Bayesian Networks

A Bayesian network, also called a Bayes net, is a probabilistic graphical model. Each node represents a random variable, and directed edges form a directed acyclic graph. Each node has a conditional probability distribution given its parent nodes. Together, the graph and local distributions factorize the joint distribution into a product of smaller conditional terms. The graph can represent conditional-independence assumptions and reduce storage compared with a table listing every possible combination of variables. For example, a diagnostic network might contain a disease node, symptom nodes, and a test-result node. If probabilities are specified, observing symptoms or test results lets the system update the probability of disease using Bayes’ rule. The network is useful when evidence is incomplete or uncertain, such as equipment diagnosis or document classification. Results depend on variable definitions, graph structure, and probability values; a poorly specified model can produce misleading updates. A common mistake is to read every arrow as proven cause. In a Bayesian network used to represent a joint probability distribution, arrows encode factorization and conditional-dependence assumptions; they do not by themselves establish causation. Causal interpretation requires assumptions about how variables are generated and often evidence from study design or intervention. A clear model documents the origin of its graph, conditional probability tables, and assumptions. It should report uncertainty and be evaluated against known cases rather than presenting posterior probabilities as certainty.