A Bayesian network, Bayes network, belief network or directed acyclic graphical model is a probabilistic graphical model

Graphical model

A graphical model is a probabilistic model for which a graph denotes the conditional independence structure between random variables. They are commonly used in probability theory, statistics—particularly Bayesian statistics—and machine learning....

 that represents a set of random variables and their conditional dependencies

Conditional independence

In probability theory, two events R and B are conditionally independent given a third event Y precisely if the occurrence or non-occurrence of R and the occurrence or non-occurrence of B are independent events in their conditional probability distribution given Y...

 via a directed acyclic graph

Directed acyclic graph

In mathematics and computer science, a directed acyclic graph , is a directed graph with no directed cycles. That is, it is formed by a collection of vertices and directed edges, each edge connecting one vertex to another, such that there is no way to start at some vertex v and follow a sequence of...

 (DAG). For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases.

Formally, Bayesian networks are directed acyclic graph

Directed acyclic graph

In mathematics and computer science, a directed acyclic graph , is a directed graph with no directed cycles. That is, it is formed by a collection of vertices and directed edges, each edge connecting one vertex to another, such that there is no way to start at some vertex v and follow a sequence of...

s whose nodes represent random variables in the Bayesian

Bayesian probability

Bayesian probability is one of the different interpretations of the concept of probability and belongs to the category of evidential probabilities. The Bayesian interpretation of probability can be seen as an extension of logic that enables reasoning with propositions, whose truth or falsity is...

 sense: they may be observable quantities, latent variable

Latent variable

In statistics, latent variables , are variables that are not directly observed but are rather inferred from other variables that are observed . Mathematical models that aim to explain observed variables in terms of latent variables are called latent variable models...

s, unknown parameters or hypotheses.