An influence diagram is a simple visual method for describing relationships. It looks like a flow chart and usually contains shapes with text connected by arrows. An influence diagram might describe precise mathematical connections between components, or it might just provide a rough overview of how a complex system fits together. Influence diagrams are notable because they are an effective way to visualize various outcomes in the decision-making process; they show which variables can be directly influenced by the decision maker and which are strictly affected by outside influences.
The shapes in an influence diagram, called nodes, represent different types of variables. If the diagram is being prepared for a decision-maker at a company, for example, it will make clear which variables that person has the power to influence and which ones will be determined by outside factors. By convention, controllable decisions are shown as rectangles; outside uncertainty manifests as ovals; and objectives appear as diamonds, hexagons, or octagons. Different types of arrows can represent information, causality, or probability.
An effective influence diagram will guide the process of decision-making. If the goal is to maximize some final variable such as output or profit, the influence diagram should clearly show how a given decision will affect that variable. Ideally, the influence diagram should make it possible to calculate how likely a specific decision is to have a specific outcome.
Consider someone trying to model nuclear proliferation in the Middle East. Her model might contain events such as Iranian nuclearization, the beginning of an Egyptian weapons program, and the disclosure of Israeli nuclear weapons. The occurrence of any of these events can have an effect on the expected probability of the others. The Iranian weapons program may have an effect on Egypt not only directly, but also through its effects on Israel. An influence diagram might attempt to represent the options for an American policy-maker. Each policy has direct effects on the probable behaviors of the countries involved, in addition to secondary effects that might result from these behaviors. Ideally, the policy-maker would have the ability to see the ultimate effects of each policy on such outcomes as total weapons or probability of conflict.
The concept of the influence diagram comes from the mathematical concept of the Bayesian network. Bayesian modeling tries to represent a large set of events with interconnected probabilities. This type of model allows for variables to have effects on each other that extend throughout the network.
Influence diagrams — and Bayesian models — have essentially replaced decision trees as systems for making calculations and decisions. Decision trees use constantly dividing branches to go from a starting point to one of many outcomes. Formally, decision trees can often produce the same outcome as influence diagrams; they are, however, usually much larger and require repetitions of the same element many times across branches. They are not as flexible as influence diagrams and cannot effectively represent loops of influence.