CLASSIFICATION OF SYSTEM STATES BY VECTOR PARAMETERS
Abstract
The aim of the article is to study the algorithms for classifying the states of the modeled economic system according to the vector of parameters. The economy is seen as an emergent system for which the general principles of existence and development of complex systems are valid. It is the property of emergence that can cause the structural heterogeneity of the mathematical model of the system, which in turn is the result of abrupt changes in parameters, uncertainty of the functional relationship between exogenous and endogenous model variables. The adequacy of mathematical models of such problems is determined primarily by the presence of structured input information – numerical, probabilistic, descriptive estimates of the interaction of exogenous and endogenous factors of different nature, which can be formalized mathematically as model parameters. An analytical algorithm for classifying the states of a complex system identified by a vector of parameters is described. The algorithm for determining the state of a complex system is based on the principles of discriminant analysis. The set of system classes is considered as a set of multidimensional random variables determined to the nearest parameter values. The basis for the application of discriminant analysis is the assumption of a normal distribution of a multidimensional random variable – a vector of system state parameters. In practical calculations, the classification error is interpreted as the average classification error, which can be represented as a matrix of losses (fines, risks), due to incorrect classification of the system. The average value of the classification error can be determined by the Bayesian decision rule, one of the intermediate results of which is to determine statistical estimates of a priori probabilities of belonging of the studied system to each class. The obtained estimates are used in the tasks of optimizing decision-making in conditions of potential economic risks. The Bayesian approach is not a new algorithm for optimal classification, but its application to applied modeling problems requires analytical adaptation.
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