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Concept
Influence diagram
Summary
An influence diagram (ID) (also called a relevance diagram, decision diagram or a decision network) is a compact graphical and mathematical representation of a decision situation. It is a generalization of a Bayesian network, in which not only probabilistic inference problems but also decision making problems (following the maximum expected utility criterion) can be modeled and solved.
ID was first developed in the mid-1970s by decision analysts with an intuitive semantic that is easy to understand. It is now adopted widely and becoming an alternative to the decision tree which typically suffers from exponential growth in number of branches with each variable modeled. ID is directly applicable in team decision analysis, since it allows incomplete sharing of information among team members to be modeled and solved explicitly. Extensions of ID also find their use in game theory as an alternative representation of the game tree.
An ID is a directed acyclic graph with three types (plus one subtype) of node and three types of arc (or arrow) between nodes.
Nodes:
Decision node (corresponding to each decision to be made) is drawn as a rectangle.
Uncertainty node (corresponding to each uncertainty to be modeled) is drawn as an oval.
Deterministic node (corresponding to special kind of uncertainty that its outcome is deterministically known whenever the outcome of some other uncertainties are also known) is drawn as a double oval.
Value node (corresponding to each component of additively separable Von Neumann-Morgenstern utility function) is drawn as an octagon (or diamond).
Arcs:
Functional arcs (ending in value node) indicate that one of the components of additively separable utility function is a function of all the nodes at their tails.
Conditional arcs (ending in uncertainty node) indicate that the uncertainty at their heads is probabilistically conditioned on all the nodes at their tails.
Conditional arcs (ending in deterministic node) indicate that the uncertainty at their heads is deterministically conditioned on all the nodes at their tails.
Official source
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Ontological neighbourhood
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Related concepts (4)
Decision analysis
Decision analysis (DA) is the discipline comprising the philosophy, methodology, and professional practice necessary to address important decisions in a formal manner. Decision analysis includes many procedures, methods, and tools for identifying, clearly representing, and formally assessing important aspects of a decision; for prescribing a recommended course of action by applying the maximum expected-utility axiom to a well-formed representation of the decision; and for translating the formal representation of a decision and its corresponding recommendation into insight for the decision maker, and other corporate and non-corporate stakeholders.
Decision tree
A decision tree is a decision support hierarchical model that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning.
Operations research
Operations research (operational research) (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a discipline that deals with the development and application of analytical methods to improve decision-making. The term management science is occasionally used as a synonym. Employing techniques from other mathematical sciences, such as modeling, statistics, and optimization, operations research arrives at optimal or near-optimal solutions to decision-making problems.