Bayesian Networks

Bayesian Networks use directed acyclic graphs (DAGs) where nodes represent variables and edges represent probabilistic dependencies. Each node has a probability distribution conditioned on its parent nodes. The network structure encodes conditional independence assumptions, allowing efficient representation and inference of joint probability distributions over multiple variables. The network combines prior knowledge with observed data using Bayes' theorem to update probabilities.

Financial risk assessment, medical diagnosis systems, fault diagnosis in industrial systems, weather forecasting, and student performance prediction in educational software.