A new development of a conditional test (specially its sequential version) for contingency tables and the related problems

本研究的目的是发展列联表的顺序条件检验理论。利用创建算子构造了a -超几何偏微分方程组的顺序条件检验。这个想法是由Takayama等人关于整数规划问题的工作所激发的。2001年对双向表测试的实现问题及其功率性能进行了研究。结果表明，对于中等大小的双路表，顺序测试在PC上表现良好。这一结果发表在几个国际会议上，布拉格的ICPR、首尔的53^ rd b> ISI和大阪的ICNCB。2002年，研究了3x3x3型三向表的序贯条件检验的构造。演出很好。该研究结果发表在2002年佛罗里达国际学术会议上。然后我们的顺序测试是基于由Takemura和Aoki开发的最小马尔可夫基。因此，我们现在更多地研究由Takemura和Aoki提出的构造三路表最小马尔可夫基的代数理论。在日本计算统计学会2016年年会的专题讲座中，我们讨论了列联表集上MCMC代数理论的最新进展。Sakata和Sawae进一步考虑了大都会在列联表集上行走的量子版本。这篇文章发表在《量子化学杂志》上。Sakata， Sawae和Nomakuchi进一步考虑了成分相关性约束假设的相关矩阵集上的Gibbs行走。这是由Chandra Gulti等人编辑的《统计学、组合学及相关领域的进展》一书。Sakata和Jeffery Xu Yu在《无线网络》中发表了基于请求的接入频率估计问题。Sasabuchi在世界著名的期刊上发表了两篇关于限制推理的论文。野口发表了三篇关于限制推理的论文。jeffrey Xu Yu发表了许多关于数据挖掘的论文，并在许多国际会议上发表了演讲。结果，我们的项目成功地发表了几篇论文。少

The aim of this research was to develop a theory of the sequential conditional test for contingency tables. The sequential conditional test was constructed via the creation operator for A-hypergeometric partial differential equation systems. This idea was motivated by the works of Takayama et al. for integer programming problems. The implementation problem of the test and its power performance for the two way tables was examined in the year 2001. It was shown that for moderate size of two way tables the sequential test performs well on PC. The result was published in the several international conference, ICPR in Prague and 53^<rd> ISI in Seoul and ICNCB in Osaka. The second year 2002, we attacked the construction of the sequential conditional test for three way tables of type 3x3x3. The performance was good. The result was published in the international conference SCI2002, in Florida. Then our sequential test is based on the minimal Markov basis developed by Takemura and Aoki. Therefor … More e we are now pursuing the algebraic theory of constructing minimal Markov basis for three way tables initiated by Takemura and Aoki. The recent development of the algebraic theory of MCMC on the set of contingency tables was discussed in our special lecture of 16^<th> annual meeting of the Japanese computational statistical society. Further Sakata and Sawae considered the quantum version of Metropolis walk on the set of contingency tables. This was published in Journal of quantum chemistry. Further Sakata, Sawae and Nomakuchi considered the Gibbs walks on the set of correlation matrix for the constraind hypothesis of components correlation. This was published the book of Advance in Statistics, Combinatrics and related fields edited by Chandra Gulti et.al. Sakata and Jeffery Xu Yu published in Wireless Network about the estimating problem of access frequency from the request. Sasabuchi published two paper for the worldwide famous journal about the restricted inference. Nomakuchi published three papers about restricted inference. Jeferry Xu Yu published many papers and gave talks at many international conferences about Data Mining. As a result our project produced several refereed papers successfully. Less