The use of the concept of plausibility is proposed for the comparison of psychological or physical images of an object with extremely complex structure. This concept helps the process of developing new image of an object that is not captured by the past observational data. It is argued that this process is the essential aspect of statistical thinking developed by original thinkers in various fields of scientific research with the aid of a model. The use of plausibility helps this process of thinking. A practical example is given by the analysis of golf swing motion.

The authors evaluated the effect of photomask pattern shape for a counter-electrode on critical current I-c uniformity and controllability in Nb/AlOx/Nb junctions. Circular, square, and 2 kinds of optical proximity correction (OPC) square patterns were used as the mask pattern shape. Although there was no difference in the I-c uniformity between square and OPC junctions, the OPC junctions exhibited smaller shrinkage in junction size than the square junction. In addition, the OPC junctions improved the chip-to-chip variation in the shrinkage. The circular junction exhibited the smallest variation in the shrinkage, and had an advantage in I-c uniformity for smaller than 1.0 mu m(2) junctions in comparison with the other junctions. The shrinkage of the circular junction was the largest of all the junctions. This paper describes the recommended choice of the photomask pattern shape for several Nb LSI technologies.

The role of a model is to provide adequate knowledge to handle a particular problem. The work of modeling starts on the basis of the feel and knowledge of the object and proceeds by developing guesses about the structure of the object. In this paper characteristics of this process are demonstrated with the example of the analysis of the golf swing motion.

At present, the spectral method is used very commonly for the analysis. of an electrical or mechanical system. The spectral method is used not only for the estimation of the individual spectral density functions of the input and output of the system but also for the estimation of the frequency characteristics of the system. The statistical method of estimation of the frequency characteristics of a system is best suited for this purpose as it can be applied without disturbing the normal operation of the system and even under the existence of the additive disturbance of extraneous noises. Statistical method for the estimation of the power spectral density has been brought to a considerable development by the valuable contributions of many statisticians, for example, those of' J. W. Tukey [4, 9]. As for the estimation of the frequency response function of a linear. and timeinvariant system we have a paper by N. R. Goodman [8]. The method described by Goodman was a direct application of the method of estimation of the spectral density to that of the crosspectral density, but some experimenters who applied this kind of method to their numerical data experienced the very low coherency of their estimates. As far as we know, this fact was first recognized experimentally and announced by J. F. Darzell and Y. Yamanouchi [6]. The fruitful results of the method of estimation of the spectral density are mainly due to its success in reducing the variance by using proper smoothing operations. Methods of smoothing or averaging such as those named " hanning" and "hamming" and so forth were derived as those which have desirable properties of concentration of the effective range of smoothing. The smoothing operation is carried out by taking the product of the sample covariance function and a smoothing kernel or a lag window. It is well known that the autocovariance function does not contain any information about the phase of each frequency component contained in the original data. However, the crosscovariance function contains information of the phase, and the alignment of the phase shift of the frequency response function at frequencies in the effective range of the smoothing is most important to get a valid estimate of the amplitude gain. In Goodman's paper little attention was paid to

Statistical reasoning procedes by forming an expectation and verifying it by proper use of informational data set composed of the available knowledge and observational data. Typical views of statistics are briefly reviewed and two published examples of motion analysis are discussed to illustrate the limitation of the identification by the conventional use of statistical procedures. The identification of the golf swing is discussed to illustrate the process of statistical reasoning. The concept of constructive identification is introduced and the necessity of treating identification as a highly intentellectual activity is emphasized.

In this paper the informational approach to statistics based on an informational interpretation of log likelihood of a statistical model is contrasted with the conventional Fisherian framework. It is pointed out that for the recognition of practical importance of statistical science more emphasis should be placed on the development of new models than the refinement of mathematical analysis of existing procedures, although the latter activity should never be ignored. This is based on the observation that it is the contribution of statistics to the development of new hypotheses for the interpretation of data that creates the importance of the subject. It is argued that the informational approach prepares a basis for the rapid expansion of the area of application of statistics by providing a theoretical foundation for the development and evaluation of new statistical models in diverse fields.

Informational approach represents a new trend in the development of statistical science. This paper is intended for the discussion of the informational outlook in relation to the development of statistics or statistical science.

The development of statistical models is realized through the accumulation of successful experiences of the analysis of real data. As is discussed in Akaike (1992) statistical modeling activity contains highly subjective or personal aspect which Polanyi (1962) related to the scientific talent of the researcher. However, scientific activity is never isolated from the society and Turing (1969) explicitly characterized the search for new techniques as the ‘ cultural search ’. This paper is intended to provide the background information of some of the experiences of the author on time series modeling. It is hoped that the description of the interaction between the author and his environment will provide some suggestion for those who intend to organize effective statistical modeling activity in the future.

In this paper it is shown that the classical maximum likelihood principle can be considered to be a method of asymptotic realization of an optimum estimate with respect to a very general information theoretic criterion. This observation shows an extension of the principle to provide answers to many practical problems of statistical model fitting.

The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting when it is viewed as the choice of a Bayesian model. This observation shows that the area of application of AIC can be much wider than the conventional i.i.d. type models on which the original derivation of the criterion was based. The observation of the Bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings.

The necessity of using statistical models for the development of efficient statistical signal processing procedures is explained with simple examples of the time series analysis. Recent extensions of the use of the concept of the likelihood of a statistical model are reviewd from the point of view of the entropy maximization principle, Particular emphasis is placed on the proper use of Bayesian models.

The emergence of the magic number 2 in recent statistical literature is explained by adopting the predictive point of view of statistics with entropy as the basic criterion of the goodness of a fitted model. The historical development of the concept of entropy is reviewed, and its relation to statistics is explained by examples. The importance of the entropy maximization principle as a basis of the unification of conventional and Bayesian statistics is discussed.

The Bayesian modeling allows very flexible handling of time series data. This is realized by the explicit representation of possible alternative situations by the model. The negative psychological reaction to the use of Bayesian models can be eliminated once we know how to handle the models.

This chapter provides an overview of statistical inference and the measurement of entropy. Boltzmann developed an interpretation of the thermodynamic entropy as the logarithm of the probability of a molecular distribution which defines the thermodynamic state of the system. Based on the recognition that the probabilistic interpretation of entropy is the key concept that connects statistics with probability, the chapter presents the entropy maximization principle. The method of maximum likelihood may be considered as a procedure of maximizing the entropies. The thermodynamic entropy is a relative concept in the sense that only the difference has a physical meaning. This relative property is inherited by the log likelihood. The robustness of the Bayesian statistical model is obtained by throwing in the prior information through the specification of the prior distribution. The chapter presented examples, which clearly demonstrate the importance of the measurement of entropies in a scientific investigation where progress takes place only through the generation of hypotheses.