BNs are graphical models that set probabilistic relationships among variables of interest. They depict the relationships between causes and effects. The BNs are strong knowledge representation and reasoning tool under conditions of uncertainty. The BNs are a directed acyclic graph having nodes and arcs with a conditional probability distribution linked for each node. Nodes stand for domain variables, and arcs between nodes stand for probabilistic dependencies. Set of nodes and a set of directed links between them must not form a cycle. Each node represents a random variable that can take discrete or continuous finite, mutually exclusive values. These values depend on a probability distribution, which can be different for each node. Each link states probabilistic cause-effect relations among the linked variables. A link is shown by an arc starting from the affecting variable (parent node) and ending on the affected variable (child node).
We will use BNs to represent risk. For example, Figure 3.1 shows BN for "Decreased profits" risk. By linking together different risks we can model multiple risks in a project and we will look at this property in Chapter 5.
Bayes' Theorem was developed after Rev. Thomas Bayes, an 18th century mathematician and theologian. ...Show more