Influence diagrams are visual representations of relationships between variables, often used in decision making. They use shapes and arrows to show mathematical connections or provide an overview of complex systems. The shapes represent different variables, and different arrows represent information, causation, or probability. Influence diagrams can guide decision making by showing how a decision will affect a specific outcome. They are more flexible than decision trees and can represent influence cycles. They are based on the mathematical concept of Bayesian networks.
An influence diagram is a simple, visual method of describing relationships. It looks like a flowchart and usually contains shapes with text connected by arrows. An influence diagram could describe precise mathematical connections between components, or it could simply 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 decision making; show which variables can be directly influenced by the decision maker and which are strictly influenced by external influences.
The shapes in an influence diagram, called nodes, represent different types of variables. If the diagram is being prepared for a decision maker in a company, for example, it will clarify which variables that person has the power to influence and which will be determined by external factors. By convention, testable decisions are shown as rectangles; external uncertainty manifests itself as ovals; and targets appear as diamonds, hexagons, or octagons. Different types of arrows can represent information, causation, or probability.
An effective influence diagram will guide the decision making process. If the goal is to maximize an end 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 allow you to calculate the probability that a specific decision will have a specific outcome.
Consider someone trying to model nuclear proliferation in the Middle East. The model of him could contain events such as Iranian nuclearization, the start of an Egyptian weapons program and the disclosure of Israeli nuclear weapons. The occurrence of one of these events can have an effect on the expected probability of the others. Iran’s weapons program could affect Egypt not only directly, but also through its effects on Israel. An influence diagram might attempt to depict options for an American policy maker. Each policy has direct effects on the likely behavior of the countries involved, as well as secondary effects that could arise from such behavior. Ideally, the policy maker would have the ability to see the ultimate effects of any policy on outcomes such as total weapons or likelihood of conflict.
The concept of influence diagram comes from the mathematical concept of the Bayesian network. Bayesian modeling seeks to represent a large set of events with interconnected probabilities. This type of model allows 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 making decisions. Decision trees use constantly dividing branches to move from one starting point to one of many outcomes. Formally, decision trees can often produce the same result as influence diagrams; they are, however, usually much larger and require repeating the same element many times through the branches. They are not as flexible as influence diagrams and cannot effectively represent influence cycles.
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