebner basis of Segre-Veronese configuration for testing independence in group-wise selections

摘要： 我们考虑在组选择中检验独立性，并且对选择组合施加一些限制。 我们提出了针对选择频率数据的模型，通过马尔可夫链蒙特卡洛（MCMC）方法可以很容易地执行条件检验。 当组合的限制可以用Segre-Veronese配置来描述时，用于马尔可夫链的二阶移动的Gröbner基的显式形式可以轻松获得。 我们以日本大学入学考试国立中心测验为例说明我们的设定。 我们还应用我们的方法来检验涉及多于一个位点上的基因型或同一染色体上等位基因单倍型的独立性假设。 显示英文摘要

摘要： We consider testing independence in group-wise selections with some restrictions on combinations of choices. We present models for frequency data of selections for which it is easy to perform conditional tests by Markov chain Monte Carlo (MCMC) methods. When the restrictions on the combinations can be described in terms of a Segre-Veronese configuration, an explicit form of a Gr\"obner basis consisting of moves of degree two is readily available for performing a Markov chain. We illustrate our setting with the National Center Test for university entrance examinations in Japan. We also apply our method to testing independence hypotheses involving genotypes at more than one locus or haplotypes of alleles on the same chromosome.