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Models are very useful for predicting and reproducing the behaviour of phenomena, as well as for describing the roles or functions that such phenomena fulfil. Here, the term “model” refers to a mathematical expression that represents various states of a phenomenon numerically according to a certain set of rules. Traditionally, models have been constructed on the basis of the fundamental principles underlying the phenomena concerned. However, for phenomena whose fundamental principles have not yet been sufficiently clarified, it is not possible to construct such conventional models.

On the other hand, observing phenomena and obtaining data from them is comparatively straightforward. Nevertheless, even when data can be observed, it does not necessarily mean that all the elements involved in the phenomenon can also be observed. In some cases, the only available data are those of the phenomenon itself. Even under such difficult circumstances, where the available information is incomplete and insufficient, it is still possible to construct statistical models using the observed data. A good statistical model is one that adequately captures the characteristics of the original data, and such a model is capable of reproducing behaviour similar to that of the original data.

However, a constructed statistical model is not always a good one. In such cases, it is necessary to revise the structure and assumptions of the model, as well as the variables employed, while repeatedly refining the modelling process through trial and error. If, through this process, a statistical model succeeds in reproducing behaviour similar to that of the original data, then the model may be regarded as containing information that is both important and essential to the phenomenon. Furthermore, through this iterative process, it also becomes possible to identify elements that are not essential to the phenomenon, as well as those that in fact play an important role.

Explaining phenomena through theorems and laws is unquestionably one of the most fundamental and important approaches in science. However, real-world phenomena generally involve a complex interplay of diverse factors, and even when causal relationships can be explained in broad terms, it is often difficult to provide concrete and practical methods for understanding or dealing with the phenomenon itself. In contrast, statistical models offer a realistic and practical approach. Provided that no inconsistencies or serious problems are found in a statistical model that successfully reproduces behaviour similar to that of the original data, such a model may reasonably be treated as a practically useful representation of the phenomenon.