A Bayesian network is a probabilistic graphical model consisting of an acyclic digraph whose vertices represent random variables.
Each vertex is assigned a conditional distribution
given the variables at its parent vertices. If 
are ordered consistently with the graph, their joint
probability mass function or density 
factors as
![p(x_1,...,x_n)=product_(i=1)^np[x_i|x_(Pa(i))],](/images/equations/BayesianNetwork/NumberedEquation1.svg) |
where 
denotes the set of parents of vertex 
and 
denotes their values.
The graph thereby encodes conditional independence statements. Whether a path is blocked depends on the directions of its edges and on which vertices or descendants are conditioned upon. Different acyclic digraphs can encode the same set of conditional independence statements. A Bayesian network specifies a factorization; its parameters need not themselves be estimated by Bayesian inference.
