Using the Bayesian method to improve measurement accuracy in conditions of uncertainty and lack of information from information and measurement systems

RELEVANCE of the research lies in the need to improve the accuracy and reliability of information and measurement systems (AIS) in conditions of uncertainty and incompleteness of information. Modern AIS are being widely implemented in critical areas, where their effectiveness directly depends on their ability to cope with two types of uncertainty: stochastic (random) and epistemic (systemic). Classical methods of mathematical statistics have difficulty formalizing epistemic uncertainty, which makes it urgent to search for new approaches. THE PURPOSE of the work is to substantiate the effectiveness of using the Bayesian approach to solve problems of improving the accuracy of AIS in conditions of uncertainty. METHODS. The Bayesian approach to probability theory is applied, which treats probability as a measure of confidence. The key tool is Bayes' theorem, which allows combining a priori knowledge of magnitude with information from new experimental data to obtain a refined, a posteriori estimate. The article examines the application of the Bayesian approach to the typical problem of estimating a physical quantity, and discusses more complex models such as hierarchical Bayesian models and Bayesian networks. RESULTS. The Bayesian approach to probability theory is applied, which treats probability as a measure of confidence. The key tool is Bayes' theorem, which allows combining a priori knowledge of magnitude with information from new experimental data to obtain a refined, a posteriori estimate. The article examines the application of the Bayesian approach to the typical problem of estimating a physical quantity, and discusses more complex models such as hierarchical Bayesian models and Bayesian networks. results. Bayesian analysis allows us to obtain not just a point estimate, but a complete a posteriori probability distribution that contains comprehensive information about the measured value. This makes it possible to more adequately assess uncertainty and make decisions with minimal risk. Using the example of a typical task, it is shown that Bayesian information synthesis always leads to a decrease in uncertainty and an increase in estimation accuracy. The application of the Bayesian approach in the concept of Bayesian measurement intellectualization is discussed, which leads to the creation of adaptive AIS capable of continuously updating their internal models. CONCLUSION. Using the Bayesian approach is an effective and versatile strategy to improve the accuracy and reliability of an AIS. Despite the computational complexity and challenges associated with the choice of a priori distributions, this approach provides a unified theoretical framework for solving a wide range of problems. This opens up prospects for creating a new generation of AIS capable of efficiently working with heterogeneous data and providing the required quality of measurement information in difficult conditions.

1. Bormotov I.V. Methodology of Bayesian intelligent measurements for information systems and its application to the study of the value world of Russian youth // International Conference on Soft Computing and Measurements. 2023. Vol. 1. pp. 6-9.

2. Zakharov I.P. Estimation of extended measurement uncertainty in the implementation of the Bayesian approach // Measuring technology. 2018. No. 4. pp. 18-21.

3. Lepesh A.G. Bayesian technologies of development and decision-making in the management of enterprises (organizations) // Technical and technological problems of service. 2016. No. 1(35). pp. 68-71.

4. Nedosekin D.D., Prokopchina S.V., Chernyavsky E.A. Information technologies of intellectualization of measuring processes. St. Petersburg: Energoatomizdat, 1995. 187 p.

5. Prokopchina S.V. Bayesian intelligent technologies in problems of modeling the distribution law under conditions of uncertainty monograph. M. Publishing House "SCIENTIFIC LIBRARY", 2020. 292 p.

6. Prokopchina S.V. The concept of Bayesian intellectualization of measurements in monitoring tasks of complex objects // News of artificial intelligence, M. 1997. № 3. pp. 7-56.

7. Prokopchina S.V. Organization of measurement processes in conditions of uncertainty. The regularizing Bayesian approach. St. Petersburg. Collection of reports of the International Conference on Soft Computing and Measurements SCM-98. 1998. Vol. 1. pp. 30-44.

8. Prokopchina S.V. Methods of Bayesian mathematical statistics in training a convolutional neural network based on a regularizing Bayesian approach / S. V. Prokopchina // Soft measurements and calculations. 2022. Vol. 58, No. 9. pp. 32-46.

9. Prokopchina S.V. Application of Bayesian intelligent technologies and intelligent IIoT (IIoT) in the management of cyberphysical systems in conditions of uncertainty / S. V. Prokopchina // Soft measurements and calculations. 2021. Vol. 42. No. 5. pp. 38-54.

10. Ptushkin A.I., Reshetnikov D.V., Shapovalov D.V., Stepenko A.N. Bayesian approach to accounting for epistemic uncertainty of parameters of probabilistic models of risk analysis of decisions // Modern science-intensive technologies. 2020. No. 11-1. pp. 67-72.