Theory of the foundation of mathematical statistics to analyze the biological information and its applications

生物信息学、医学等信息分析中统计数学基础理论的研究。特别是考虑了序贯试验的选择问题，并在临床试验中提出了一种使两种治疗方案的应用方案的预期效果最大化的方法。在两样本问题的推断中起重要作用的统计量在许多情况下服从非中心分布。解析地推导了奇数自由度非中心卡方分布的一个百分点的近似公式，并从幂和非中心性的角度对非中心分布的近似性进行了数值评价.进一步推导了非中心t-统计量百分点的高阶近似公式，并数值验证了该公式在各种分布下的准确性。

The research on basic theory of statistical mathematics in the information analysis of bioinformatics, medical sciences, etc. In particular, we consider the problem on sequential experiment of choice, and develop a procedure which maximizes the expected effect in an application plan of 2 treatments in clinical trials. The statistic playing an important role in the inference of two-sample problem follows a non-central distribution in many cases. We analytically derive an approximation formula of a percentage point of the non-central chi-square distribution with the odd degree of freedom, and numerically evaluate the goodness of the approximation of the non-central distribution from the viewpoint of the power and the non-centrality. Further, we derive a higher order approximation formula of the percentage point of the non-central t-statistic, and numerically verify the accuracy of the formula under various distributions.