Study on theoretical framework of statistical methods

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Mathematical theory of statistical inference has been extensively developed in the last century, but in the last few decades it reached to more or less maturity, and theoretical research effort within the conventional framework now suffers diminishing rate of return. It is now required to try new directions of research, and this project was planned to review critically the present theoretical framework and to consider new formulations of theory and methods of statistical problems which are important in various fields of practical application.Statistical problems in various fields, such as clinical trials, human genome analysis, image processing, analysis of languages, financial engineering have been discussed. The common features of the problem we encounter in such fields are that we have a large amount of not uniformly controlled data, unlike small number of well controlled data in classical cases, and we cannot apply simply models characterized by few parameters to them. Also regularity conditions assumed in the classical theory often fail to hold, and various anomalies could happen. In such cases "optimum" or "best" solutions are usually difficult to be determined and we have to be satisfied with practically "workable" solutions. Also it is necessary to consider the real "objective" of practical data analysis, and "applied decision theory" approach must be taken into consideration.We got a number of results by the participants of the project, which have been and yet to be published in separate articles.