Several examples were presented in which errors observed with a homogeneous group of individuals in tasks consisting of a large number of simple performances were described by a negativebinomial distribution. As the number of errors made by each individual has a Poisson distribution, the possibility of restoring the distribution of individual parameters from the group data was discussed. The possibility of testing on site was also pointed out. If applicants are tentatively assigned to a task, it can be decided according to the sequential analysis scheme on the records of actual daily performances whether each applicant should be finally assigned to the task or not.
A new method is introduced which can explain individual differences in dissimilarity judgments by N subjects. The method is based on a weighted distance model which is a generalization of DeLeeuw and Pruzansky's model to Minkowski r metric. A set of N dissimilarity matrices is analyzed nonmetrically to derive a group stimulus configuration and a subject configuration just like as INDSCAL. The method optimizes the goodness of fit measure which is based on the stress formula two by the method of steepest descent. This optimizing measure makes the computing process independent on Minkowski constant. The method was applied to schematic face data, and gave satisfactory results.
A distribution of weights in a weighted voting system sometimes yields quite undesirable effects on the outcome of voting, which have not been foreseen until such outcomes actually occur. Examples are the existence of so-called “dummies, ” unexpected power of veto, the failure of reflecting the dominance order of weights proportionally on the order of the effective power. The present paper introduce a number of criteria to distinguish such undesirable aspects which potentially exist in some particular configurations of the weight distribution. The criteria were stated in simple relations among weights which can be checked quite easily. Mathematical relations among the criteria were also presented in theorems with their empirical interpretations. Using the proposed criteria, the recent results of the general election for the House of Representatives in Japan was analyzed.
We have given a generalized formulation of optimal scaling for arbitrarily partially ordered categories and solved it numerically by using Wolfe's reduced gradient method (Tanaka and Asano (1978), Tanaka (1979) ). The present paper discusses some computational aspects and shows that our procedure is very efficient compared with the two alternative nonlinear programming techniques, i.e. separable programming which was used by Nishisato and Arri (1975) in the case of particularly partially ordered categories, and sequential unconstrained minimization technique which is available for a nonlinear programming problem with general equality and/or inequality constraints.
An information processing model of pattern perception has been constructed and applied to computer recognition of hand-written numerals. Patterns are picked up in the form of 32 × 32 binary array and orthogonally transformed by mutual additions and substructions among the elements. The Hadamard power spectra are defined as the feature variates to make distribution memories of the patterns which are called engram. Discriminations are performed through template matching by Euclid distance minimization method. A clusteing method has been introduced as the learning process to rewrite the engram. It is possible to identify the patterns correctly, not only for their position shift but also for their changes of parts or inclination to some extent. Multidimensional scaling method is used for the appreciation of effectiveness of the model.
A new mixing index, a criterion of degree of mixedness, is proposed for onedimensional mixtures of two constitutents on the basis of a Markov model. Homogeneous, random and segregated mixtures are clearly discriminated by the values of their mixing index. Practical way for evaluating the value of the index of a mixture from the variance of spot samples is discussed. Some applications to the three-dimensional mixtures are also considered.
In spite of many efforts to establish department of statistics or biostatistics in the medical schools of Japan, none of them has ever succeeded, and its perspective is still remaining dim. The author examined the reason for such an underserved evaluation of the statistics in the field of medicine, and noticed one episodic confrontation between statisticians and medical people at the early stage of the encounter. As the views published at that time seem to be still continuing up to now, the debates are described in detail in order to analyse the value system thriving among the medical scientists as to the statistics.
We propose a generalized method of variable selection, which is applied for the case, in which the number of the criterion variables exceeds two. By using the method, we can select criterion variables as well as explanatory variables simultaneously in canonical correlation analysis, using the G.C.D Generalized Coefficient of Determination as a maximization criterion. Furthermore, the generalized method of variable selection can be applied to factor analysis, in which case forward selection method is also performed to real variables, with the number of latent factor variables as fixed. Finally, we show two numerical examples demonstrating the validity of our procedure.