data analysis, nonlinear nonstationary processes, methods of optimal and probabilistic filtering, simulation


Background. The majority of modern dynamic processes in economy, finances, ecology, technologies and many other areas of studies exhibit short- and long-term nonlinear and nonstationary behavior. That is why it is required to create for their thorough analysis modern highly developed specialized instrumentation providing for appropriate preliminary statistical data processing, simulation state and parameter estimation and quality forecasting their evolution in time to be used in decision support systems (DSS).

Objective. The purpose of the paper is to perform introductory analysis of some modern methods for filtering statistical and experimental data; to consider modern filtering techniques on the basis of probabilistic Bayesian approach, that provide a possibility for preparing the data to adequate simulation, computing high quality state and forecast estimates for dynamic systems in stochastic environment and availability of measurement errors.

Methods. To implement modern data filtering techniques appropriate simulation and optimization procedures, probabilistic Bayesian methods of data analysis are utilized; simulation algorithms for parameter estimation, and criteria bases for analyzing quality of intermediate and final results in the frames of DSS are used.

Results. A set of data filtering techniques is presented to be used together with the models describing formally selected processes dynamics. The methodology is considered for implementation of probabilistic Bayesian filter based upon modern statistical data analysis techniques including application of appropriate simulation procedures.

Conclusions. Development of effective means for simulation, state estimation and forecasting dynamics of nonlinear nonstationary processes in various areas of human activities provides a possibility for high quality state and parameter estimation and compute short and middle term forecasts for their future evolution. The methods of optimal Kalman and probabilistic Bayesian filtering considered in the review provide a possibility for performing appropriate analysis of nonlinear nonstationary processes, compute forecasts and provide for managerial decision support on the basis of the forecast estimates.


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