Modeling of Functional Relationships of Regional Economic Systems Based on Small Samples Based on Bayesian Intelligent Measurements

Regional economies, which are economic subsystems of a socio-ecological-economic system, are characterized by rapidly changing conditions affecting their functioning. Therefore, traditional approaches based on long-term trends and the construction of appropriate models are not enough for modeling and need to be over updated, including through combination with other approaches that take into account the volatility of conditions. Open sources datasets are fraught with uncertainty (different sources may have different values for the same indicator). So, some indicators are being constantly adjusted: changes are introduced into datasets from the previous periods; evaluation periods are not sufficient for model construction that would be methodologically valid from the point of view of mathematical statistics, Additionally, the results of functioning depend on influencing factors as well as measurement results. These problems lead to the need to resort to probabilistic estimates and the incompleteness and fuzziness dataset, as well as to obtain samples of sufficient volume from low-power data. The purpose of the study is to model the relationship between the volume of gross domestic product and the factors characterizing the functioning of the economic subsystem of the regions, under the conditions of uncertainty and limited data in a given period of time. The case study is constructed on The Tula region dataset. The working hypothesis is that it is possible to construct a methodologically correct econometric models using the dataset of a specific region of the Russian Federation over a certain period of time. We applied the methods of econometric modeling and the methodology of Bayesian intelligent measurements, as well as the methodology for generating a sufficient amount of data on small samples. For the Tula region and dataset for 2022, nonlinear models for the GDP by region volumes (14 sections of the NACE) were built. This made it possible to test the presented methodology based on a combination of econometric and Bayesian approaches to modeling the complex systems functioning, with conclusions having both theoretical and practical value for the region's sustainable development.