For questions related to Bayesian networks, the generic example of a directed probabilistic graphical model. Includes dynamic Bayesian networks, e.g. Hidden Markov Models (HMMs) and Kalman Filters. For applications of Bayesian networks in any field, e.g. machine learning. NOT for general questions about Bayes' theorem, Bayesian statistics, conditional probabilities, networks, or graph theory.

Bayesian networks are probabilistic graphical models which represent a set of random variables and their conditional dependencies using directed acyclic graph (DAG)... Bayesian networks are DAGs whose nodes represent random variables and whose edges represent conditional dependencies.

A dynamic Bayesian network is a Bayesian network which relates variables to each other over adjacent time steps. They generalize both Hidden Markov Models and Kalman filters.

The term hierarchical model is sometimes considered a particular type of Bayesian network, but has no formal definition. In general any moderately complex Bayesian network is usually termed "hierarchical".

Although Bayesian networks are often used to represent causal relationships, this need not be the case.

Bayesian networks are used for modeling beliefs in computational biology and bioinformatics (gene regulatory networks, protein structure, gene expression analysis, learning epistasis from GWAS data sets) medicine, biomonitoring, document classification, information retrieval, semantic search, image processing, data fusion, decision support systems, engineering, sports betting, gaming, law, study design and risk analysis.

The term "Bayesian networks" was coined by Judea Pearl in 1985.