Bayesian networks

Bayesian networks are directed acyclic graphs whose nodes represent random variables and whose edges encode conditional dependencies, allowing a joint probability distribution to be factored into local conditional distributions.

Directed acyclic graph: A directed graph with no directed cycle. Its acyclic structure orders dependencies and makes the network’s probability factorization well-defined.
Joint probability distribution: A probability distribution over all combinations of values of a set of random variables. The network represents this full distribution through a product of local conditional distributions.
Medical diagnosis: The process of identifying a disease or condition from symptoms, tests, and other evidence. A network can represent links among diseases, symptoms, and test results for probabilistic diagnosis.
Markov random field: An undirected graphical model whose graph encodes conditional dependencies among random variables. It represents dependencies with undirected edges rather than a directed acyclic graph.
Conditional probability table: A table specifying a variable’s probability distribution for each configuration of its parent variables. Each node’s table records the local probabilities used to construct the joint distribution.
Conditional probability: The probability of an event given that another event or condition holds. Node tables express each variable’s probabilities conditional on its graph parents.
Fault diagnosis: The identification of faults in a system from observed symptoms and operating data. Component dependencies let networks estimate likely causes from equipment failures.
Influence diagram: A decision model combining chance variables, decisions, and utilities in a directed graph. It adds decisions and utilities to probabilistic structure for analyzing choices.
Bayes' theorem: A rule for updating the probability of a hypothesis using evidence and conditional probabilities. Inference uses this rule to revise probabilities when evidence is observed.
Conditional independence: A relation in which two variables are independent once a specified set of variables is known. Missing edges encode conditional-independence claims under the network’s structure.

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