A Bayesian network models uncertainty.
An influence diagram models decisions.

The Extension

A Bayesian network contains only chance nodes — variables whose values are uncertain. An influence diagram adds two further node types: decision nodes (variables whose values are chosen by the decision-maker) and utility nodes (variables that represent the value of outcomes). Together the three types form a complete model for decision-making under uncertainty.

The distinction matters for how the model is used. A BN answers: given these observations, what is the probability distribution over outcomes? An influence diagram answers: given these observations, which available action maximises expected utility? The second question is the one boards actually ask. The BN is necessary but not sufficient to answer it.

Decision Nodes

A decision node represents a choice available to the decision-maker — which control to implement, which price to set, whether to investigate further, which supplier to use. Decision nodes have no probability distribution (the decision-maker chooses their value) but they have a defined set of available actions.

Decision nodes connect to downstream chance nodes through causal arrows: the action affects the probability distribution of its downstream variables. The causal mechanism encoded in the arrow is what allows the model to compute P(outcome | do(action)) — the interventional distribution that answers the Rung 2 question. This is identical to the do() operator on the action variable.

Utility Nodes

A utility node represents the value of an outcome — financial loss, casualties, regulatory penalty, or any other consequence dimension the organization cares about. Utility nodes have no children (they are terminal nodes) and their values are computed as a function of their parent chance nodes.

The utility function encodes the organization’s risk preferences — risk-neutral (expected value), risk-averse (expected utility with concave utility function), or target-based (probability of staying within a constraint). The choice of utility function determines which actions the model recommends. Making it explicit and debatable is one of the governance benefits of the influence diagram formulation.

The Query

The optimal policy is computed by backward induction through the diagram: for each decision node, choose the action that maximises expected utility given the current probability distribution over chance nodes and the value of any already-resolved information. For sequential decisions — where information arrives between decision points — the optimal policy is a mapping from information states to actions, not a fixed action.

This is the formal structure behind the pre-active, reactive, and pro-active query modes described in Bayesian Risk Decisions. The three modes are three different configurations of the same influence diagram.