Bayesian Networks and Bayes Theorem - Essay Example

BNs are graphical models that set probabilistic relationships among variables of interest. They depict the relationships between causes and effects. The BNs are a strong knowledge representation and reasoning tool under conditions of uncertainty. The BNs is 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. A 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. Bayes set out his theory of probability in an Essay about solving a problem in the doctrine of chances published in the Philosophical Transactions of the Royal Society of London in 1764. Richard Price, a friend of Bayes' sent the paper to the Royal Society and wrote:

I now send you an essay which I have found among the papers of our deceased friend Mr. Bayes, and which, in my opinion, has great merit... In an introduction which he has writ to this Essay, he says, that his design at first in thinking on the subject of it was, to find out a method by which we might judge the probability that an event has to happen, in given circumstances, upon the supposition that we know nothing concerning it but that, under the same circumstances, it has happened a certain number of times, and failed a certain another number of times.