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.
Decision variables are represented by rectangles (called decision nodes) and random variables are represented by circles (called chance nodes).
The three types of node found in a DN are the chance node, decision node, and utility node.
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, 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. For example, consider the compound gambles [g.sub.13(p)] [equivalent to] ([g.sub.1], p; [g.sub.3], (1 - p)) and [g.sub.23(p)] [equivalent to] ([g.sub.2], p; [g.sub.3], (1 - p)), where [g.sub.1], [g.sub.2], and [g.sub.3] are three gambles.
Nodes n and n[prime] are connected if, and only if, there is a branch b containing n, and a branch b[prime], containing n[prime], such that b and b[prime] diverge at a chance node [n.sub.y], which precedes both n and n[prime], and the sets R(n)\R([n.sub.y]) and R(n[prime])\R([n.sub.y]) contain only chance nodes.
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 representation contains two types of nodes: decision nodes and chance nodes. A decision node (drawn as a square node) represents a decision: an irrevocable allocation of resource.
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).
(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.
, usually drawn as circles, represent random variables that are relevant to the decision problem and cannot be controlled.