Dynamic Bayesian networks are a universal tool for modeling stochastic processes that take place over time. In the process of describing transient probabilities of dynamic Bayesian networks, Markov circuits with discrete time are used. However, there are situations where the residence time in the states of a dynamic Bayesian network can be described by an arbitrary law of distribution, due to the features of modeling the subject area. To describe transients in such networks, half-Mark processes are used. The paper describes the mathematical apparatus of the application of the theory of semi-Markov processes for constructing the probabilities of models and solving the problems of probabilistic inference of dynamic Bayesian networks. What is described is a procedure for distributing evidence in the process of transitioning between the time states of the dynamic model under consideration based on the algorithm of selection by significance.

Keywords: dynamic Bayesian network, semi-Markov chains, method of nested Markov chains, probabilistic inference, transition model, state model, algorithm of selection by significance