(untitled) (ADVANCED TECHNOLOGIES AND COMPUTER SCIENCE, 2023)
The article deals with Bayesian networks (hereinafter BS) with additional limitations due to the ideas of Markov networks (hereinafter MS). Graph models described by such networks will be called Bayesian Markov networks (BMS). These models describe many real-world problems with different types of uncertainties having different cause-and-effect relationships. The limitations imposed by the Markov property in many cases make it possible to significantly simplify calculations in Bayesian networks in the presence of evidence. At the same time, practice shows that most models reflecting real processes and built on the apparatus of Bayesian networks actually have the Markov property. The article describes the ideas of calculations in Bayesian networks with restrictions imposed by the Markov property. The differences in calculations in Bayesian networks without Markov constraints and with Markov constraints are described. The work was written within the framework of grant funding AP19679142 "Search for optimal solutions in Bayesian networks in models with linear constraints and linear functionals. Development of algorithms and programs" (2023-2025) MONV RK.