# influence diagram

(redirected from Chance node)

## influence diagram

[′in‚flü·əns ‚dī·ə‚gram]
(systems engineering)
A graph-theoretic representation of a decision, which may include four types of nodes (decision, chance, value, and deterministic), directed arcs between the nodes (which identify dependencies between them), a marginal or conditional probability distribution defined at each chance node, and a mathematical function associated with each of the other types of node.
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Chance node and deterministic node is set by CPT and the exception detection model can support the uncertain relationships among service input, service output and service operation.
Rather than calculating probabilities for each edge of a chance node, scenario trees calculate probabilities (called path probabilities) for each path (scenario) from the root node to a leaf node.
Generally, in the traditional trees chance nodes precede decision nodes only if the value of the chance variable is known to the decision maker when selecting an alternative.
The arc directed from a decision node to a chance node represent an influence on random variable exerted through an intervention from the decision alternatives at hand.
Figure 1(a) depicts a BN with three chance nodes while 1(b) depicts the extension of BN into a DN by adding utility (Y) and decision (A) nodes.
Note that, at a chance node, only moves with strictly positive probability are included.
Note that, because compound gambles are permitted as outcomes, my definition of a tree includes 'incomplete' trees in the following sense: if the gamble assigned to some terminal node in a tree is compound there is a related tree which incorporates the playing out of this gamble explicitly through an additional chance node.
A chance node (drawn as a circle) represents an uncertain variable.
When we encounter a right-most chance node, we simply compute the expected cost of its branches by multiplying the number on each branch by its corresponding probability and then summing the results for all branches.
The next chance node represents the actual risk of asymptomatic bacteriuria following the screening test (predictive value positive for a positive screening test, and one minus predictive value negative for a negative screening test).
Each chance node X in the set V takes values in a binary domain {x, [bar.
b) Internal nodes, also called chance nodes, represent one of the possible choices available at that point in the tree structure; the top edge of the node is connected to its parent node and the bottom edge is connected to its child nodes or leaf nodes.
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