Bayesian network

A Bayesian network is a directed acyclic graph that encodes probabilistic dependencies among a set of variables, factorizing a complex joint distribution into a product of local conditional probabilities. Each node represents a variable, each directed edge represents a direct probabilistic dependency, and the absence of an edge represents a conditional independence claim: given its parents, a node is independent of all non-descendants. This factorization makes Bayesian networks computationally tractable for inference and learning, and they are the foundational data structure of modern probabilistic AI, medical diagnosis, and risk assessment. But the Bayesian network is not merely a convenience for statisticians. It is a claim about the architecture of knowledge: that the world is structured in such a way that local dependencies can be composed into global coherence. The critical question — one that Bayesian networks alone cannot answer — is whether the directed edges represent mere association or genuine causation. A Bayesian network with causal edges becomes a structural causal model; a Bayesian network without causal interpretation is just a compressed representation of a joint distribution, useful for prediction but silent on intervention.