Bayesian Network
A Bayesian network encodes probabilistic relationships between variables as a directed acyclic graph. Each node carries a conditional probability table (CPT) specifying how likely it is given its parents. Click any node to set evidence — observe it as true or false — and watch belief propagation update every other node's probability. This is inference: reasoning under uncertainty, the backbone of medical diagnosis, spam filters, and causal reasoning.
How it works
Each node has a conditional probability table (CPT) that defines P(Node | Parents). When you set evidence (observe a node as true or false), the network performs exact inference by enumerating over all possible joint assignments. For each unobserved node, we compute the marginal probability by summing over all consistent assignments.
Conditional independence
In the sprinkler network, Sprinkler and Rain are conditionally independent given Cloudy. But they become dependent when you observe Wet Grass (explaining away). This is the essence of d-separation and Bayesian reasoning.
Key formula
P(A|B) = P(B|A) · P(A) / P(B) — Bayes' theorem