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ID was first developed in mid 70's within '' Decision Analysis '' community with a very intuitive semantic that is easy to understand, it is now adopted widely and becoming an alternative to 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. Extension of ID also find its use in '' Game Theory '' as an alternative representation of '' Game Tree ''. SEMANTICS An ID is a Directed Acyclic Graph with three types (plus one subtype) of Node and three types of Arc (or arrrow) between nodes. Nodes;
Arcs;
Given a properly structured ID;
''Alternative, information, and preference'' are termed ''decision basis'' in decision analysis, they represent three required components of any valid decision situation. With the nodes and arcs in an ID, sets such as Predecessor s, Successor s, and direct (immediate) predecessors and successors of a node are defined in the obvious manner. In addition to the acyclicity of the influence diagram, it is generally assumed that value nodes have no successor nodes. If the nodes in the influence diagram are connected with the arcs following the above conditions, it follows semantically that every node is Probabilistically Independent on its non-successor nodes given the outcome of its immediate predecessor nodes are known. EXAMPLE Consider the simple influence diagram representing a situation where a decision-maker is planning on her vacation.
APPLICABILITY IN VALUE OF INFORMATION The above example highlights the power of influence diagram in representing an extremely important concept in decision analysis known as Value Of Information . Consider the following three scenarios;
Scenario 1 is the best possible scenario for this decision situation since there is no longer any uncertainty on what she cares about (''Weather Condition'') when making her decision. Scenario 3, however, is the worst possible scenario for this decision situation since she needs to make her decision without any hint (''Weather Forecast'') on what she cares about (''Weather Condition'') will turn out to be. The decision-maker is usually better off (definitely no worse off) to move from scenario 3 to scenario 2 through the acquisition of new information. The most she should be willing to pay for such move is called Value Of Information on ''Weather Forecast'', which is essentially Value Of Imperfect Information on ''Weather Condition''. Likewise, it is the best for the decision-maker to move from scenario 3 to scenario 1. The most she should be willing to pay for such move is called Value Of Perfect Information on ''Weather Condition''. The applicability of this simple ID and the value of information concept is tremendous, especially in Medical Decision Making when most decisions have to be made with imperfect information about patients, diseases, etc. NOTES Influence diagrams are hierarchical and can be defined either in terms of their structure or in greater detail in terms of the functional and numerical relation between diagram elements. An ID that is consistently defined at all levels—structure, function, and number—is a well-defined mathematical representation and is referred to as a ''well-formed influence diagram'' (WFID). WFIDs can be evaluated using Reversal and Removal operations to yield answers to a large class of probabilistic, inferential, and decision questions. More recent techniques have been developed by Artificial Intelligence community with their works around Bayesian Network Inference ( Belief Propagation ). Influence diagram having only uncertainty nodes (i.e., Bayesian network) is also called relevance diagram. This is perhaps a better use of language than ''influence diagram''. An arc connecting node ''A'' to ''B'' implies not only that "''A'' is relevant to ''B''", but also that "''B'' is relevant to ''A''" (i.e., Relevance is a Symmetric relationship). The word ''influence'' implies more of a one-way relationship, which is reinforced by the arc having a defined direction. Since some arcs are easily reversed, this "one-way" thinking that somehow "''A'' influences ''B''" is incorrect (the causality could be the other way around). However, the term ''relevance diagram'' is never adopted in larger community, and the world continues to refer to ''influence diagram''. We are stuck, therefore, with a less-than-perfect nomenclature. BIBLIOGRAPHY
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