АНАЛІЗ СУЧАСНИХ ПРОБЛЕМ МАТЕМАТИЧНОГО МОДЕЛЮВАННЯ В ЕКОНОМІЧНИХ, СОЦІАЛЬНИХ ТА ПЕДАГОГІЧНИХ ДОСЛІДЖЕННЯХ

Анотація. В статті проведено аналіз актуальних проблем математичного моделювання в економічних, педагогічних та соціальних дослідженнях. Піддано критиці схильність окремих дослідників переносити методи моделювання, розроблені для технічних наук, у інші області, суттєво складніші, ніж фізичний експеримент. Обґрунтовано, що переносити методи активного експерименту, де всі фактори точно визначені, в сфери, де неможливо це зробити, є ненауковим підходом. Замість регресійного моделювання в таких умовах запропоновано проводити спектральний аналіз випадкових процесів чи полів як єдиний науковий і найбільш потужний метод математичного моделювання в умовах багатофакторної невизначеності.

Annotation. The article is devoted to the analysis of actual problems of mathematical modeling in economic, pedagogical and social studies. The tendency of some researchers to transfer the modeling methods developed for physical sciences and in the conditions of an active experiment in completely different field, are significantly more complicated than the physical experiment, in which it is impossible to control or even accurately determine the number of factor characteristics is reasonably criticized in the article. In this case, it is said that the modeling is conducted under the conditions of a passive experiment, which in fact means arbitrary treatment of the factor boundaries. Such an approach, which now appears as a scientific method, is not such and can lead not only to paradoxical, but also to tragic, irreversible consequences. To carry out the methods of an active experiment where all factors are controlled and precisely defined, in areas where it is impossible to do this, is a non-scientific approach, since the research in this case is conducted in a passive (rather helpless) experiment. Instead of regression modeling, the article proposes to use spectral analysis as the only scientific and most powerful method of mathematical modeling in conditions of multi-factor uncertainty. It is the spectral analysis that allows getting the most perfect mathematical model of the process of any complexity. Aspiring to simplicity, researchers often mistakenly believe that the residual errors of a mathematical model, whether regressive or spectral, are Gaussian. This in terms of computerization and automation of scientific experiments is a blunder, since today the volume of observations reaches thousands, tens of thousands, or even hundreds of thousands. The normal distribution law of residual error of the model under such conditions, is almost never observed. The study of the famous Cambridge Professor H. Jeffreys showed that, the hypothesis of error normality with volumes of samples n > 500, is practically and theoretically insolvent. Procedures that allow to take into account the peculiarities of the error distribution in mathematical modeling and to carry out its diagnostics, are developed in the Non-Classical Error Theory of Measurements.