Bayes’ theorem, which was formulated by Thomas Bayes in the 18th Century, mathematically combines the expert knowledge and data. Despite the long history of the Bayes’ theorem, it has been possible to make calculations on numerous interdependent numerical problems, but only with the recent development of computational capacity of new modeling tools and computers such as Bayesian networks.

Bayesian networks are effective tools for making probabilistic calculations and decision support in complex areas where there are many variables. A Bayesian network consists of graphical structure and parameters. The graphical structure of the Bayesian network has nodes representing the variables and directed edges (arrows) representing the causal relationship between the variables. Using the graphical structure of the Bayesian network, causal relations about a complex subject can be modeled as a graphical model.

Bayesian networks provide a convenient infrastructure for making models that combine expert knowledge and data. When a Bayesian network is constructed, the graphical structure, that is, the variables and the causal relationships between them, is determined by expert knowledge. The parameters of this graphical structure are then learned using data. For time-varying dynamic systems and control systems, Dynamic Bayesian Networks models, which are extensions of Bayesian networks, provide a convenient environment.