In the early 1970's, Dr. Hirotugu Akaike formulated the Akaike Information Criterion (AIC), a new practical, yet versatile criterion for the selection of statistical models, based on basic concepts of information mathematics. This criterion established a new paradigm that bridged the world of data and the world of modeling, thus contributing greatly to the information and statistical sciences.
＊This field then was Field of Mathematical Sciences.
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Statistical prediction identification, Ann.Inst.Statist.Math. 22: 203-217, 1970.
Information theory and an extension of the maximum likelihood principle, Proc.2nd International Symposium on Information Theory, Petrov, B. N. and Csaki, F.eds., Akademiai Kiado, Budapest, 267-281, 1973.
A new look at the statistical model identification, IEEE Trans. Automat. Control. 19:716 – 723, 1974.
On entropy maximization principle, in Applications of Statistics, Krishnaiah, P. R. ed., North-Holland Publishing Company, 27-41, 1977.
In the early 1970s, Dr. Hirotugu Akaike formulated the Akaike Information Criterion (AIC), a new practical, yet versatile criterion for the selection of statistical models, based on fundamental concepts of information mathematics. This criterion established a new paradigm that bridged the world of data and the world of modeling, thus contributing greatly to the information and statistical sciences.
Dr. Akaike derived the AIC based on the foundations of information mathematics, through the study of actual examples, including analysis of the processing of sericultural products, cement kiln controls, and thermal electric power plant controls, and the criterion gave a breakthrough solution to the model selection problem, a major problem common to any form of intellectual information processing. The AIC allows selecting a model that balances between the complexity of the model and goodness of its fit to the data. The AIC is widely used as a practical guideline for the selection of statistical models in a wide range of areas including medicine, epidemiology, biology, control engineering, economics, environmentology, geophysics and social sciences, as well as the fields of mathematics and statistics.
Dr. Akaike has multiple achievements, including the practical application of statistical control to various industrial plants, development of a modeling methodology in the time domain of multivariable time-series analysis, and development and promotion of the time-series analysis software TIMSAC. The widespread use of commercial statistics software packages that incorporate the idea and methodology of the AIC indicates the practicality and reliability of this criterion. Furthermore, Dr. Akaike identified the importance of the Bayesian model as early as the early 1980s, and contributed to the practical application of this model to the information and statistical sciences. Looking at the current growth of the Bayesian model in various fields that require intelligent information processing, more than 20 years after Dr. Akaike first recognized its importance, we cannot help being impressed by his scientific insight.
Today, thanks to the rapid progresses in information processing technologies, we are able to obtain an enormous amount of data and process it at a high speed. Extraction of knowledge and information, and the forecast and control of risk factors in human life have critical importance to the survival and development of human society. Based on the recognition of this situation, there is no doubt that Dr. Akaike’s criterion and the modeling methodology based thereon will become an increasingly important tool for humankind, and hence Dr. Akaike’s achievements deserve our greatest esteem.
For these reasons, the Inamori Foundation is pleased to present the 2006 Kyoto Prize in Basic Sciences to Dr. Hirotugu Akaike.
From my early childhood, I loved to examine tools and toys with moving parts to see how they worked. I ended up studying statistical mathematics, which is directly related to understanding the movements of objects, and continued scrutinizing the existing methodologies.
2. Mathematics of prediction
In order to handle problems under the circumstance where the outcome is unknown, we attempt to predict the outcome to determine what measures should be taken. The mathematical expression of expectation in this case is probability.
Trying to develop an interpretation of observational data with probabilistic view often suggests useful information for making a prediction. Often a method of statistical processing of observational data can be obtained by organizing this procedure mathematically.
3. Application to practical problems
In the era of Japan’s post-war reconstruction, I aspired to work on problems that were unique to Japan. I concentrated on the analysis and control of phenomena that fluctuated with time, and collaborating with researchers in related fields successfully developed models and methods for practical applications, such as the statistical control of the silk reeling process, analysis of the random vibrations of automobiles and the oscillations of ships, and the automatic control of cement kilns that showed random fluctuations, and also developed necessary software. The results were often an advance over what was known by overseas researchers at that time.
4. Clarification of the concept of likelihood
The model used here expresses the probabilistic mechanism that generates the observational data and includes adjustable parameters. Using the observational data, we adjust the parameters to maximize the likelihood to determine the model. In this case, increasing the number of parameters results in an apparent better fit to the observational data, but adding unnecessary parameters raises the possibility of increasing the prediction errors.
5. The information criterion
In the information criterion AIC (An Information Criterion), the evaluated score based on the likelihood is reduced by twice the number of parameters. This is a realization of the method of logic that discourages bringing in unnecessary elements. The definitional equation is simple and easy to apply. The information criterion can be viewed as a method to measure the closeness of a model to the hypothetical truth (true structure), and allows the comparison of differently structured models. This characteristic encouraged the development of new models and the field of application of the information criterion has been expanding continuously.