Diagnostic methods for multinomial response regression methods are developed as an extension of the regression diagnostic procedure introduced by Pregibon for the case of the binomial logistic regression. For multinomial responses, there exist various indices of association, such as multinomial logit, cumulative logit, adjacent logit, and so on, according to the nominal or ordinal nature of the responses and concepts of the ordering. Regression models are used to reveal the relations of a designated index and possible explanatory variables. We develop diagnostic tools for these regression problems of moderately wide range and evaluate their usefulness and limitations via the applications of the diagnostics for the analyses of a few published data sets.

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On correspondence analysis, the simultaneous representation depends on profiles of rows and columns, and does not depend on sample size. So, if all of the profiles are equivalent for two data sets, the simultaneous representation is the same in spite of difference of the sample size. But reliability of simultaneous representation depends on the sample size. In this paper, we regard asymptotic confidence regions of frequencies as a reliability of each profile, and adding this to configuration, we can verify reliability of simultaneous representation.

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Spectral analysis is a Well-known and effective technique to understand random process and turbulence flow. For short data, however, the applicability is not clarified for the existing spectral analysis methods. This paper compares the spectral resolution and accuracy of the three methods of Blackman-Tukey (B-T), Discrete Fourier Transform (DFT) and Maximum Entropy Method (MEM) when applied to the five kinds of known random spectral data. It is found that MEM is best among these three methods and that the goodness of fit in the ensemble averaged power spectra by MEM can be improved by optimizing number of terms for large sample size.

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In the situation of multiple comparison with arbitrary contrasts, we must calculate multiple numerical integration. Such a direct method has been considered infeasible. Recent progress of high-speed computer suggests feasibility of it. Our program by SAS/IML language can calculate up to 4-variate multiple normal distribution function. The result was applied to the problem of drug-effect evaluation in clinical trials. We propose Cochran-Armitage test with appropriate coefficients, which has high power to the pattern of plausible dose-response dependency and small loss for multiplicity.

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In this paper, we propose a new dynamic graphical method for multivariate data, Dynamic Scatterplot Matrix. This method is an extension of the scatterplot matrix with rotation. The scatterplot matrix is one of the fundamental graphical methods for multidimensional data, which is all pairwise scatterplots arranged in a rectangular array so that adjacent plots share an axis in common. It is difficult to investigate the relations among more than two variables with the scatterplot matrix. Another graphical method for multidimensional data is rotation. Rotation allows us to explore the joint structure of any three of the variables. But no single low-dimensional view will capture the whole structure that is interesting about multidimensional data. Dynamic scatterplot matrix is developed to overcome the defects of the scatterplot matrix and rotation. We also show the system for Dynamic scatterplot matrix on a UNIX workstation. The system is developed with the language C and X lib.

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Group sequential procedures are to test the equivalence of two treatments for comparing the superiority among two treatments in clinical trials. The procedures are practical and applicable in the areas of sequential clinical trials. In this study, the group sequential designs are characterized by using the iterative formulas based on the trinomial random walk on a lattice diagram which adopts the untied and the tied pairs on the double-dichotomous responses. Furthermore, we will deal with the delayed observations where there exists a time lag between the administration of the treatment and the availability of the response. The designs are realized from Colton's Model, minimizing the expected loss function due to the consequence of being treated by the inferior among two treatments. The study is to determine an optimum group sequential design based on the evaluation of minimum expected loss by using the delayed observations.

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The circular statistic, proposed by Protheore, was extended to be utilized in the field of the particle astronomy. It might be applied to recognition small (n<200) datasets with somewhat higher S/N ratio from those with very low ratio. The statistic was tried for the data-sets obtained by our muon spectrometer (Okayama Muon Telescope). The applicability was well-ascertained, although some problems are left to be solved.

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Linguistics in the 20th century have had a great influence on the general concept of intelligent fuzzy computing. The modern view of language is that the essence of language can be found in its everyday use. I believe that human intelligence is created by using language. Therefore, if we consider the implementation of intelligent systems, then we must take into consideration language itself and/or it's direct correlation to human linguistic ability. Fuzzy computing is related to language by both the vagueness of language and linguistic modeling. In the human linguistic system, Systemic Functional Linguistics proposed by Halliday, has had the greatest influence on the theory in which language is treated as a system of meanings rather than a system of grammar. In the paradigm of intelligent fuzzy computing, language is regarded as a metalanguage for dealing with the meaning of information, and the Systemic Functional Linguistics theory interprets the sense of language. Intelligent computing uses the techniques of the fuzzy computing, as it deals with the meanings of language. In order to do this, a large scale database is needed. The construction of such a database is not beyond reality, due to the limited sphere of human activities.

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[in Japanese]

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