| Abstract [eng] |
The era of big data opens up new opportunities to model the dynamics of complex natural, engineering, and social systems, but leveraging these opportunities is inseparable from the ability to efficiently process an ever-growing amount of information. Therefore, it becomes critically important to develop efficient algorithms for estimating the parameters of stochastic dynamic system models that provide optimal estimates and exhibit high computational speed. Such algorithms can be constructed using the maximum likelihood method and recursive computation, with their application based on a “bottom-up” approach. On this basis, the work examines a cumulative structural equation model to demonstrate the steps of data transformation, covariance matrix decomposition, likelihood function dimensionality reduction, and recursive computation of estimates—resulting in an efficient algorithm for estimating the parameters of the examined model given a fixed dataset. The constructed algorithm is then transformed into an efficient real-time parameter estimation algorithm, suitable for continuously updating model parameter estimates based on new information. Although the developed algorithms are easy to implement, in the context of practical applications, the selection of a model compatible with the phenomenon being modeled and the available data becomes as important as parameter estimation. This aspect is examined in the work by modeling the dynamics of the COVID-19 pandemic and social capital. |
