What It Is
A Bayesian network is a directed acyclic graph — nodes are variables, arrows are causal claims — combined with a set of conditional probability tables that quantify the strength of each causal relationship. The graph encodes the structure of causation. The tables encode the magnitudes.
The graph is drawn by domain experts, not inferred from data. Every arrow is a claim the expert is willing to defend: this variable causes that one, through this mechanism. The direction matters: an arrow from A to B is not the same as an arrow from B to A, even if A and B are perfectly correlated in the historical data.
This is what distinguishes a Bayesian network from a statistical model. A regression model encodes correlations. A Bayesian network encodes mechanisms. The difference determines what questions the model can answer.
Three Components
Nodes and directed arrows. Encodes which variables cause which others. Drawn by experts. Not inferred from data alone.
For each node, the probability distribution over its values given the values of its causes. Estimated from data, elicited from experts, or both.
Belief propagation distributes the implications of new evidence through the network — updating every connected node’s probability given what has been observed.
What It Can Answer
The same model answers three operationally distinct types of query:
Forward (predictive): Given these input conditions, what is the probability distribution over outcomes? This is standard risk assessment — given the current state of the system, what is the probability of failure?
Backward (diagnostic): Given that this outcome was observed, what is the most probable combination of upstream causes? This is root cause analysis — given that the failure occurred, what conditions most probably caused it?
Interventional / counterfactual: Given a forced change to one variable, how does the outcome distribution shift? Or: given that this outcome occurred, what would the outcome have been under different conditions? These are Rung 2 and Rung 3 queries. They require a Structural Causal Model — the full treatment is on What Data Cannot Tell You.
All three query directions run on the same graph with the same parameters. Building the model once produces all three capabilities simultaneously.
A thirty-minute conversation is usually enough to determine whether a Bayesian network addresses your problem — or whether the problem requires a different tool.
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