The Long-Run Behavior of Continuous Time Bayesian Networks

The continuous time Bayesian network (CTBN) is a temporal model consisting of interdepen-dent continuous time Markov chains (Markov processes). One common analysis performed on Markov processes is determining their long-run behavior, such as their stationary distribu-tions. While the CTBN can be transformed into a single Markov process of all nodes ’ state com-binations, the size is exponential in the num-ber of nodes, making traditional long-run anal-ysis intractable. To address this, we show how to perform “long-run ” node marginalization that removes a node’s conditional dependence while preserving its long-run behavior. This allows long-run analysis of CTBNs to be performed in a top-down process without dealing with the entire network all at once.