Relevance Diagram

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A relevance diagram (RD) is a graphical and mathematical representation of probabilistic inference and decision problems. An RD is a directed acyclic graph with two types of nodes—decision and chance—and two types of arrows (or arcs) between nodes—conditioning (ending in a chance node) and informational (ending in a decision node). Often, a single chance node in an RD is identified as its value node. In an RD, sets such as the predecessors, successors, direct predecessors, and direct successors of a node are defined in the obvious manner. An RD represents a particular expansion of the joint probability distribution of its uncertain variables and the informational constraints of its decision variables. Of particular importance in an RD are arrows that are absent—the absence of an arrow between two nodes denotes their conditional independence given their direct predecessors.

Relevance diagrams are hierarchical and can be defined either solely in terms of their structure or in greater detail in terms of the functional and numerical relation between diagram elements. An RD 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 relevance diagram (WFRD). When a WFRD contains at least one decision node directly or indirectly relevant to a value node and meets both the no-forgetting and the single-decision-maker conditions, it is referred to as a well-formed decision relevance diagram (WFDRD). WFRDs can be evaluated using addition, reversal, and removal operations to yield answers to a large class of probabilistic inference and decision questions. WFDRDs can also be evaluated to produce a recommended course of action. RDs are a generalisation of decision trees and, unlike trees, emphasise the structure of a problem rather than its description at the level of number.

The original term for relevance diagram was influence diagram. However, it is more accurate to say “node A is relevant to node B” (shown by connection with an arrow), rather than “node A influences node B”, since there is no causality implied. Hence the newer and more accurate use of language.

See also: asymmetric decision basis, background state of information, barren node, basic relevance diagram, border node, conditional probability distribution, creating a node, decision network, decision tree network, deleting, deterministic node, direct neighbour, editing a relevance diagram, evaluating a relevance diagram, flipping, frontier node, generalised reversal, indirect neighbour, indirect predecessor, indirect successor, knowledge map, linking, neighbour, probabilistic, stochastic node, well-formed partial decision relevance diagram and well-formed partial relevance diagram.