Dynamic Bayesian network

A dynamic Bayesian network (DBN) extends the static framework of Bayesian networks to temporal processes by modeling how variables evolve over discrete time steps. Rather than representing a single snapshot of conditional dependencies, a DBN encodes the transition dynamics: the state of each variable at time t depends on its own previous state and the states of its parents at time t−1, according to a repeated graphical structure called a time-slice. The network is thus a compact specification of an infinitely repeating pattern, a probabilistic graphical model unrolled across time.

The key insight is that the graph's topology is stationary — the same dependencies repeat at every time step — but the probabilities need not be. A DBN can model non-stationary processes by allowing the transition probabilities themselves to vary, either as functions of exogenous variables or as outputs of higher-level inference. This makes DBNs the natural bridge between static probabilistic reasoning and the dynamical systems tradition, connecting graphical sparsity to temporal evolution. The framework has been applied to speech recognition, gene regulatory dynamics, and financial time series, wherever the question is not what is the structure? but how does the structure move?

The dynamic Bayesian network is what you get when you stop taking photographs of a system and start filming it. The graph is no longer a map of dependencies; it is a choreography.