Bayesian Networks

A Bayesian Network is a directed acyclic graph (DAG) whose nodes represent random variables and whose edges encode conditional dependencies. Each node has a conditional probability table/distribution given its parents.

The joint distribution factorizes as:

[P(X_1,\ldots,X_n)=\prod_i P(X_i\mid Parents(X_i))]

For example, Rain → WetGrass ← Sprinkler represents two possible causes of wet grass. Bayesian networks support probabilistic inference, diagnosis and reasoning under uncertainty. The graph structure encodes conditional independence assumptions; incorrect structure or probabilities can lead to poor inferences.